Aeroelasticity. Lecture 7: Practical Aircraft Aeroelasticity. G. Dimitriadis. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7
|
|
- Francine Farmer
- 5 years ago
- Views:
Transcription
1 Aeroelasticity Lecture 7: Practical Aircraft Aeroelasticity G. Dimitriadis AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 1
2 Non-sinusoidal motion Theodorsen analysis requires that the equations of motion are only valid at zero airspeed or at the flutter condition. They are also valid in the case of forced sinusoidal excitation. We can calculate the response of an aeroelastic system with Theodorsen aerodynamics to any excitation force AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 2
3 Forced response Until now we have only considered unforced motion:! " m S No we will consider an external loads (e.g. control input) applied on one of the degrees of freedom. E.g. force on plunge:! " m S S I α $! & %" Or moment on pitch:! " m S S I α $! & %" S I α AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 $! & %" h!! $!!! α & + K h 0 % " 0 K α h!! $!!! α & + K h 0 % " 0 K α h!! $!!! α & + K h 0 % " 0 K α $! & %" $! & %" h α h α $! & %" h α $! &+ % " $! &+ % " $! & = % " l(t) m(t) l(t) m(t) l(t) m(t) $ & % $! & = F h t % " 0 ( ) $! & = 0 % M α ( t " ) $ & % $ & % 3
4 Sinusoidal force If Theodorsen analysis is to be applied, the force must be sinusoidal, e.g. F h = F 0 e jωt M α = M 0 e jωt The steady-state response of the pitch-plunge wing will also be sinusoidal once all the transients have died out, i.e. α = α 0 e jωt h = h 0 e jωt Substituting into the complete equations of motion: AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 4
5 Forced equations of motion " $ $ $ $ $ $ $ $ $ $ $ $ $ $ Force in plunge K h ω 2 m + πρucc ( k) jω ω 2 ρπb ω 2 S πρuecc ( k) jω " + x f c % $ 'ρπb 2 ω 2 2 & " ω 2 S + ρπb 2 Ujω + ρπb 2 x f c % $ 'ω 2 2 & " " +πρucc ( k) U c x % % $ $ f ' jω ' & & " K α ω 2 I α c x % $ f 'ρπb 2 Ujω & πρuecc k " " ( ) $ U + $ 3 4 c x f % % ' jω ' & & x f c 2 " % $ ' ρπb 2 ω 2 ρπb4 2 & 8 ω 2 % ' ' ' ' ' '" ' ' $ ' ' ' ' ' ' & h 0 α 0 % " ' = F 0 $ & 0 % ' & AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 With k=ωb/u 5
6 FRF Matrix This equation is of the form H(ω)q 0 =F where H -1 (ω) is the Frequency Response Function Matrix. Note that, since H is is a function of ω, the response amplitude q 0 will also be a function of ω. The response is still sinusoidal. But what happens if F is also a function of ω? AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 6
7 Fourier Transforms Using Fourier analysis, any force time signal F h (t) can be transformed to the frequency domain and written as: F 0 (ω)e jwt The signal that is of particular interest here is the impulse. Its Fourier Transform is F 0 (ω)=1 This means that if we set F 0 (ω)=1 and then calculate q 0 (ω)=h -1 (ω)f the resulting response amplitude q 0 (ω), will be the Frequency Response Function (FRF). AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 7
8 FRF for pitch-plunge system 9 FRF of h The two modes are clearly present 632!5!& !'!&(!'!&!'!!( :8;<+1=>132!5!& " &!!&!! " $ % &! )*+,-+./012345!"! " $ % &! )*+,-+./ FRF of α The first mode is present as an antiresonance 632!5!& 617.1"!'!!'!9!'!"!'!& :8;<+1=>132!5!& 17.1"!'(!!!'(!&!&'(!"!"'(!! " $ % &! )*+,-+./012345!9! " $ % &! )*+,-+./ AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 8
9 Impulse Response Function The Impulse Response Function (IRF) is the inverse Fourier Transform of the FRF. As we have calculated the FRF, q 0 (ω), we can simply apply the inverse Fourier Transform to it and calculate the IRF. The IRF is a time domain signal and it is not sinusoidal. For a dynamic system, the IRF is typically an exponentially decaying sinusoid. For a fluttering aeroelastic system, the IRF is an exponentially increasing sinusoid. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 9
10 Impulse response of pitch-plunge airfoil '(&!!) 9:&),;/<('=;>:!? &'( )*&!! :;"(-<0=*)><?;!' 1,234/-(5-/267/-(+7(8 "!!"! * *,8*9 &!'(!!!'(!&!$! " $ % &! &" & &$ &% *+,-(./0 " '(&!!!&'(! " $ % &! &" & &$ &% +,-.*/01 )*&!! 1,234/-(5-/267/-(+7(!! * *,8*! "!!"!"! " $ % &! &" & &$ &% *+,-(./0 V=15m/s! " $ % &! &" & &$ &% +,-.*/01 V=25m/s AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 10
11 Damped sinusoidal motion The previous discussion shows that: Theodorsen aerodynamics is only valid for sinusoidal motion. Yet Theodorsen aerodynamics can also be used to calculate impulse responses. The form of the impulse response can tell is if the system is stable or unstable. Stability analysis is slow and can be less accurate when performed on impulse responses. We need a method for calculating the damping at all airspeeds directly from the equations of motion. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 11
12 The p-k Method The p-k method is the most popular technique for obtaining aeroelastic solutions from Theodorsen-type aeroelastic systems It was proposed in the 80s and since then has become the industrial standard Virtually all aircraft flying today have been designed using the p-k method AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 12
13 Basics The p-k method uses the structural equations of motion in the standard form! " m S S I α $! & %" h!! $!!! α & + K h 0 % " 0 K α Coupled with Theodorsen aerodynamic forces of the form $! & %" h α $! & = % " l(t) m(t) $ & % With k=ωb/u AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 13
14 Time-Frequency domain The equations of motion have coefficients that depend on the frequency. They are known as time-frequency domain equations. The complete equations are! " m S S I α $!!! $! h & %"!! α & + K h 0 % " 0 K α $! & %"! h $ & 1 α % 2 ρu 2 " 4πC( k) jk + 2πk 2 2πcC ( k) 2πbjk 4πC( k) 3 4 c x f 4πecC k! ( ) jk 2π x c " f 2 $ &k 2 % 2πec 2 C k +4πecC k! " ( ) c x f! " ( ) 3 4 c x f! " $ &πbjk % $ & jk 2πb 2 k 2 % $ % & jk + 2π x c 2! $ " f 2 & k 2 + π b2 % 4 k 2 $ & & &! & &" & & & % h α $! & = % " 0 0 $ & % and their general form is M s!!q + K s q 1 2 ρu 2 Q( k)q = 0 AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 14
15 Basics Solving time-frequency equations of motion is a nonlinear eigenvalue problem. The basis of the p-k method is to define so that p d dt!!q = p 2 q We then re-write the equations of motion as " $ p 2 M s + K s 1 2 ρu 2 Q k ( ) AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 % 'q = 0 & 15
16 Eigenvalue estimation These equations of motion are clearly an eigenvalue problem. For a non-trivial solution: " p 2 I + M 1 s $ K s 1 2 ρu 2 Q k This is one equation with two unknowns, we need a second condition. Note that p 2 is an eigenvalue of the matrix - M s 1 ( ) " $ K s 1 2 ρu 2 Q k ( ) % ' = 0 & % ' & (1) AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 16
17 Eigenvalue estimation (2) But k is a frequency: k=ωb/u. Recall that the imaginary part of the eigenvalue is the frequency. Therefore, our second equation is:!" = % & ' (2) The problem consists of finding an eigenvalue and a frequency that satisfy both equations (1) and (2). AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 17
18 The p-k solution The solution of these equations is iterative. We guess a value for the frequency k and then we calculate p from the resulting eigenvalue problem (1). The values of p and k should satisfy equation (2). If they do not, we change the value of k and re-calculate p until equation (2) is satisfied. This is called frequency matching. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 18
19 Frequency matching 1. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 19
20 p-k method characteristics Converges very quickly to the correct eigenvalue. Suitable for large computational problems. Calculates complete eigenvalues and therefore damping ratios and natural frequencies. Valid at all airspeeds, not just the flutter speed. Estimated flutter speeds are very similar to those obtained from the flutter determinant solution. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 20
21 Sample result AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 21
22 Roger s Approximation Another way to solve the p-k equations is to transform them completely to the time domain using Roger s Approximation. The frequency-dependent part of equations of motion, Q(k), is approximated as: Q( k) = A 0 + A 1 jk + A 2 ( jk) 2 jk + A 2+n Where n l is the number of aerodynamic lags and γ n are aerodynamic lag coefficients. n l (3) n=1 jk +γ n AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 22
23 Roger s EOMs The equations of motion of the complete aeroelastic system then become: Where q = Usually: $ & & & & & % M 1 C M 1 K M 1 A 3 M 1 A nl +2 I I Vγ 1 /bi 0 0 I 0 Vγ nl /bi M = M s 1 2 ρb2 A 2, C = C s 1 2 ρuba 1, K = K s 1 2 ρu 2 A 0, A j = 1 2 ρu 2 A j n l = 4, γ n = 1.7k max ' ) ) ) q ) ) ( n ( n l +1), k 2 max = maximum k of interest AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 23
24 Roger details The matrices A 0, A 1 etc are obtained from equation (3) by performing a least-squares curve fit of Q(k) for several values of k. If the aeroelastic system has n degrees of freedom, Roger s equations of motion will have (n l +2)n states. Of those, n l n states are aerodynamic states. There are similar but more efficient schemes for improving the curve fit of Q(k) and reducing n l, e.g. the minimum state method. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 24
25 Practical Aeroelasticity For an aircraft, the matrix Q(k) is obtained using a panel method-based aerodynamic model. The modelling is usually performed by means of commercial packages, such as MSC.Nastran or Z- Aero. For a chosen set of k values, e.g. k 1, k 2,, k m, the corresponding Q matrices are returned. The Q matrices are then used in conjunction with the p-k method to obtain the flutter solution or time-domain responses. The values of Q at intermediate k values are obtained by interpolation. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 25
26 Wings are 3D All the methods described until now concern 2D wing sections These results must now be extended to 3D wings because all wings are 3D There are two methods for 3D wing aeroelasticity: Strip theory Panel methods AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 26
27 Strip theory Strip theory breaks the wing into spanwise small strips The instantaneous lift and moment acting on each strip are given by the 2D sectional lift and moment theories (quasi-steady, unsteady etc) S dy y AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 27
28 Panel methods The wing is replaced by its camber surface. The surface itself is replaced by panels of mathematical singularities, solutions of Laplace s equation 0z x y c i,j s i,j+1 i+1,j i+1,j+1 Wake Panels AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 28
29 Hancock Model A simple 3D wing model is used to introduce 3D aeroelasticity A rigid flat plate of span s, chord c and thickness t, suspended through an axis x f by two torsional springs, one in roll (K γ ) and one in pitch (K θ ). The wing has two degrees of freedom, roll (γ) and pitch (θ). 0!"%!" /*+,- 1*+,-!!!"$!!" $!"'!"& )*+,-! "!!!"!!" ).!!"$! (!"$!" AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 29
30 Equations of motion As with the 2D pitch plunge wing, the equations of motion are derived using energy considerations. The kinetic energy of a small mass element dm of the wing is given by ( ( ) θ ) 2 dt = 1 z 2 2 dm = 1 2 dm y γ + x x f The total kinetic energy of the wing is: ( ( ) γ θ + 2( c 2 2 3x f c + 3x ) f θ 2 ) T = m 12 2s2 γ 2 + 3s c 2x f AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 30
31 Structural equations The potential energy of the wing is simply V = 1 2 K γγ K θθ 2 The full structural equations of motion are then: $ & % I γ I γθ I γθ I θ '* γ - ) + (., θ / + $ K γ 0 '* & ) γ - +. % 0 K θ (, θ/ = * M 1- +., M 2 / I γ = ms 2 /3, I γθ = m( c 2x f )s/4, I θ = m( c 2 2 3x f c + 3x ) f /3 AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 31
32 Strip theory The quasi-steady or unsteady approximations for the lift and moment around the flexural axis are applied to infinitesimal strips of wing The lift and moment on these strips are integrated over the entire span of the wing The result is a quasi-steady pseudo-3d lift and moment acting on the Hancock wing M 1 = s 0 yl( y)dy M 2 = m x f y s 0 ( ) dy AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 32
33 Quasi-steady strip theory Denote, θ=α and h=yγ. Then l m xf Carrying out the strip theory integrations will yield the total moments around the y=0 and x=x f axes. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 33
34 3D Quasi-steady equations of motion The full 3D quasi-steady equations of motion are given by They can be solved as usual AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 34
35 Natural frequencies and damping ratios AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 35
36 Theodorsen function aerodynamics Again, Theodorsen function aerodynamics (unsteady frequency domain) can be implemented directly using strip theory: l m xf AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 36
37 Flutter determinant The flutter determinant for the Hancock model is given by And is solved in exactly the same was as for the 2D pitch-plunge model. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 37
38 p-k solution Instead of solving the flutter determinant, we can apply the p- k method. The process is exactly as presented in the 2D case. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 38
39 Comparison of flutter speeds Wagner and Theodorsen solutions are identical. Quasi-steady solution is the most conservative Ignore the other solutions AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 39
40 Comparison of 3D and strip theory, static case The 3D lift distribution is completely different to the strip theory result! Strip theory: C L = 2πα Lifting line method: C L = 2π AR AR + 2 α AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 40
41 Vortex lattice aerodynamics Strip theory is a very gross approximation that is only exact when the wing s aspect ratio is infinite. It is approximately correct when the aspect ratio is very large It becomes completely unsatisfactory at moderate and small aspect ratios (less than 8-10). AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 41
42 Vortex lattice method The basis of the VLM is the division of the wing planform into panels on which lie vortex rings, usually called a vortex lattice A vortex ring is a rectangle made up of four straight line vortex segments. It is an elementary solution of Laplace s equation. z y x r i,j w P v i,j u i,j+1 n i,j i+1,j i+1,j+1 AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 42
43 Characteristics of a vortex ring The vector n ij is a unit vector normal to the ring and positioned at its midpoint (the intersection of the two diagonals - also termed the collocation point) The vorticity, Γ, is constant over all the 4 segments of a vortex ring. Each segment is inducing a velocity [u v w] at a general point P. In the case where the point P lies on a vortex ring segment, the velocity induced is 0. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 43
44 Panelling up and solving The process starts by dividing a wing planform into panels. The wing can be swept, tapered and twisted. It cannot have thickness; the panels lie on the wing s camber surface. The wake must also be panelled up. The object of the VLM is to calculate the values of the vorticities Γ on each wing panel at each instance in time. The vorticity of the wake panels does not change in time. Only the vorticities of the wing panels are unknowns. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 44
45 Boundary conditions The vorticities Γ on each wing panel at each instance in time are calculated by enforcing boundary conditions: Impermeability: there is no flow normal to the panel at its collocation point. This conditions gives all the Γ values. Kutta condition: the flow must separate at the trailing edge. This condition is satisfied automatically by placing the leading edge of each vortex ring on the quarter-chord of its corresponding geometric panel. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 45
46 Calculating forces Once the vorticities on the wing panels are known, the lift and moment acting on the wing can be calculated These are calculated from the pressure difference acting on each panel Summing the pressure differences of the entire wing yields the total forces and moments AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 46
47 Panels for static wing Even if the wing is not moving, the wake must still be modelled because it describes the downwash induced on the wing s surface and, hence, the induced drag. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 47
48 Wake shapes Wake shape behind a rectangular wing that underwent an impulsive start from rest. The aspect ratio of the wing is 4 and the angle of attack 5 degrees. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 48
49 Effect of Aspect Ratio on lift coefficient Lift coefficient variation with time for an impulsively started rectangular wing of varying Aspect Ratio. It can be clearly seen that the 3D results approach Wagner s function (2D result) as the Aspect Ratio increases. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 49
50 Free wakes Free wake behind a flapping goose wing. Airspeed: 18m/s. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 50
51 Industrial use Unsteady wakes are beautiful but expensive to calculate. For practical purposes, a fixed wake is used with unsteady vorticity, just like Theodorsen s method. The wake propagates at the free stream airspeed and in the free stream direction. Only a short length of the wake is simulated (a few chord-lengths). The result is a linearized aerodynamic model. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 51
52 Aerodynamic force coefficient matrices 3D aerodynamic calculations can be further speeded up by calculating everything in terms of the mode shapes of the structure. This treatment allows the expression of the aerodynamic forces as modal aerodynamic forces, written in terms of aerodynamic force coefficients matrix Q(k). These are square matrices with dimensions equal to the number of retained modes. They also depend on response frequency. Therefore, the complete aeroelastic system can be written as a set of linear ODEs with frequencydependent matrices, to be solved using the p-k method. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 52
53 Case study The plate is still not perfectly symmetric but, as it is swept, no static deformations appear. The oscillations start at 16.8m/s. They combine bending and torsion at the same frequency. At the highest airspeeds the motion becomes slightly irregular in bending. On balance, the oscillations are less complex than in the zero sweep case. U=0 m/s U=21 m/s AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7
54 Mode shapes Mode 1 Mode 2 2 z 2 z y x y x 0.2 z Mode 3 4 Mode 3 2 z y AERO0032-1, Aeroelasticity and Experimental x Aerodynamics, Lecture y x 0.2
55 VLM calculation The wing is always flat and never deforms. The wake propagates with the free stream and never deforms. The downwash on the panels depends on the free stream, angle of attack and modal outof-plane displacements. Only the lift does work on the structure. The lift equation is Fourier Transformed and a frequencydependent generalized force matrix is developed. The number of chordwise and spanwise panels is 30 each. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7
56 VLM maths Applying impermeability boundary condition: where Transforming to the frequency domain: where So that, finally AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7
57 VLM maths (2) This means that, in the frequency domain, we can calculate the bound vorticity exclusively as a function of the modal downwash and free stream. The linearized lift is a multiple of the bound vorticity: So that we can now calculate the work done by the lift, i.e. the generalized aerodynamic force matrix: AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7
58 Flutter solution 10 o sweep, AR=4, 5 structural modes Flutter airspeed 15.8 m/s, flutter frequency 5.3 Hz. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7
59 Flutter speed predictions Comparison of simulated and experimental flutter airspeeds and frequencies for all AR=4 wings. Linear structure, p-k solution. Flutter speed (m/s) Experiment VLM Flutter frequency (Hz) Experiment VLM AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 Sweep angle (deg) Sweep angle (deg)
60 Commercial packages There are two major commercial packages that can calculate 3D unsteady aerodynamics using panel methods: MSC.Nastran (MSC Software) ZAERO (ZONA Technology) They can both deal with complex aircraft geometries. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 60
61 ZAERO AFA example The examples manual of ZAERO features an Advanced Fighter Aircraft model. Aerodynamic model Structural model AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 61
62 BAH Example Bisplinghoff, Ashley and Halfman wing FEM with 12 nodes and 72 dof AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 62
63 First 5 modes of BAH wing AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 63
64 GTA Example Here is a very simple aeroelastic model for a Generic Transport Aircraft Finite element model: Bar elements with 678 degrees of freedom Aerodynamic model: 2500 doublet lattice panels AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 64
65 Flutter plots for GTA First 7 flexible modes. Clear flutter mechanism between first and third mode (first wing bending and aileron deflection) AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 65
66 Time domain plots for the GTA V<V F V=V F AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 66
67 The SST was a proposal for the replacement of the Concorde. The aeroelastic model is a halfmodel The aerodynamics features the wing and a rectangle for the wall Supersonic Transport AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 67
68 Flutter plots for SST First 9 flexible modes. Clear flutter mechanism between first and third mode. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 68
69 Summary Aeroelastic design in industry is almost exclusively carried out using lattice methods (vortex or doublet) combined with a Finite Element model with few retained modes (generally fewer than 100). Panel methods (source and doublet) are also used for more detailed geometric representation, including thickness. The aerodynamic forces are written in the form of Aerodynamic Force Coefficient Matrices that depend on frequency. The flutter solution is obtained using the p-k method. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 69
Aeroelasticity. Lecture 9: Supersonic Aeroelasticity. G. Dimitriadis. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 9
Aeroelasticity Lecture 9: Supersonic Aeroelasticity G. Dimitriadis AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 9 1 Introduction All the material presented up to now concerned incompressible
More informationAeroelastic Analysis Of Membrane Wings
Aeroelastic Analysis Of Membrane Wings Soumitra P. Banerjee and Mayuresh J. Patil Virginia Polytechnic Institute and State University, Blacksburg, Virginia 46-3 The physics of flapping is very important
More informationExperimental Aerodynamics. Experimental Aerodynamics
Lecture 3: Vortex shedding and buffeting G. Dimitriadis Buffeting! All structures exposed to a wind have the tendency to vibrate.! These vibrations are normally of small amplitude and have stochastic character!
More informationFREQUENCY DOMAIN FLUTTER ANALYSIS OF AIRCRAFT WING IN SUBSONIC FLOW
FREQUENCY DOMAIN FLUTTER ANALYSIS OF AIRCRAFT WING IN SUBSONIC FLOW Ms.K.Niranjana 1, Mr.A.Daniel Antony 2 1 UG Student, Department of Aerospace Engineering, Karunya University, (India) 2 Assistant professor,
More information( ) (where v = pr ) v V
Problem # The DOF idealized wing whose cross-section is shown in Figure. has leading edge and trailing edge control surfaces. There is no initial angle of attack when the two control surfaces are undeflected.
More informationOPTIMIZATION OF TAPERED WING STRUCTURE WITH AEROELASTIC CONSTRAINT
ICAS 000 CONGRESS OPTIMIZATION OF TAPERED WING STRUCTURE WITH AEROELASTIC CONSTRAINT Harijono Djojodihardjo, I Wayan Tjatra, Ismojo Harjanto 3 Computational Aeroelastic Group, Aerospace Engineering Department
More informationAeroelastic Gust Response
Aeroelastic Gust Response Civil Transport Aircraft - xxx Presented By: Fausto Gill Di Vincenzo 04-06-2012 What is Aeroelasticity? Aeroelasticity studies the effect of aerodynamic loads on flexible structures,
More informationFLUTTER PREDICTION OF A SWEPT BACK PLATE USING EXPERIMENTAL MODAL PARAMETERS
Symposium on Applied Aerodynamics and Design of Aerospace Vehicle (SAROD 2011) November 16-18, 2011, Bangalore, India FLUTTER PREDICTION OF A SWEPT BACK PLATE USING EXPERIMENTAL MODAL PARAMETERS A.C.Pankaj*,
More informationNumerical Simulation of Unsteady Aerodynamic Coefficients for Wing Moving Near Ground
ISSN -6 International Journal of Advances in Computer Science and Technology (IJACST), Vol., No., Pages : -7 Special Issue of ICCEeT - Held during -5 November, Dubai Numerical Simulation of Unsteady Aerodynamic
More informationAir Loads. Airfoil Geometry. Upper surface. Lower surface
AE1 Jha Loads-1 Air Loads Airfoil Geometry z LE circle (radius) Chord line Upper surface thickness Zt camber Zc Zl Zu Lower surface TE thickness Camber line line joining the midpoints between upper and
More informationDynamic Response of an Aircraft to Atmospheric Turbulence Cissy Thomas Civil Engineering Dept, M.G university
Dynamic Response of an Aircraft to Atmospheric Turbulence Cissy Thomas Civil Engineering Dept, M.G university cissyvp@gmail.com Jancy Rose K Scientist/Engineer,VSSC, Thiruvananthapuram, India R Neetha
More informationAero-Propulsive-Elastic Modeling Using OpenVSP
Aero-Propulsive-Elastic Modeling Using OpenVSP August 8, 213 Kevin W. Reynolds Intelligent Systems Division, Code TI NASA Ames Research Center Our Introduction To OpenVSP Overview! Motivation and Background!
More informationAE 714 Aeroelastic Effects in Structures Term Project (Revised Version 20/05/2009) Flutter Analysis of a Tapered Wing Using Assumed Modes Method
AE 714 Aeroelastic Effects in Structures Term Project (Revised Version 20/05/2009) Flutter Analysis of a Tapered Wing Using Assumed Modes Method Project Description In this project, you will perform classical
More informationAerodynamic Resonance in Transonic Airfoil Flow. J. Nitzsche, R. H. M. Giepman. Institute of Aeroelasticity, German Aerospace Center (DLR), Göttingen
Aerodynamic Resonance in Transonic Airfoil Flow J. Nitzsche, R. H. M. Giepman Institute of Aeroelasticity, German Aerospace Center (DLR), Göttingen Source: A. Šoda, PhD thesis, 2006 Slide 2/39 Introduction
More informationNumerical Study on Performance of Innovative Wind Turbine Blade for Load Reduction
Numerical Study on Performance of Innovative Wind Turbine Blade for Load Reduction T. Maggio F. Grasso D.P. Coiro This paper has been presented at the EWEA 011, Brussels, Belgium, 14-17 March 011 ECN-M-11-036
More informationWind Tunnel Experiments of Stall Flutter with Structural Nonlinearity
Wind Tunnel Experiments of Stall Flutter with Structural Nonlinearity Ahmad Faris R.Razaami School of Aerospace Engineering, Universiti Sains Malaysia, Penang, MALAYSIA Norizham Abdul Razak School of Aerospace
More informationGiven the water behaves as shown above, which direction will the cylinder rotate?
water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0
More informationImprovement of flight regarding safety and comfort
Prediction of the aeroelastic behavior An application to wind-tunnel models Mickaël Roucou Royal Institute of Technology KTH - Stockholm, Sweden Department of Aerospace and Vehicle Engineering Email: roucou@kth.se
More informationAeroelasticity. Lecture 4: Flight Flutter Testing. G. Dimitriadis. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 4
Aeroelasticity Lecture 4: Flight Flutter Testing G. Dimitriadis AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 4 1 Main reference A Historical Overview of Flight Flutter Testing, Michael
More informationA method for identification of non-linear multi-degree-of-freedom systems
87 A method for identification of non-linear multi-degree-of-freedom systems G Dimitriadis and J E Cooper School of Engineering, Aerospace Division, The University of Manchester Abstract: System identification
More informationResearch Article Numerical Study of Flutter of a Two-Dimensional Aeroelastic System
ISRN Mechanical Volume 213, Article ID 127123, 4 pages http://dx.doi.org/1.1155/213/127123 Research Article Numerical Study of Flutter of a Two-Dimensional Aeroelastic System Riccy Kurniawan Department
More informationINSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 AERONAUTICAL ENGINEERING TUTORIAL QUESTION BANK Course Name : LOW SPEED AERODYNAMICS Course Code : AAE004 Regulation : IARE
More informationA HARMONIC BALANCE APPROACH FOR MODELING THREE-DIMENSIONAL NONLINEAR UNSTEADY AERODYNAMICS AND AEROELASTICITY
' - ' Proceedings of ASME International Mechanical Engineering Conference and Exposition November 17-22, 22, New Orleans, Louisiana, USA IMECE-22-3232 A HARMONIC ALANCE APPROACH FOR MODELING THREE-DIMENSIONAL
More informationSimulation of Aeroelastic System with Aerodynamic Nonlinearity
Simulation of Aeroelastic System with Aerodynamic Nonlinearity Muhamad Khairil Hafizi Mohd Zorkipli School of Aerospace Engineering, Universiti Sains Malaysia, Penang, MALAYSIA Norizham Abdul Razak School
More informationStrain-Based Analysis for Geometrically Nonlinear Beams: A Modal Approach
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference2th AI 23-26 April 212, Honolulu, Hawaii AIAA 212-1713 Strain-Based Analysis for Geometrically Nonlinear Beams: A
More informationAerodynamics. High-Lift Devices
High-Lift Devices Devices to increase the lift coefficient by geometry changes (camber and/or chord) and/or boundary-layer control (avoid flow separation - Flaps, trailing edge devices - Slats, leading
More informationSome effects of large blade deflections on aeroelastic stability
47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition 5-8 January 29, Orlando, Florida AIAA 29-839 Some effects of large blade deflections on aeroelastic stability
More informationModal Analysis: What it is and is not Gerrit Visser
Modal Analysis: What it is and is not Gerrit Visser What is a Modal Analysis? What answers do we get out of it? How is it useful? What does it not tell us? In this article, we ll discuss where a modal
More informationTHE ANALYSIS OF LAMINATE LAY-UP EFFECT ON THE FLUTTER SPEED OF COMPOSITE STABILIZERS
THE ANALYSIS OF LAMINATE LAY-UP EFFECT ON THE FLUTTER SPEED OF COMPOSITE STABILIZERS Mirko DINULOVIĆ*, Boško RAŠUO* and Branimir KRSTIĆ** * University of Belgrade, Faculty of Mechanical Engineering, **
More informationFlight Dynamics and Control. Lecture 3: Longitudinal stability Derivatives G. Dimitriadis University of Liege
Flight Dynamics and Control Lecture 3: Longitudinal stability Derivatives G. Dimitriadis University of Liege Previously on AERO0003-1 We developed linearized equations of motion Longitudinal direction
More informationGiven a stream function for a cylinder in a uniform flow with circulation: a) Sketch the flow pattern in terms of streamlines.
Question Given a stream function for a cylinder in a uniform flow with circulation: R Γ r ψ = U r sinθ + ln r π R a) Sketch the flow pattern in terms of streamlines. b) Derive an expression for the angular
More informationMasters in Mechanical Engineering Aerodynamics 1 st Semester 2015/16
Masters in Mechanical Engineering Aerodynamics st Semester 05/6 Exam st season, 8 January 06 Name : Time : 8:30 Number: Duration : 3 hours st Part : No textbooks/notes allowed nd Part : Textbooks allowed
More informationNonlinear buffeting response of bridge deck using the Band Superposition approach: comparison between rheological models and convolution integrals.
Nonlinear buffeting response of bridge deck using the Band Superposition approach: comparison between rheological models and convolution integrals. Argentini, T. ), Diana, G. ), Portentoso, M. * ), Rocchi,
More informationMatthew Lucas Guertin, 2d Lt USAF
Copyright Matthew Lucas Guertin, 2d Lt USAF 2012 ABSTRACT The Application of Finite Element Methods to Aeroelastic Lifting Surface Flutter by Matthew Lucas Guertin, 2d Lt USAF Aeroelastic behavior prediction
More informationBernoulli's equation: 1 p h t p t. near the far from plate the plate. p u
UNSTEADY FLOW let s re-visit the Kutta condition when the flow is unsteady: p u p l Bernoulli's equation: 2 φ v 1 + + = () = + p h t p t 2 2 near the far from plate the plate as a statement of the Kutta
More informationAeroelastic Stability of a 2D Airfoil Section equipped with a Trailing Edge Flap
Downloaded from orbit.dtu.dk on: Apr 27, 2018 Aeroelastic Stability of a 2D Airfoil Section equipped with a Trailing Edge Flap Bergami, Leonardo Publication date: 2008 Document Version Publisher's PDF,
More informationFIFTH INTERNATIONAL CONGRESSON SOUND AND VIBRATION DECEMBER15-18, 1997 ADELAIDE,SOUTHAUSTRALIA
FIFTH INTERNATIONAL CONGRESSON SOUND AND VIBRATION DECEMBER15-18, 1997 ADELAIDE,SOUTHAUSTRALIA Aeroelastic Response Of A Three Degree Of Freedom Wing-Aileron System With Structural Non-Linearity S. A.
More informationFLIGHT DYNAMICS. Robert F. Stengel. Princeton University Press Princeton and Oxford
FLIGHT DYNAMICS Robert F. Stengel Princeton University Press Princeton and Oxford Preface XV Chapter One Introduction 1 1.1 ELEMENTS OF THE AIRPLANE 1 Airframe Components 1 Propulsion Systems 4 1.2 REPRESENTATIVE
More informationNumerical Study on Performance of Curved Wind Turbine Blade for Loads Reduction
Numerical Study on Performance of Curved Wind Turbine Blade for Loads Reduction T. Maggio F. Grasso D.P. Coiro 13th International Conference Wind Engineering (ICWE13), 10-15 July 011, Amsterdam, the Netherlands.
More informationStability and Control
Stability and Control Introduction An important concept that must be considered when designing an aircraft, missile, or other type of vehicle, is that of stability and control. The study of stability is
More informationOptimization Framework for Design of Morphing Wings
Optimization Framework for Design of Morphing Wings Jian Yang, Raj Nangia & Jonathan Cooper Department of Aerospace Engineering, University of Bristol, UK & John Simpson Fraunhofer IBP, Germany AIAA Aviation
More informationAeroelastic Wind Tunnel Testing of Very Flexible High-Aspect-Ratio Wings
Aeroelastic Wind Tunnel Testing of Very Flexible High-Aspect-Ratio Wings Justin Jaworski Workshop on Recent Advances in Aeroelasticity, Experiment and Theory July 2, 2010 Problem and Scope High altitude
More informationThe future of non-linear modelling of aeroelastic gust interaction
The future of non-linear modelling of aeroelastic gust interaction C. J. A. Wales, C. Valente, R. G. Cook, A. L. Gaitonde, D. P. Jones, J. E. Cooper University of Bristol AVIATION, 25 29 June 2018 Hyatt
More informationStructural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian
Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: Mode-Superposition Method Mode-Superposition Method:
More informationNON-LINEAR BEHAVIOUR OF A WING DUE TO UNDERWING STORES
NON-LINEAR BEHAVIOUR OF A WING DUE TO UNDERWING STORES G.A. Vio,, D.S. Stanley, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney NSW 6, Australia gareth.vio@sydney.edu.au;
More informationWings and Bodies in Compressible Flows
Wings and Bodies in Compressible Flows Prandtl-Glauert-Goethert Transformation Potential equation: 1 If we choose and Laplace eqn. The transformation has stretched the x co-ordinate by 2 Values of at corresponding
More informationReduced reliance on wind tunnel data
Reduced reliance on wind tunnel data The recreation of the industrial gust loads process, using CFD in place of experimental data Investigation of the underlying assumptions of the current industrial gust
More informationCOPYRIGHTED MATERIAL. Index
Index A Admissible function, 163 Amplification factor, 36 Amplitude, 1, 22 Amplitude-modulated carrier, 630 Amplitude ratio, 36 Antinodes, 612 Approximate analytical methods, 647 Assumed modes method,
More informationUnsteady Panel Method for Complex Configurations Including Wake Modeling
JOURNAL OF AIRCRAFT Vol. 45, No., January February 8 Unsteady Panel Method for Complex Configurations Including Wake Modeling Louw H. van Zyl Council for Scientific and Industrial Research, Pretoria, South
More informationLimit Cycle Oscillations of a Typical Airfoil in Transonic Flow
Limit Cycle Oscillations of a Typical Airfoil in Transonic Flow Denis B. Kholodar, United States Air Force Academy, Colorado Springs, CO 88 Earl H. Dowell, Jeffrey P. Thomas, and Kenneth C. Hall Duke University,
More informationActive Flutter Control using an Adjoint Method
44th AIAA Aerospace Sciences Meeting and Exhibit 9-12 January 26, Reno, Nevada AIAA 26-844 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 9 12 Jan, 26. Active Flutter Control using an
More informationAERO-STRUCTURAL MDO OF A SPAR-TANK-TYPE WING FOR AIRCRAFT CONCEPTUAL DESIGN
1 26th INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES AERO-STRUCTURAL MDO OF A SPAR-TANK-TYPE WING FOR AIRCRAFT CONCEPTUAL DESIGN Paulo R. Caixeta Jr., Álvaro M. Abdalla, Flávio D. Marques, Fernando
More information1. Fluid Dynamics Around Airfoils
1. Fluid Dynamics Around Airfoils Two-dimensional flow around a streamlined shape Foces on an airfoil Distribution of pressue coefficient over an airfoil The variation of the lift coefficient with the
More informationFlight Vehicle Terminology
Flight Vehicle Terminology 1.0 Axes Systems There are 3 axes systems which can be used in Aeronautics, Aerodynamics & Flight Mechanics: Ground Axes G(x 0, y 0, z 0 ) Body Axes G(x, y, z) Aerodynamic Axes
More information02 Introduction to Structural Dynamics & Aeroelasticity
02 Introduction to Structural Dynamics & Aeroelasticity Vibraciones y Aeroelasticidad Dpto. de Vehículos Aeroespaciales P. García-Fogeda Núñez & F. Arévalo Lozano ESCUELA TÉCNICA SUPERIOR DE INGENIERÍA
More informationInvestigation potential flow about swept back wing using panel method
INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENT Volume 7, Issue 4, 2016 pp.317-326 Journal homepage: www.ijee.ieefoundation.org Investigation potential flow about swept back wing using panel method Wakkas
More informationTransonic Flutter Prediction of Supersonic Jet Trainer with Various External Store Configurations
Transonic Flutter Prediction of Supersonic Jet Trainer with Various External Store Configurations In Lee * Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Korea Hyuk-Jun Kwon Agency
More informationConsider a wing of finite span with an elliptic circulation distribution:
Question 1 (a) onsider a wing of finite span with an elliptic circulation distribution: Γ( y) Γo y + b = 1, - s y s where s=b/ denotes the wing semi-span. Use this equation, in conjunction with the Kutta-Joukowsky
More informationUnsteady Aerodynamic Vortex Lattice of Moving Aircraft. Master thesis
Unsteady Aerodynamic Vortex Lattice of Moving Aircraft September 3, 211 Master thesis Author: Enrique Mata Bueso Supervisors: Arthur Rizzi Jesper Oppelstrup Aeronautical and Vehicle engineering department,
More informationCopyright 2007 N. Komerath. Other rights may be specified with individual items. All rights reserved.
Low Speed Aerodynamics Notes 5: Potential ti Flow Method Objective: Get a method to describe flow velocity fields and relate them to surface shapes consistently. Strategy: Describe the flow field as the
More informationABSTRACT. Thomas Woodrow Sukut, 2d Lt USAF
ABSTRACT Nonlinear Aeroelastic Analysis of UAVs: Deterministic and Stochastic Approaches By Thomas Woodrow Sukut, 2d Lt USAF Aeroelastic aspects of unmanned aerial vehicles (UAVs) is analyzed by treatment
More informationRandom Problems. Problem 1 (30 pts)
Random Problems Problem (3 pts) An untwisted wing with an elliptical planform has an aspect ratio of 6 and a span of m. The wing loading (defined as the lift per unit area of the wing) is 9N/m when flying
More informationIntroduction to Flight Dynamics
Chapter 1 Introduction to Flight Dynamics Flight dynamics deals principally with the response of aerospace vehicles to perturbations in their flight environments and to control inputs. In order to understand
More informationDYNAMIC RESPONSE OF AN AIRPLANE ELASTIC STRUCTURE IN TRANSONIC FLOW
DYNAMIC RESPONSE OF AN AIRPLANE ELASTIC STRUCTURE IN TRANSONIC FLOW S. Kuzmina*, F. Ishmuratov*, O. Karas*, A.Chizhov* * Central Aerohydrodynamic Institute (TsAGI), Zhukovsky, Russia Keywords: aeroelasticity,
More informationAdvanced Vibrations. Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian
Advanced Vibrations Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian ahmadian@iust.ac.ir Distributed-Parameter Systems: Exact Solutions Relation between Discrete and Distributed
More informationImplementing a Partitioned Algorithm for Fluid-Structure Interaction of Flexible Flapping Wings within Overture
10 th Symposimum on Overset Composite Grids and Solution Technology, NASA Ames Research Center Moffett Field, California, USA 1 Implementing a Partitioned Algorithm for Fluid-Structure Interaction of Flexible
More informationGerman Aerospace Center (DLR)
German Aerospace Center (DLR) AEROGUST M30 Progress Meeting 23-24 November 2017, Bordeaux Presented by P. Bekemeryer / J. Nitzsche With contributions of C. Kaiser 1, S. Görtz 2, R. Heinrich 2, J. Nitzsche
More informationMULTIDISCPLINARY OPTIMIZATION AND SENSITIVITY ANALYSIS OF FLUTTER OF AN AIRCRAFT WING WITH UNDERWING STORE IN TRANSONIC REGIME
MULTIDISCPLINARY OPTIMIZATION AND SENSITIVITY ANALYSIS OF FLUTTER OF AN AIRCRAFT WING WITH UNDERWING STORE IN TRANSONIC REGIME A thesis submitted in partial fulfillment of the requirements for the degree
More informationA First Order Model of a Variable Camber Wing for a Civil Passenger Aircraft
A First Order Model of a Variable Camber Wing for a Civil Passenger Aircraft Tristan Martindale A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand,
More informationState-Space Representation of Unsteady Aerodynamic Models
State-Space Representation of Unsteady Aerodynamic Models -./,1231-44567 &! %! $! #! "! x α α k+1 A ERA x = 1 t α 1 α x C L (k t) = C ERA C Lα C L α α α ERA Model fast dynamics k + B ERA t quasi-steady
More informationREPORT DOCUMENTATION PAGE Form Approved OMB No
REPORT DOCUMENTATION PAGE Form Approved OMB No. 74-188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions,
More informationUnconstrained flight and stability analysis of a flexible rocket using a detailed finite-element based procedure
Computational Ballistics II 357 Unconstrained flight and stability analysis of a flexible rocket using a detailed finite-element based procedure D. J. McTavish, D. R. Greatrix & K. Davidson Ryerson University,
More informationParameter Sensitivities Affecting the Flutter Speed of a MW-Sized Blade
Parameter Sensitivities Affecting the Flutter Speed of a MW-Sized Blade Don W. Lobitz Sandia National Laboratories, 1 P. O. Box 5800, MS0708, Albuquerque, NM 87185-0708 e-mail: dwlobit@sandia.gov With
More informationFlight Dynamics and Control
Flight Dynamics and Control Lecture 1: Introduction G. Dimitriadis University of Liege Reference material Lecture Notes Flight Dynamics Principles, M.V. Cook, Arnold, 1997 Fundamentals of Airplane Flight
More informationOptimum Design of a PID Controller for the Adaptive Torsion Wing Using GA
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference20th AI 23-26 April 2012, Honolulu, Hawaii AIAA 2012-1739 Optimum Design of a PID Controller for the Adaptive Torsion
More informationMechanics of Flight. Warren F. Phillips. John Wiley & Sons, Inc. Professor Mechanical and Aerospace Engineering Utah State University WILEY
Mechanics of Flight Warren F. Phillips Professor Mechanical and Aerospace Engineering Utah State University WILEY John Wiley & Sons, Inc. CONTENTS Preface Acknowledgments xi xiii 1. Overview of Aerodynamics
More informationStructural and Aerodynamic Models in the Nonlinear Flight. Dynamics of Very Flexible Aircraft
Structural and Aerodynamic Models in the Nonlinear Flight Dynamics of Very Flexible Aircraft Rafael Palacios, Joseba Murua 2, and Robert Cook 3 Imperial College, London SW7 2AZ, United Kingdom An evaluation
More informationUniversity of Bristol - Explore Bristol Research
Stodieck, O. A., Cooper, J. E., & Weaver, P. M. (2016). Interpretation of Bending/Torsion Coupling for Swept, Nonhomogenous Wings. Journal of Aircraft, 53(4), 892-899. DOI: 10.2514/1.C033186 Peer reviewed
More informationNonlinear Aeroelastic Analysis of a Wing with Control Surface Freeplay
Copyright c 7 ICCES ICCES, vol., no.3, pp.75-8, 7 Nonlinear Aeroelastic Analysis of a with Control Surface Freeplay K.S. Kim 1,J.H.Yoo,J.S.Bae 3 and I. Lee 1 Summary In this paper, nonlinear aeroelastic
More informationAdvanced Vibrations. Elements of Analytical Dynamics. By: H. Ahmadian Lecture One
Advanced Vibrations Lecture One Elements of Analytical Dynamics By: H. Ahmadian ahmadian@iust.ac.ir Elements of Analytical Dynamics Newton's laws were formulated for a single particle Can be extended to
More informationCOMPUTATION OF CASCADE FLUTTER WITH A COUPLED AERODYNAMIC AND STRUCTURAL MODEL
COMPUTATION OF CASCADE FLUTTER WITH A COUPLED AERODYNAMIC AND STRUCTURAL MODEL M. SADEGHI AND F. LIU Department of Mechanical and Aerospace Engineering University of California, Irvine, CA 92697-3975,
More informationME 563 HOMEWORK # 7 SOLUTIONS Fall 2010
ME 563 HOMEWORK # 7 SOLUTIONS Fall 2010 PROBLEM 1: Given the mass matrix and two undamped natural frequencies for a general two degree-of-freedom system with a symmetric stiffness matrix, find the stiffness
More informationAN ENHANCED CORRECTION FACTOR TECHNIQUE FOR AERODYNAMIC INFLUENCE COEFFICIENT METHODS
AN ENHANCED CORRECTION ACTOR TECHNIQUE OR AERODYNAMIC INLUENCE COEICIENT METHODS Ioan Jadic, Dayton Hartley and Jagannath Giri Raytheon Aircraft Company, Wichita, Kansas 67-85 Phone: 36-676-436 E-mail:
More informationUnsteady Subsonic Aerodynamic Characteristics of Wing in Fold Motion
Technical Paper DOI:10.5139/IJASS.2011.12.1.63 Unsteady Subsonic Aerodynamic Characteristics of Wing in Fold Motion Yoo-Yeon Jung* School of Mechanical and Aerospace Engineering, Seoul National University,
More informationApril 15, 2011 Sample Quiz and Exam Questions D. A. Caughey Page 1 of 9
April 15, 2011 Sample Quiz Exam Questions D. A. Caughey Page 1 of 9 These pages include virtually all Quiz, Midterm, Final Examination questions I have used in M&AE 5070 over the years. Note that some
More informationEnclosure enhancement of flight performance
THEORETICAL & APPLIED MECHANICS LETTERS, 23 (21) Enclosure enhancement of flight performance Mehdi Ghommem, 1, a) Daniel Garcia, 2 Victor M. Calo 3 1) Center for Numerical Porous Media (NumPor), King Abdullah
More informationLecture #AC 3. Aircraft Lateral Dynamics. Spiral, Roll, and Dutch Roll Modes
Lecture #AC 3 Aircraft Lateral Dynamics Spiral, Roll, and Dutch Roll Modes Copy right 2003 by Jon at h an H ow 1 Spring 2003 16.61 AC 3 2 Aircraft Lateral Dynamics Using a procedure similar to the longitudinal
More informationUniversity of Bristol - Explore Bristol Research
Castellani, M., Cooper, J. E., & Lemmens, Y. (6). Flight Loads Prediction of High Aspect Ratio Wing Aircraft using Dynamics. SAE International Journal of Aerospace, 6, [48587]. DOI:.55/6/48587 Publisher's
More informationStatic Aeroelasticity Considerations in Aerodynamic Adaptation of Wings for Low Drag
ABSTRACT EDWARD NICHOLAS SHIPLEY, JUNIOR. Static Aeroelasticity Considerations in Aerodynamic Adaptation of Wings for Low Drag. (Under the direction of Dr. Ashok Gopalarathnam.) This thesis presents a
More informationCoupled Mode Flutter for Advanced Turbofans. Stephen Thomas Clark. Department of Mechanical Engineering Duke University. Date: March 19, 2010
Coupled Mode Flutter for Advanced Turbofans by Stephen Thomas Clark Department of Mechanical Engineering Duke University Date: March 19, 2010 Approved: Dr. Robert E. Kielb, Supervisor Dr. Earl H. Dowell
More informationEfficient Modeling of Dynamic Blockage Effects for Unsteady Wind Tunnel Testing
Efficient Modeling of Dynamic Blockage Effects for Unsteady Wind Tunnel Testing Sumant Sharma ssharma46@gatech.edu Undergraduate Research Assistant Narayanan Komerath komerath@gatech.edu Professor Vrishank
More informationFlight Dynamics, Simulation, and Control
Flight Dynamics, Simulation, and Control For Rigid and Flexible Aircraft Ranjan Vepa CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an
More informationν δ - 1 -
ν δ - 1 - δ ν ν δ ν ν - 2 - ρ δ ρ θ θ θ δ τ ρ θ δ δ θ δ δ δ δ τ μ δ μ δ ν δ δ δ - 3 - τ ρ δ ρ δ ρ δ δ δ δ δ δ δ δ δ δ δ - 4 - ρ μ ρ μ ρ ρ μ μ ρ - 5 - ρ τ μ τ μ ρ δ δ δ - 6 - τ ρ μ τ ρ μ ρ δ θ θ δ θ - 7
More informationMestrado Integrado em Engenharia Mecânica Aerodynamics 1 st Semester 2012/13
Mestrado Integrado em Engenharia Mecânica Aerodynamics 1 st Semester 212/13 Exam 2ª época, 2 February 213 Name : Time : 8: Number: Duration : 3 hours 1 st Part : No textbooks/notes allowed 2 nd Part :
More information13.4 to "wutter' Substituting these values in Eq. (13.57) we obtain
568 Elementary aeroelasticity where the origin for z is taken at the built-in end and a is a constant term which includes the tip load and the flexural rigidity of the beam. From Eq. (i) d2 V V(L) = 2aL3
More informationNumerical Implementation of a Frequency-Domain Panel Method for Flutter Prediction of a 3D Wing
Numerical Implementation of a Frequency-Domain Panel Method for Flutter Prediction of a 3D Wing Eduardo Manuel Pizarro Gomes Pepe pizarropepe@tecnico.ulisboa.pt Instituto Superior Técnico, Lisboa, Portugal
More informationNonlinear Aerodynamic Predictions Of Aircraft and Missiles Employing Trailing-Edge Flaps
Nonlinear Aerodynamic Predictions Of Aircraft and Missiles Employing Trailing-Edge Flaps Daniel J. Lesieutre 1 Nielsen Engineering & Research, Inc., Santa Clara, CA, 95054 The nonlinear missile aerodynamic
More informationFLUID STRUCTURE INTERACTIONS PREAMBLE. There are two types of vibrations: resonance and instability.
FLUID STRUCTURE INTERACTIONS PREAMBLE There are two types of vibrations: resonance and instability. Resonance occurs when a structure is excited at a natural frequency. When damping is low, the structure
More informationDYNAMIC STALL ONSET VARIATION WITH REDUCED FREQUENCY FOR THREE STALL MECHANISMS
International Forum on Aeroelasticity and Structural Dynamics IFASD 27 25-28 June 27 Como, Italy DYNAMIC STALL ONSET VARIATION WITH REDUCED FREQUENCY FOR THREE STALL MECHANISMS Boutet Johan, Dimitriadis
More informationCONTROL LAW DESIGN IN A COMPUTATIONAL AEROELASTICITY ENVIRONMENT
CONTROL LAW DESIGN IN A COMPUTATIONAL AEROELASTICITY ENVIRONMENT Jerry R. Newsom Harry H. Robertshaw Rakesh K. Kapania NASA LaRC Virginia Tech Virginia Tech Hampton, VA Blacksburg, VA Blacksburg, VA 757-864-65
More information