functionally graded material, piezoelectric material, circular plates, uniform electric potential, direct displacement
|
|
- Ashlynn Cathleen Moore
- 6 years ago
- Views:
Transcription
1 Science in China Series G: Physics, Mechanics & Astronomy 008 SCIENCE IN CHINA PRESS Springer-Verlag phys.scichina.com Three-dimensional analytical solution for a transversely isotropic functionally graded pieoelectric circular plate subject to a uniform electric potential difference LI XiangYu, DING HaoJiang & CHEN WeiQiu Department of Civil Engineering, Zhejiang University, Hanghou 31007, China This paper studies the problem of a functionally graded pieoelectric circular plate subjected to a uniform electric potential difference between the upper and lower surfaces. By assuming the generalied displacements in appropriate forms, five differential equations governing the generalied displacement functions are derived from the equilibrium equations. These displacement functions are then obtained in an explicit form, which still involve four undetermined integral constants, through a step-by-step integration which properly incorporates the boundary conditions at the upper and lower surfaces. The boundary conditions at the cylindrical surface are then used to determine the integral constants. Hence, three-dimensional analytical solutions for electrically loaded functionally graded pieoelectric circular plates with free or simply-supported edge are completely determined. These solutions can account for an arbitrary material variation along the thickness, and thus can be readily degenerated into those for a homogenous plate. A numerical example is finally given to show the validity of the analysis, and the effect of material inhomogeneity on the elastic and electric fields is discussed. functionally graded material, pieoelectric material, circular plates, uniform electric potential, direct displacement method The time-line of humankind is located at the dawn of a new age, namely, the Smart Materials Age [1]. Now, the functionally graded pieoelectric materials (FGPMs), as intelligent materials, have been used extensively in applications of sensors and actuators in the micro-electro-mechanical system (MEMS) [,3] and smart structures [4-9], especially in the medical and aerospace industry [10]. Generally, FGPMs are inhomogeneous with material properties varying spatially in a continuous manner, hence exhibiting more attractive features when compared to conventional laminated ma- Received August 4, 006; accepted August 6, 007 doi: /s Corresponding author ( dinghj@ju.edu.cn) Supported by the National Natural Science Foundation of China (Grant Nos and ) and the Specialied Research Fund for the Doctoral Program of Higher Education of China (Grant No ) Sci China Ser G-Phys Mech Astron Aug. 008 vol. 51 no
2 terials. Consequently, more and more attention from researchers in various relevant fields has been paid to the response of the FGPM structures to externally applied loads. The transfer matrix method incorporating the asymptotic expansion technique has been extensively adopted to analye the response of the FGPM structures by Cheng et al. [11-15]. Introducing two displacement functions as well as two stress functions, Chen and Ding [16,17] established a new state-space model (SSM) to examine the bending and free vibration of transversely isotropic FGPM plates. Chen et al. [18] obtained a three-dimensional analytical solution of a functionally graded pieoelectric spherical shell rotating at a constant angular velocity. Wu et al. [19] derived a high-order theory for functionally graded pieoelectric shells based on the generalied Hamilton s principle. Zhong and Shang [0], for the first time, presented a 3D exact analysis of simply supported FGPM rectangular plates via SSM when the material constants vary exponentially along the thickness of the plate. Chen et al. [1] employed SSM along with a layerwise approximation model to analye the free vibration of a functionally graded pieoelectric hollow cylinder filled with compressible fluid. Pan and Han [] obtained the Green s functions for transversely isotropic pieoelectric functionally graded multilayered half space by virtue of two systems of vector functions and the propagator matrix method. Recently, the Stroh-like formulae have been developed to study the mechanical and electric response of simply supported plates [3,4]. However, to the authors knowledge, no analytical solution pertinent to FGPM circular plates has been reported yet. This paper develops a 3D analysis of electrically loaded transversely isotropic FGPM circular plates with free or simply supported edge by virtue of the direct displacement method, which expresses the displacements and electric potential in terms of appropriate polynomials of r, the radial coordinate, with coefficients being undetermined functions of, the axial coordinate. The derived analytical solutions satisfy exactly the boundary conditions on the upper and lower surfaces of the plate, while approximately the circumferential boundary conditions in the Saint Venant s sense. Provided certain integrable conditions and the positive definiteness of energy function are ensured, the material properties of FGPM plates can be of arbitrary functions of. Hence the derived solutions apply to homogeneous plates naturally, for which the elastic and electric fields can be expressed in explicit forms. A numerical example of a particular FGPM circular plate, with only two material constants being functions of the thickness coordinate, is finally considered to clearly show the effect of material inhomogeneity on the elastic and electric fields in the plate. 1 Basic equations and the direct displacement method When referred to the cylindrical coordinates ( r, θ, ), the basic equations for the axisymmetric problem of a transversely isotropic FGPM body are 1 1 σ + τ + r σ σ = 0, τ + r τ + σ = 0, (1) ( ) rr, r, r θ rr, r, 1 Drr, r Dr D, 0, 1 1 r = c11u, r + c1r u+ c13 w, + e31 φ, = c1 u, r + c11r u+ c13 w, + e31 φ, 1 = c13 u, r + r u + c33 w, + e33φ,, τr = c44( u, + w, r) + e15 φ, r, ( ) + + = () σ, σ θ, σ 1 ( r ) D = e ( u + w ) ε φ, D = e u + r u + e w ε φ, (4) r 15,, r 11, r 31, 33, 33, where σ r, σθ, σ and τ r are the stress components; D r and (3) D are the electric displacement LI XiangYu et al. Sci China Ser G-Phys Mech Astron Aug. 008 vol. 51 no
3 components; u and w are the displacement components in r-direction and -direction, respectively; φ is the electric potential; the comma denotes differentiation with respect to the indicated variable. c ij, e ij and ε ij are the elastic, pieoelectric and dielectric coefficients, respectively. In this paper, we consider functionally graded materials, whose material coefficients in eqs. (3) and (4) are functions of, i.e., c = c ( ), ε = ε ( ) and e = e ( ). For homogeneous materials, these ij ij ij ij coefficients are constant. We start the analysis directly from the generalied displacements (mechanical displacements and electric potential) by assuming that u = ru (5) ij ( ) 1, ( ) ( ) φ φ ( ) 0 0 ij w= w + r w, =, (6) i where u 1 ( ) and w ( ) are referred to as displacement functions, and φ 0 ( ) as electric functions. Substituting eqs. (5) and (6) into eqs. (3) and (4) yields σ r = ( c11 + c1 ) u1 + c13w0, + e31φ 0, + r c13w,, σθ = ( c11 + c1 ) u1 + c13w0, + e31φ 0, + r c13w,, σ = c u + c w + e φ + r c w, τ = rc u + w, , 33 0 r ( ) ( ) ε φ 13, 33, 44 1, D = re u + w, D = e u + e w + r e w. (8) r 15 1, , 33 0, 33, Introducing eqs. (7) and (8) into eqs. (1) and (), respectively, we obtain the following equations governing the generalied displacement functions: e w = 0, (9) ( 33, ), ( 33, ) 0,, c44 ( u1, w ) + + c, 13w, = 0, ( e31u1 e33w0, ε33φ0, ) e15 ( u1, ), w ( c13u1 c33w0, e33φ 0, ) c44 ( u1, w ) (7) c w = (10) (11) = 0, (1) = 0. (13) Circular plate subject to uniform electric potentials, Consider a circular plate with radius a and height h, subject to uniform electric potential k 1 on the upper surface = h and k on the lower surface = h, as shown in Figure 1. The boundary conditions on the surfaces =± h are = h : σ = 0, τr = 0, φ = k1, (14) and = h : σ = 0, τ = 0, φ = k. (15) Substitution of the expressions for in eqs. (14) and (15) leads to σ, r τ r and φ in eqs. (7) and (6) into the boundary conditions 1118 LI XiangYu et al. Sci China Ser G-Phys Mech Astron Aug. 008 vol. 51 no
4 and =± h ; Figure 1 FGPM circular plate subject to uniform electric potentials at = ±h/. ( ) φ ( ) φ h = k, h = k, (16) w, = 0, (17) c u + c w + e φ = 0, (18) , 33 0, u + w = 0. (19) 1, Integrating eq. (10) once from the lower limit /, using eq. (17) and noticing c 33 > 0, we obtain w, = 0, (0) which satisfies eq. (9) automatically. w is thus obtained from eq. (0): w = a (1) 1, where a 1 is an integral constant. Introducing eq. (0) into eq. (11), integrating once from the lower limits /, using the boundary condition eq. (19) and noticing 44 0 c >, we obtain u + w = 0. () 1, Substituting eq. (1) into eq. () and integrating once from the lower limit / give u = a + a, (3) 1 1 where a is an integral constant. Introducing eq. () into eqs. (1) and (13), integrating them and utiliing the boundary condition (18) yield c u + c w + e φ = 0, (4) , 33 0, e u + e w ε φ = a, (5) , 33 0, 3 where a 3 is an integral constant. Solving eqs. (4) and (5) simultaneously and making use of eq. (3) give rise to w = 4 a F( ) a F ( ) + a F ( ), (6) where 0, φ = 4 ag( ) a G ( ), (7) 0, ε J = e + c, F ( ) = J e, = ε33 = ε33 F( ) J ( e e c ), F ( ) J ( e e c ), = = G ( ) J ( c e e c ), G ( ) J ( c e e c ). (8) LI XiangYu et al. Sci China Ser G-Phys Mech Astron Aug. 008 vol. 51 no
5 Now w 0 and φ 0 can be obtained without any difficulty by integrating eqs. (6) and (7) from the lower limit /: where a 4 and a 5 are integral constants, and w = 4 a f ( ) a f ( ) + a f ( ) + a, (9) φ = 4 ag( ) ag ( ) + a, (30) gi( ) = Gi( ξ) d ξ, ( i = 1,), (31) f j( ) = Fj( ξ) d ξ, ( j = 1,,3). (3) Introducing eq. (30) into the boundary condition (16), we obtain a 5 1, (33) 4 ag 1 1( h) ag ( h) = k k1 = k, (34) where k is the difference between the electric potentials on the upper and lower surfaces. It is seen that there are totally 5 integral constants ai ( i = 1,,,5), among which a 5 has been fixed and a 1 and a should satisfy eq. (34); boundary conditions at r = a should be employed to fix the four constants ai ( i = 1,,3,4) in addition to eq. (34). It should be noted that a 4 corresponds to a rigid-body translation in the axial direction and a 5 is related to a reference electric potential. Both a 4 and a 5 exert no influence on the distribution of stresses and electric displacement. Substituting the expressions for displacement functions and electric functions into eqs. (5) (8) yields u = r a a, (35) ( ) 1 w= a 1 r 4 f1( ) + af( ) + a3f3( ) + a4, (36) φ = 4 ag 1 1( ) ag ( ) + k1, (37) σ = τ r = 0, σr = σθ = a1[ c13f1( ) + e31g1( ) ( c11 + c1) ] (38) a c F ( ) + e G ( ) ( c + c ) + a c F ( ), [ ] Dr = 0, D = a3. (39) From eqs. (38) and (39), we can observe that: (1) σ r and σ θ are independent of r, being a function of variable only; () The axial electric displacement is constant while the radial electric displacement vanishes in the present problem. It is easy to obtain the expressions for the radial resultant force N and the bending moment M by virtue of σ r in eq. (38): where h σ rd , (40) N = a N a N + a N h σ rd , (41) M = a N a N + a N [ ] h i i1 = N c F ( ) e G ( ) ( c c ) d, 110 LI XiangYu et al. Sci China Ser G-Phys Mech Astron Aug. 008 vol. 51 no
6 [ ] h i i = N c F ( ) e G ( ) ( c c ) d, h i i N = c F ( )d, ( i = 0,1). (4) 3 The determination of remaining integral constants First, consider an FGPM circular plate with free edge. The boundary conditions at r = a are Na ( ) = 0, Ma ( ) = 0, τ r = 0, Dr = 0, (43) where the last two conditions have been satisfied automatically as seen from eqs. (38) and (39). Introducing eqs. (40) and (41) into the first two conditions in eq. (43), we arrive at an 1 01 an 0 + an 3 03 = 0, (44) an 1 11 an 1 + an 3 13 = 0. (45) Solving eqs. (34), (44) and (45) simultaneously, we obtain ai = kai, ( i = 1,,3), (46) where A1 = ( N03N1 N13N0) (4 D), A = ( N03N11 N13N01) ( D), A3 = ( N0N11 N01N1 ) ( D), (47) D= g1( h ) ( N03N1 N13N0 ) g( h ) ( N03N11 N13N01). Substituting eq. (46) into eqs. (35)-(39), we can derive the expressions for displacements, electric potential and electric displacements as follows: u = rk A A, (48) ( ) 1 { } w= k A1 r + 4 f1( ) Af( ) + A3f3( ) + a4, (49) φ = k[ Ag 1 1( ) Ag( ) ] + k1. (50) σ = τ r = 0, σr = σθ = k{ A1[ c13f1( ) + e31g1( ) ( c11 + c1) ] (51) A c F ( ) + e G ( ) ( c + c ) + A c F ( ). [ ] } Dr = 0, D = ka3. (5) For a simply-supported circular plate, since the axial displacement is constrained at r = a, we may simply take a4 = ka 1 a 4 f1(0) + + kaf(0) ka3f3(0) in eq. (49) while eqs. (48) and (50)-(5) keep unaltered.. For homogeneous materials, i.e., cij = const, eij = const and ε ij = const, all functions involved become polynomials of. Calculation according to eq. (47) gives rise to the explicit expressions for Ai ( i = 1,, 3). The corresponding expressions for stresses, displacements, electric potential and electric displacements are u = rk ( Ch), w= k( + h ) C5 ( Ch) + a4, (53) φ = k h+ 1 + k, (54) ( ) 1 LI XiangYu et al. Sci China Ser G-Phys Mech Astron Aug. 008 vol. 51 no
7 where 1 σ = τr = σr = σθ = 0, (55) D = 0, D = C k ( c C C h), (56) r ε33 = = 33 C = J ( e e c ), C J ( c e e c ), C J e, [ e ] 1 13C = C4 = c + e C ( c c ), C c ( c c ) C. Comparison of eqs. (48)-(5) with eqs. (53)-(56) reveals that: (1) The radial displacement of a homogeneous plate, varying linearly with r, is independent of, while for an inhomogeneous plate, the radial displacement depends upon in a linear manner; () The deflection of a homogeneous plate w, being a linear function of, does not vary with r, whereas in the FGPM case, the expression of deflection involves r. Hence the neutral surface ( = 0) of the FGPM plate becomes a curved surface after deformation; while that of a homogeneous plate remains a plane parallel to the upper and lower surfaces; (3) All stresses in a homogeneous plate vanish, while σ r and σ θ generally are not ero in an FGPM plate. Similarly, if we assign a4 = kc5 (4 C), eqs. (53)-(56) apply to a simply supported plate. 4 Numerical results and discussion We consider a particular form of FGPM as follows: λη+ ( 1) 0 c = c, c = c, c = c, c = c e, c = c, (58) where c 0 ij, 0 e ij and ij (57) e = e, e = e, e = e, (59) 0 0 ( 1) ε ε, ε ε e λη + = =, (60) ε are the material coefficients at the upper surface = h, 1 η = h 1 is the dimensionless thickness coordinate, and λ is the gradient index. Particularly when λ = 0, the material becomes homogenous. For this particular FGPM, all elastic and electric field quantities can be obtained explicitly, however, they are omitted here for the sake of simplicity. The numerical calculation is carried out for a simply supported circular plate, and the following dimensionless quantities are introduced: r σ r D w φ ξ =, 0 ξ 1, σξ =, D, W,. 0 η = = Φ = (61) a c 0 0 c ε h k We take the electric potentials k 1 = 0 V, k = 100 V, the radius of the plate a = 1 m, and the height h = 0.1 m. The material property at = h is identical to PZT-5H [5,6], with material constants shown in Table 1. Table 1 Material properties of PZT-5H Property Elastic (10 10 N/m ) Pieoelectric (C/m ) Dielectric (10 11 F/m) PZT-5H c = 1.6, c = 5.5, c = 5.3, c = 11.7, c = e = 17.0, e = 6.5, e = ε33 ε = 1510, = LI XiangYu et al. Sci China Ser G-Phys Mech Astron Aug. 008 vol. 51 no
8 As known from the earlier analysis, σ ξ is independent of r, being a function of only, and its distribution along the thickness is depicted in Figure, which shows that the curve for λ = 1 tends to be parabolic, the one for λ = 0 is a horiontal straight line, while that for λ = 1 decreases with η. The axial electric displacement ( D η ) is a constant as shown in eq. (39), but varies with parameters, as shown in Figure 3. It is seen that D η for λ = 0 is larger than those for λ =± 1. Figure Dimensionless radial stresses of a circular plate subject to uniform electric potentials at η = ±1/. Figure 3 Dimensionless normal electric displacements of a circular plate subject to uniform electric potentials at η = ±1/. Figure 4 shows the distribution curves of the dimensionless deflection W on the middle plane. From Figure 4, we can see that the curve for λ = 0 is a straight line, i.e., W ( ξ ) = 0 ; the one for λ = 1 is concave and W ( ξ ) 0 ; while the one for λ = 1 is convex and W ( ξ ) 0. The distribution of the dimensionless electric potential Φ at the center ξ = 0 along the thickness η is shown in Figure 5, which illustrates that Φ changes in a linear way when λ = 0 and is larger than those corresponding to λ =± 1. Figure 4 Dimensionless normal deflections of a circular plate subject to uniform electric potentials at η = ±1/. Figure 5 Dimensionless electric potentials of a circular plate subject to uniform electric potentials at η = ±1/. LI XiangYu et al. Sci China Ser G-Phys Mech Astron Aug. 008 vol. 51 no
9 5 Conclusions Three-dimensional analytical solutions were derived for the axisymmetric problem of transversely isotropic circular plates made of functionally graded pieoelectric materials. The material constants can vary along the thickness in an arbitrary way and the plate is simply supported or with free edges. The present solutions are independent of the material eigenvalues and can be degenerated into those for homogenous materials. Numerical results show that the material inhomogeneity exerts an important effect on the elastic and electric fields in the plate. Hence, optimum design may be performed to obtain the desired results through the proper choice of material property variation along the thickness. Since no ad hoc hypotheses on the distributions of elastic and electric fields are introduced, the present analytical solutions could provide a useful meaning of checking the validity of various approximate theories and numerical methods. 1 Gandhi M V, Thompson B S. Smart Materials and Structures. London: Chapman & Hall, 199 Yee Y, Nam H J, Lee S H, et al. PZT Actuator micromirror for finite-tracking mechanism of high-density optical data storage. Sens Actuat A, 001, 89: [DOI] 3 Wang S, Li J F, Wakabayashi K, et al. Lost silicon mold process for PZT microstructure. Adv Mater, 1999, 10: Taya M, Almajid A A, Dunn M, et al. Design of bimorphpieo-composite actuators with functionally graded microstructure. Sens Actuat A, 003, 107: 48-60[DOI] 5 Wu C C M, Kahn M, Moy W. Pieoelectric ceramics with functionally gradients, a new application in material design. J Am Ceram Soc, 1999, 79: Ichinose N, Miyamoto M, Takahashi S. Ultrasonic transducers with functionally graded pieoelastic ceramics. J Euro Ceram Soc, 004, 4: [DOI] 7 Zhu X H, Meng Z Y. Operational principle, fabrication and displacement characteristic of a functionally gradient pieoelectric ceramic actuator. Sens Actuat A, 1995, 48: [DOI] 8 Yan W, Chen W Q. Electro-mechanical response of functionally graded beams with imperfectly integrated surface pieoelectric layers. Sci China Ser G-Phys Mech Astron, 006, 49 (5): [DOI] 9 Yu T, Zhong Z. Bending analysis of functionally graded pieoelectric cantilever beam. Sci China Ser G-Phys Mech Astron, 007, 50(1): Bernhard A P F, Chopra I. Trailing edge flag activated by a pieo-induced bending-torsion coupled beam. J Am Helicopter Soc, 1999, 44: Cheng Z Q, Lim C W, Kitipornchai S. Three-dimensional exact solution for inhomogeneous and laminated pieoelectric plates. Int J Solids Struct, 1999, 37: Cheng Z Q, Batra R C. Three-dimensional asymptotic scheme for pieothermoelastic laminates. J Thermal Stresses, 000, 3: [DOI] 13 Cheng Z Q, Lim C W, Kitipornchai S. Three-dimensional asymptotic approach to inhomogeneous and laminated pieoelectric plates. Int J Solids Struct, 000, 37: [DOI] 14 Cheng Z Q, Batra R C. Three-dimensional asymptotic analysis of multi-electroded pieoelectric laminates. AIAA J, 000, 38(): Reddy J N, Cheng Z Q. Three-dimensional solutions of smart functionally graded plates. J Appl Mech, 001, 68: [DOI] 16 Chen W Q, Ding H J. Bending of functionally graded pieoelectric rectangular plates. Acta Mech Solid Sin, 000, 13(4): 114 LI XiangYu et al. Sci China Ser G-Phys Mech Astron Aug. 008 vol. 51 no
10 31-319[DOI] 17 Chen W Q, Ding H J. On free vibration of a functionally graded pieoelectric rectangular plate. Acta Mech, 00, 153: 07-16[DOI] 18 Chen W Q, Ding H J, Liang J. The exact elasto-electric field of a rotating pieoceramic spherical shell with a functionally graded property. Int J Solids Struct, 001, 38: [DOI] 19 Wu X H, Chen C Q, Shen Y P, et al. A high order theory for functionally graded pieoelectric shells. Int J Solids Struct, 00, 39: [DOI] 0 Zhong Z, Shang E T. Three-dimensional exact analysis of a simply supported functionally gradient pieoelectric plate. Int J Solids Struct, 003, 40: [DOI] 1 Chen W Q, Bian Z G, Lü C F, et al. 3D free vibration analysis of a functionally graded pieoelectric hollow cylinder filled with compressible fluid. Int J Solids Struct, 004, 41: [DOI] Pan E, Han F. Green s functions for transversely isotropic pieoelectric functionally graded multilayered half space. Int J Solids Struct, 005, 4: [DOI] 3 Lu P, Lee H P, Lu C. An exact solution for simply supported functionally graded pieoelectric laminates in cylindrical bending. Int J Mech Sci, 005, 47: [DOI] 4 Lu P, Lee H P, Lu C. Exact solutions for simply supported functionally graded pieoelectric laminates by Stroh-like formalism. Compos Struct, 006, 7: [DOI] 5 Ding H J, Liang J. The fundamental solutions for semi-infinite transversely isotropic pieoelectricity and boundary element method. Comput Struct, 1999, 77: [DOI] 6 Ding H J, Chen W Q. Three Dimensional Problems of Pieoelasticity. New York: Nova Science Publishers, 001 LI XiangYu et al. Sci China Ser G-Phys Mech Astron Aug. 008 vol. 51 no
The Rotating Inhomogeneous Elastic Cylinders of. Variable-Thickness and Density
Applied Mathematics & Information Sciences 23 2008, 237 257 An International Journal c 2008 Dixie W Publishing Corporation, U. S. A. The Rotating Inhomogeneous Elastic Cylinders of Variable-Thickness and
More informationBending analysis of a functionally graded piezoelectric cantilever beam
Science in Cina Series G: Pysics Mecanics & Astronomy 7 Science in Cina Press Springer-Verlag Bending analysis of a functionally graded pieoelectric cantilever beam YU Tao & ZHONG Zeng Scool of Aerospace
More information3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1
Math Problem a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 3 6 Solve the initial value problem u ( t) = Au( t) with u (0) =. 3 1 u 1 =, u 1 3 = b- True or false and why 1. if A is
More informationCHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES
CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric
More informationLaminated Composite Plates and Shells
Jianqiao Ye Laminated Composite Plates and Shells 3D Modelling With 62 Figures Springer Table of Contents 1. Introduction to Composite Materials 1 1.1 Introduction 1 1.2 Classification of Composite Materials
More informationA simple plane-strain solution for functionally graded multilayered isotropic cylinders
Structural Engineering and Mechanics, Vol. 24, o. 6 (2006) 000-000 1 A simple plane-strain solution for functionally graded multilayered isotropic cylinders E. Pan Department of Civil Engineering, The
More informationPiezoelectric Control of Multi-functional Composite Shells Subjected to an Electromagnetic Field
Piezoelectric Control of Multi-functional Composite Shells Subjected to an Electromagnetic Field *Sang-Yun Park 1) and Ohseop Song 2) 1), 2) Department of Mechanical Engineering, Chungnam National University,
More informationA Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core
Commun. Theor. Phys. 56 774 778 Vol. 56, No. 4, October 5, A Piezoelectric Screw Dislocation Interacting with an Elliptical Piezoelectric Inhomogeneity Containing a Confocal Elliptical Rigid Core JIANG
More informationSemi-Membrane and Effective Length Theory of Hybrid Anisotropic Materials
International Journal of Composite Materials 2017, 7(3): 103-114 DOI: 10.5923/j.cmaterials.20170703.03 Semi-Membrane and Effective Length Theory of Hybrid Anisotropic Materials S. W. Chung 1,*, G. S. Ju
More informationThe New Boundary Condition Effect on The Free Vibration Analysis of Micro-beams Based on The Modified Couple Stress Theory
International Research Journal of Applied and Basic Sciences 2015 Available online at www.irjabs.com ISSN 2251-838X / Vol, 9 (3): 274-279 Science Explorer Publications The New Boundary Condition Effect
More informationOptimum material gradient composition for the functionally graded piezoelectric beams
MultiCraft International Journal of Engineering, Science and Technology Vol. 5, No. 4, 2013, pp. 80-99 INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY www.ijest-ng.com www.ajol.info/index.php/ijest
More informationSmall-Scale Effect on the Static Deflection of a Clamped Graphene Sheet
Copyright 05 Tech Science Press CMC, vol.8, no., pp.03-7, 05 Small-Scale Effect on the Static Deflection of a Clamped Graphene Sheet G. Q. Xie, J. P. Wang, Q. L. Zhang Abstract: Small-scale effect on the
More informationInhomogeneity Material Effect on Electromechanical Stresses, Displacement and Electric Potential in FGM Piezoelectric Hollow Rotating Disk
Journal of Solid Mechanics Vol. 2, No. 2 (2010) pp. 144-155 Inhomogeneity Material Effect on Electromechanical Stresses, Displacement and Electric Potential in FGM Piezoelectric Hollow Rotating Disk A.
More informationThe Ultimate Load-Carrying Capacity of a Thin-Walled Shuttle Cylinder Structure with Cracks under Eccentric Compressive Force
The Ultimate Load-Carrying Capacity of a Thin-Walled Shuttle Cylinder Structure with Cracks under Eccentric Compressive Force Cai-qin Cao *, Kan Liu, Jun-zhe Dong School of Science, Xi an University of
More informationStress analysis of functionally graded discs under mechanical and thermal loads
Indian Journal of Engineering & Materials Sciences Vol. 8, April 0, pp. -8 Stress analysis of functionally graded discs under mechanical and thermal loads Hasan Çallioğlu, Metin Sayer* & Ersin Demir Department
More informationVIBRATION CONTROL OF RECTANGULAR CROSS-PLY FRP PLATES USING PZT MATERIALS
Journal of Engineering Science and Technology Vol. 12, No. 12 (217) 3398-3411 School of Engineering, Taylor s University VIBRATION CONTROL OF RECTANGULAR CROSS-PLY FRP PLATES USING PZT MATERIALS DILEEP
More informationNUMERICAL MLPG ANALYSIS OF PIEZOELECTRIC SENSOR IN STRUCTURES
DOI: 10.2478/sjce-2014-0009 NUMERICAL MLPG ANALYSIS OF PIEZOELECTRIC SENSOR IN STRUCTURES Peter STAŇÁK 1*, Ján SLÁDEK 1, Vladimír SLÁDEK 1, Slavomír KRAHULEC 1 Abstract The paper deals with a numerical
More informationFree Vibration Analysis of Functionally Graded Material Plates with Various Types of Cutouts using Finite Element Method
International Journal of Current Engineering and Technology E-ISSN 2277 4106, P-ISSN 2347 5161 2018 INPRESSCO, All Rights Reserved Available at http://inpressco.com/category/ijcet Research Article Free
More informationAnalytical Strip Method for Thin Isotropic Cylindrical Shells
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 14, Issue 4 Ver. III (Jul. Aug. 2017), PP 24-38 www.iosrjournals.org Analytical Strip Method for
More informationThree-dimensional thermoelastic deformations of a functionally graded elliptic plate
JCOMB Composites: Part B () 9 6 www.elsevier.com/locate/compositesb Three-dimensional thermoelastic deformations of a functionally graded elliptic plate Z.-Q. Cheng a, R.C. Batra b, * a Department of Modern
More informationNONLINEAR ANALYSIS OF A FUNCTIONALLY GRADED BEAM RESTING ON THE ELASTIC NONLINEAR FOUNDATION
Journal of Theoretical and Applied Mechanics, Sofia, 2014, vol. 44, No. 2, pp. 71 82 NONLINEAR ANALYSIS OF A FUNCTIONALLY GRADED BEAM RESTING ON THE ELASTIC NONLINEAR FOUNDATION M. Arefi Department of
More informationOn the torsion of functionally graded anisotropic linearly elastic bars
IMA Journal of Applied Mathematics (2007) 72, 556 562 doi:10.1093/imamat/hxm027 Advance Access publication on September 25, 2007 edicated with admiration to Robin Knops On the torsion of functionally graded
More informationTHERMOELASTIC ANALYSIS OF THICK-WALLED FINITE-LENGTH CYLINDERS OF FUNCTIONALLY GRADED MATERIALS
Journal of Thermal Stresses, 28: 391 408, 2005 Copyright # Taylor & Francis Inc. ISSN: 0149-5739 print/1521-074x online DOI: 10.1080/01495730590916623 THERMOELASTIC ANALYSIS OF THICK-WALLED FINITE-LENGTH
More informationIntroduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams.
Outline of Continuous Systems. Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams. Vibrations of Flexible Strings. Torsional Vibration of Rods. Bernoulli-Euler Beams.
More informationCHAPTER 4 DESIGN AND ANALYSIS OF CANTILEVER BEAM ELECTROSTATIC ACTUATORS
61 CHAPTER 4 DESIGN AND ANALYSIS OF CANTILEVER BEAM ELECTROSTATIC ACTUATORS 4.1 INTRODUCTION The analysis of cantilever beams of small dimensions taking into the effect of fringing fields is studied and
More informationBending Analysis of a Cantilever Nanobeam With End Forces by Laplace Transform
International Journal of Engineering & Applied Sciences (IJEAS) Vol.9, Issue (Special Issue: Composite Structures) (07) 03- http://.doi.org/0.407/ijeas.34635 Int J Eng Appl Sci 9() (07) 03- Bending Analysis
More informationAEROELASTIC ANALYSIS OF SPHERICAL SHELLS
11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) E. Oñate, J. Oliver
More information(This is a sample cover image for this issue. The actual cover is not yet available at this time.)
(This is a sample cover image for this issue. The actual cover is not yet available at this time. This article appeared in a journal published by Elsevier. The attached copy is furnished to the author
More informationDAMPING OF GENERALIZED THERMO ELASTIC WAVES IN A HOMOGENEOUS ISOTROPIC PLATE
Materials Physics and Mechanics 4 () 64-73 Received: April 9 DAMPING OF GENERALIZED THERMO ELASTIC WAVES IN A HOMOGENEOUS ISOTROPIC PLATE R. Selvamani * P. Ponnusamy Department of Mathematics Karunya University
More informationMechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002
student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity
More informationApplication of piezoelectric actuators to active control of composite spherical caps
Smart Mater. Struct. 8 (1999 18. Printed in the UK PII: S964-176(991661-4 Application of piezoelectric actuators to active control of composite spherical caps Victor Birman, Gareth J Knowles and John J
More informationRadial Growth of a Micro-Void in a Class of. Compressible Hyperelastic Cylinder. Under an Axial Pre-Strain *
dv. Theor. ppl. Mech., Vol. 5, 2012, no. 6, 257-262 Radial Growth of a Micro-Void in a Class of Compressible Hyperelastic Cylinder Under an xial Pre-Strain * Yuxia Song, Datian Niu and Xuegang Yuan College
More informationMechanical Design in Optical Engineering
Torsion Torsion: Torsion refers to the twisting of a structural member that is loaded by couples (torque) that produce rotation about the member s longitudinal axis. In other words, the member is loaded
More informationA parametric study on the elastic-plastic deformation of a centrally heated two-layered composite cylinder with free ends
Arch. Mech., 68, 3, pp. 03 8, Warszawa 06 A parametric study on the elastic-plastic deformation of a centrally heated two-layered composite cylinder with free ends F. YALCIN ), A. OZTURK ), M. GULGEC 3)
More informationCRITERIA FOR SELECTION OF FEM MODELS.
CRITERIA FOR SELECTION OF FEM MODELS. Prof. P. C.Vasani,Applied Mechanics Department, L. D. College of Engineering,Ahmedabad- 380015 Ph.(079) 7486320 [R] E-mail:pcv-im@eth.net 1. Criteria for Convergence.
More informationThickness Optimization of a Piezoelectric Converter for Energy Harvesting
Excerpt from the Proceedings of the COMSOL Conference 29 Milan Thickness Optimization of a Piezoelectric Converter for Energy Harvesting M. Guizzetti* 1, V. Ferrari 1, D. Marioli 1 and T. Zawada 2 1 Dept.
More informationLarge bending deformations of pressurized curved tubes
Arch. Mech., 63, 5 6, pp. 57 56, Warszawa Large bending deformations of pressurized curved tubes A. M. KOLESNIKOV Theory of Elasticity Department Southern Federal University Rostov-on-Don, 344, Russian
More informationMoving screw dislocations in piezoelectric bimaterials
phys stat sol (b) 38 No 1 10 16 (003) / DOI 10100/pssb00301805 Moving screw dislocations in piezoelectric bimaterials Xiang-Fa Wu *1 Yuris A Dzenis 1 and Wen-Sheng Zou 1 Department of Engineering Mechanics
More informationMaterial tailoring and moduli homogenization for finite twisting deformations of functionally graded Mooney-Rivlin hollow cylinders
Acta Mech 224, 811 818 (2013) DOI 10.1007/s00707-012-0784-z J. R. Dryden R. C. Batra Material tailoring and moduli homogenization for finite twisting deformations of functionally graded Mooney-Rivlin hollow
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 informationTable of Contents. Preface... 13
Table of Contents Preface... 13 Chapter 1. Vibrations of Continuous Elastic Solid Media... 17 1.1. Objective of the chapter... 17 1.2. Equations of motion and boundary conditions of continuous media...
More informationRadial Breathing Mode Frequency of Multi-Walled Carbon Nanotube Via Multiple-Elastic Thin Shell Theory
Int. J. anosci. anotechnol. Vol. 7 o. 3 Sep. 011 pp. 137-14 adial Breathing Mode Frequency of Multi-Walled Carbon anotube Via Multiple-Elastic Thin Shell Theory S. Basir Jafari 1. Malekfar 1* and S. E.
More informationAPPLICATION OF ISOTENSOID-BASED CROSS SECTIONS TO FILAMENT-WOUND TOROIDAL PRESSURE VESSELS
APPLICATION OF ISOTENSOID-BASED CROSS SECTIONS TO FILAMENT-WOUND TOROIDAL PRESSURE VESSELS L. Zu, S. Koussios and A. Beukers Design and Production of Composite Structures, Faculty of Aerospace Engineering
More informationModeling of Variable Lamé s Modulii for a FGM Generalized Thermoelastic Half Space
75 Modeling of Variable Lamé s Modulii for a FGM Generalized Thermoelastic Half Space Abstract In this work we consider a problem in the contet of the generalized theory of thermoelasticity for a half
More information903. Free vibration studies of functionally graded magneto-electro-elastic plates/shells by using solid-shell elements
903 Free vibration studies of functionally graded magneto-electro-elastic plates/shells by using solid-shell elements Zheng Shijie Fen Yan 2 Wang Hongtao 3 2 State Key Laboratory of Mechanics and Control
More informationSTRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS
1 UNIT I STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define: Stress When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The
More informationMechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection
Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts
More informationSCIENCE CHINA Physics, Mechanics & Astronomy. Effect of mechanical force field on the electromechanical stability of dielectric elastomers
SCIC CHIA Physics Mechanics & Astronomy Article January 0 Vol.55 o.: 94 0 doi: 0.007/s4-0-457-0 ffect of mechanical force field on the electromechanical stability of dielectric elastomers ZHAG Zhen LIU
More informationNumerical study on scanning radiation acoustic field in formations generated from a borehole
Science in China Ser. G Physics, Mechanics & Astronomy 5 Vol.48 No. 47 56 47 Numerical study on scanning radiation acoustic field in formations generated from a borehole CHE Xiaohua 1, ZHANG Hailan 1,
More informationVIBRATION CHARACTERISTICS OF EMBEDDED DOUBLE WALLED CARBON NANOTUBES SUBJECTED TO AN AXIAL PRESSURE
18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS VIBRATION CHARACTERISTICS OF EMBEDDED DOUBLE WALLED CARBON NANOTUBES SUBJECTED TO AN AXIAL PRESSURE X. W. Lei 1, T. Natsuki 2, J. X. Shi 1, Q. Q. Ni
More informationTHE SCATTERING FROM AN ELLIPTIC CYLINDER IRRADIATED BY AN ELECTROMAGNETIC WAVE WITH ARBITRARY DIRECTION AND POLARIZATION
Progress In Electromagnetics Research Letters, Vol. 5, 137 149, 2008 THE SCATTERING FROM AN ELLIPTIC CYLINDER IRRADIATED BY AN ELECTROMAGNETIC WAVE WITH ARBITRARY DIRECTION AND POLARIZATION Y.-L. Li, M.-J.
More informationReceived 23 January 2016; received in revised form 20 May 2016; accepted 21 June 2016 DOI
2084. A unified formulation for vibration analysis of open cylindrical shells coupled with annular sector plates under general boundary and coupling conditions Huimin Liu 1, Fanming Liu 2, Haoran Bai 3,
More informationApplications of Pure Membrane, Pseudo Membrane, and Semi Membrane Shell Theories of Hybrid Anisotropic Materials
International Journal of Composite Materials 2018, 8(4): 73-90 DOI: 10.5923/j.cmaterials.20180804.01 Applications of Pure Membrane, Pseudo Membrane, and Semi Membrane Shell Theories of Hybrid Anisotropic
More informationChapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationRecent Advances on Mechanics, Materials, Mechanical Engineering and Chemical Engineering
Size-dependent pull-in analysis of electrically actuated micro-plates based on the modified couple stress theory Arman Mohsenzadeh,a, Masoud Tahani,b*, Amir Reza Askari,c,, Department of Mechanical Engineering,
More informationINVESTIGATING THERMAL EFFECTS IN NONLINEAR BUCKLING ANALYSIS OF MICRO BEAMS USING MODIFIED STRAIN GRADIENT THEORY *
IJST, Transactions of Mechanical Engineering, Vol. 38, No. M2, pp 33-32 Printed in The Islamic Republic of Iran, 214 Shiraz University INVESTIGATING THERMAL EFFECTS IN NONLINEAR BUCKLING ANALYSIS OF MICRO
More informationThermal deformation compensation of a composite beam using piezoelectric actuators
INSTITUTE OF PHYSICS PUBLISHING Smart Mater. Struct. 13 (24) 3 37 SMART MATERIALS AND STRUCTURES PII: S964-1726(4)7973-8 Thermal deformation compensation of a composite beam using piezoelectric actuators
More informationBuckling Analysis of Ring-Stiffened Laminated Composite Cylindrical Shells by Fourier-Expansion Based Differential Quadrature Method
Applied Mechanics and Materials Vol. 225 (2012) pp 207-212 (2012) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/amm.225.207 Buckling Analysis of Ring-Stiffened Laminated Composite
More informationISSN: X (p); (e)
TORSIONA SURFACE WAVE IN SEF-REINFORCED AYER SANDWICHED BETWEEN TWO VISCO-EASIC HAF-SPACES UNDER THE INITIA STRESS Nidhi Dewangan, Sanjeev A. Sahu and Soniya Chaudhary S.G.G. Govt P.G. College, Kurud,
More informationRigid Flexible Contact Analysis of an Inflated Membrane Balloon with Various Contact Conditions
roceedings Rigid Flexible Contact Analysis of an Inflated Membrane Balloon with Various Contact Conditions MengXiong Liu and XiDe Li * Department of Engineering Mechanics, Tghua University, Beijing 100084,
More informationChapter 3. Load and Stress Analysis. Lecture Slides
Lecture Slides Chapter 3 Load and Stress Analysis 2015 by McGraw Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner.
More informationCellular solid structures with unbounded thermal expansion. Roderic Lakes. Journal of Materials Science Letters, 15, (1996).
1 Cellular solid structures with unbounded thermal expansion Roderic Lakes Journal of Materials Science Letters, 15, 475-477 (1996). Abstract Material microstructures are presented which can exhibit coefficients
More informationUNIT-I Introduction & Plane Stress and Plane Strain Analysis
SIDDHARTH INSTITUTE OF ENGINEERING & TECHNOLOGY:: PUTTUR (AUTONOMOUS) Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Advanced Solid Mechanics (18CE1002) Year
More informationMechanical Design in Optical Engineering
OPTI Buckling Buckling and Stability: As we learned in the previous lectures, structures may fail in a variety of ways, depending on the materials, load and support conditions. We had two primary concerns:
More informationEffect of elastic foundations on vibrations of thickwalled hollow poroelastic cylinders
Journal of Physics: Conference Series PAPER OPEN ACCESS Effect of elastic foundations on vibrations of thickwalled hollow poroelastic cylinders To cite this article: Srisailam Aleti and Manjula Ramagiri
More informationDetails of Semi-Membrane Shell Theory of Hybrid Anisotropic Materials
International Journal of Composite Materials 2018, 8(3): 47-56 DOI: 10.5923/j.cmaterials.20180803.01 Details of Semi-Membrane Shell Theory of Hybrid Anisotropic Materials S. W. Chung 1,*, G. S. Ju 2 1
More informationWave propagation in a magneto-electroelastic
Science in China Series G: Physics Mechanics & Astronomy 008 SCIENCE IN CHINA PRESS Springer-Verlag www.scichina.com phys.scichina.com www.springerlink.com Wave propagation in a magneto-electroelastic
More informationFINITE ELEMENT MODELLING OF COMPOSITES USING PIEZOELECTRIC MATERIAL
International Journal of Engineering Research and General Science Volume 3, Issue 4, July-August, 2015 FINITE ELEMENT MODELLING OF COMPOSITES USING PIEZOELECTRIC MATERIAL K.TEJASWINI, tejaswinikota11@gmail.com.,
More informationANALYSIS AND NUMERICAL MODELLING OF CERAMIC PIEZOELECTRIC BEAM BEHAVIOR UNDER THE EFFECT OF EXTERNAL SOLICITATIONS
Third International Conference on Energy, Materials, Applied Energetics and Pollution. ICEMAEP016, October 30-31, 016, Constantine,Algeria. ANALYSIS AND NUMERICAL MODELLING OF CERAMIC PIEZOELECTRIC BEAM
More informationMechanics of Materials and Structures
Journal of Mechanics of Materials and Structures ON TORSIONAL VIBRATIONS OF INFINITE HOLLOW POROELASTIC CYLINDERS M. Tajuddin and S. Ahmed Shah Volume 2, Nº 1 January 27 mathematical sciences publishers
More informationTorsional Buckling of Double-Walled Carbon Nanotubes
Torsional Buckling of Double-Walled Carbon Nanotubes S. H. Soong Engineering Science Programme, National University of Singapore Kent Ridge, Singapore 119260 ABSTRACT This paper is concerned with the torsional
More informationJournal of Theoretical and Applied Mechanics, Sofia, 2015, vol. 45, No. 1, pp
Journal of Theoretical and Applied Mechanics, Sofia, 2015, vol. 45, No. 1, pp. 69 86 SOLID MECHANICS DOI: 10.1515/jtam-2015-0005 PROPAGATION OF SURFACE WAVES IN A HOMOGENEOUS LAYER OF FINITE THICKNESS
More information7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment
7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment à It is more difficult to obtain an exact solution to this problem since the presence of the shear force means that
More informationPresented By: EAS 6939 Aerospace Structural Composites
A Beam Theory for Laminated Composites and Application to Torsion Problems Dr. BhavaniV. Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1 Introduction Composite beams have
More informationNumerical and Analytical Approach of Thermo-Mechanical Stresses in FGM Beams
Numerical and Analytical Approach of Thermo-Mechanical Stresses in FGM Beams Fatemeh Farhatnia, Gholam-Ali Sharifi and Saeid Rasouli Abstract In this paper, thermo-mechanical stress distribution has been
More informationActive control for a flexible beam with nonlinear hysteresis and time delay
THEORETICAL & APPLIED MECHANICS LETTERS 3, 635 (23) Active control for a flexible beam with nonlinear hysteresis and time delay Kun Liu, Longxiang Chen,, 2, a) and Guoping Cai ) Department of Engineering
More informationDesign and Test of a PZT Wind Generator Excited by Rotary Magnet
5th International Conference on Advanced Design and Manufacturing Engineering (ICADME 05) Design and Test of a PZT Wind Generator Excited by Rotary Magnet M.J. YAN, S.Y. WANG, C.T. FAN, W.J. WU & J.W.
More informationStress Analysis of Elastic Roof with Boundary Element Formulations
Copyright 211 Tech Science Press CMC, vol.26, no.3, pp.187-2, 211 Stress Analysis of Elastic Roof with Boundary Element Formulations Dan Ma 1,2 and Xianbiao Mao 1 Abstract: Roof is one of the most important
More informationBENDING VIBRATIONS OF ROTATING NON-UNIFORM COMPOSITE TIMOSHENKO BEAMS WITH AN ELASTICALLY RESTRAINED ROOT
BENDING VIBRATIONS OF ROTATING NON-UNIFORM COMPOSITE TIMOSHENKO BEAMS WITH AN EASTICAY RESTRAINED ROOT Sen Yung ee and Jin Tang Yang Department of Mechanical Engineering, National Cheng Kung University,
More informationBending Analysis of Symmetrically Laminated Plates
Leonardo Journal of Sciences ISSN 1583-0233 Issue 16, January-June 2010 p. 105-116 Bending Analysis of Symmetrically Laminated Plates Bouazza MOKHTAR 1, Hammadi FODIL 2 and Khadir MOSTAPHA 2 1 Department
More informationDESIGN, FABRICATION AND ELECTROMECHANICAL CHARACTERISTICS OF A MEMS BASED MICROMIRROR
XIX IMEKO World Congress Fundamental and Applied Metrology September 6 11, 2009, Lisbon, Portugal DESIGN, FABRICATION AND ELECTROMECHANICAL CHARACTERISTICS OF A MEMS BASED MICROMIRROR Talari Rambabu 1,
More informationCHAPTER -6- BENDING Part -1-
Ishik University / Sulaimani Civil Engineering Department Mechanics of Materials CE 211 CHAPTER -6- BENDING Part -1-1 CHAPTER -6- Bending Outlines of this chapter: 6.1. Chapter Objectives 6.2. Shear and
More informationVibration of Thin Beams by PIM and RPIM methods. *B. Kanber¹, and O. M. Tufik 1
APCOM & ISCM -4 th December, 23, Singapore Vibration of Thin Beams by PIM and RPIM methods *B. Kanber¹, and O. M. Tufik Mechanical Engineering Department, University of Gaziantep, Turkey. *Corresponding
More informationSimulation of Piezoelectric Induced Lamb Waves in Plates
Simulation of Piezoelectric Induced Lamb Waves in Plates C. WILLBERG, J. M. VIVAR-PEREZ, Z. AHMAD and U. GABBERT ABSTRACT The use of Lamb waves for damage detection and non-destructive evaluation have
More informationSponsored document from International Journal of Solids and Structures
Sponsored document from International Journal of Solids and Structures Asymptotic splitting in the three-dimensional problem of elasticity for non-homogeneous piezoelectric plates Yury Vetyukov a,b,, Alexey
More informationA HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS
A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A. Kroker, W. Becker TU Darmstadt, Department of Mechanical Engineering, Chair of Structural Mechanics Hochschulstr. 1, D-64289 Darmstadt, Germany kroker@mechanik.tu-darmstadt.de,
More informationNonlinear Free Vibration of Nanobeams Subjected to Magnetic Field Based on Nonlocal Elasticity Theory
Nonlinear Free Vibration of Nanobeams Subjected to Magnetic Field Based on Nonlocal Elasticity Theory Tai-Ping Chang 1 and Quey-Jen Yeh 1 Department of Construction Engineering, National Kaohsiung First
More informationThe effect of rigidity on torsional vibrations in a two layered poroelastic cylinder
Int. J. Adv. Appl. Math. and Mech. 3(1) (2015) 116 121 (ISSN: 2347-2529) Journal homepage: www.ijaamm.com International Journal of Advances in Applied Mathematics and Mechanics The effect of rigidity on
More informationInterfacial effects in electromagnetic coupling within piezoelectric phononic crystals
Acta Mech Sin (29) 25:95 99 DOI 1.17/s149-8-21-y RESEARCH PAPER Interfacial effects in electromagnetic coupling within pieoelectric phononic crystals F. J. Sabina A. B. Movchan Received: 14 July 28 / Accepted:
More informationConsider an elastic spring as shown in the Fig.2.4. When the spring is slowly
.3 Strain Energy Consider an elastic spring as shown in the Fig..4. When the spring is slowly pulled, it deflects by a small amount u 1. When the load is removed from the spring, it goes back to the original
More informationAvailable online at ScienceDirect. Procedia Engineering 144 (2016 )
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 44 (06 ) 46 467 th International Conference on Vibration Problems, ICOVP 05 Propagation of Love waves in composite layered structures
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 informationVibro-acoustic response of FGM plates considering the thermal effects Tieliang Yang1, a, Qibai Huang1, *
3rd International Conference on Materials Engineering, Manufacturing Technology and Control (ICMEMTC 2016) Vibro-acoustic response of FGM plates considering the thermal effects Tieliang Yang1, a, Qibai
More informationTuesday, February 11, Chapter 3. Load and Stress Analysis. Dr. Mohammad Suliman Abuhaiba, PE
1 Chapter 3 Load and Stress Analysis 2 Chapter Outline Equilibrium & Free-Body Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for
More informationA study of forming pressure in the tube-hydroforming process
Journal of Materials Processing Technology 192 19 (2007) 404 409 A study of forming pressure in the tube-hydroforming process Fuh-Kuo Chen, Shao-Jun Wang, Ray-Hau Lin Department of Mechanical Engineering,
More informationGeometry-dependent MITC method for a 2-node iso-beam element
Structural Engineering and Mechanics, Vol. 9, No. (8) 3-3 Geometry-dependent MITC method for a -node iso-beam element Phill-Seung Lee Samsung Heavy Industries, Seocho, Seoul 37-857, Korea Hyu-Chun Noh
More informationPractice Final Examination. Please initial the statement below to show that you have read it
EN175: Advanced Mechanics of Solids Practice Final Examination School of Engineering Brown University NAME: General Instructions No collaboration of any kind is permitted on this examination. You may use
More informationA three-dimensional peano series solution for the vibration of functionally graded piezoelectric laminates in cylindrical bending
Scientia Iranica A (2016) 23(3), 788{801 Sharif University of Technology Scientia Iranica Transactions A: Civil Engineering www.scientiairanica.com A three-dimensional peano series solution for the vibration
More informationINFLUENCE OF TEMPERATURE ON BEHAVIOR OF THE INTERFACIAL CRACK BETWEEN THE TWO LAYERS
Djoković, J. M., et.al.: Influence of Temperature on Behavior of the Interfacial THERMAL SCIENCE: Year 010, Vol. 14, Suppl., pp. S59-S68 S59 INFLUENCE OF TEMPERATURE ON BEHAVIOR OF THE INTERFACIAL CRACK
More informationFree transverse vibrations of cracked nanobeams using a nonlocal elasticity model
Free transverse vibrations of cracked nanobeams using a nonlocal elasticity model J. Loya, J. López-Puente, R. Zaera, and J. Fernández-Sáez a Department of Continuum Mechanics and Structural Analysis,
More information