MEG6007: Advanced Dynamics -Principles and Computational Methods (Fall, 2017) Lecture DOF Modeling of Shock Absorbers. This lecture covers:
|
|
- Karen James
- 6 years ago
- Views:
Transcription
1 MEG6007: Advanced Dynamics -Principles and Computational Methods (Fall, 207) Lecture 4. 2-DOF Modeling of Shock Absorbers This lecture covers: Revisit 2-DOF Spring-Mass System Understand the den Hartog Invariant points as a design application Learn a particular optimization for minimizing vibrations There is a plenty of room for 2-DOF system to learn and apply!
2 x x 2 m 2 M f2 f C 2 k 2 /2 K /2 Two DOF Spring-Mass-Damper Suspension Model Fig.. 2-DOF Shock Isolation Model 4. Invariant Points of the Den Hartog- Ormondroyd Model Consider a Two-DOF system as shown Figure. The governing equations for the system is given by M ẍ + K x + k 2 (x x 2 ) + c 2 (ẋ ẋ 2 ) = f (t) m 2 ẍ 2 + k 2 (x 2 x ) + c 2 (ẋ 2 ẋ ) = f 2 (t) (4.) Assume that the excitation acts directly to M in the form f (t) = F e jωt, f 2 (t) = 0 (4.2) The solution of (4.) assumes x (t) = X e jωt, x 2 (t) = X 2 e jωt (4.3) Substituting these into (4.) yields the coupled equations in the frequency domain as 2
3 ( M ω 2 + K + k 2 + icω)x (k 2 + jcω)x 2 = F (k 2 + jcω)x + ( m 2 ω 2 + k 2 + jcω)x 2 = 0 (4.4) X obtained from the above equation reads: X (ω) F = ( m 2 ω 2 + k 2 + jcω) [( M ω 2 + K )( m 2 ω 2 + k 2 ) m 2 ω 2 k 2 ] + jωc[k (M + m 2 )ω 2 ] (4.5) Let us parameterize the model as Ω = K /M, ω 2 = k 2 /m 2, c = 2ζm 2 Ω, µ = m 2 /M, s = ω/ω, = F /K, f = ω 2 /Ω, c c = 2m 2 Ω (4.6) The ratio of X (ω) to is the amplification factor from the static to the dynamic response, which can be expressed as X (ω) = [ (2 c c c s) 2 + (s 2 f 2 ) 2 (2 c c c s) 2 (s 2 + µs 2 ) 2 + [µf 2 s 2 (s 2 )(s 2 f 2 )] 2 ] 2 (4.7) Figure 2 plots { X (ω) } vs. the driving (or exciting) frequency, ω, for various damping coefficients (ζ), i.e., by varying ζ while keeping other parameters constants. Note that there are two points, marked by red dots in the figures, the curves pass through for all damping ratios. We will call these two points as den Hartog s invariant points and will exploit its properties in two ways: one is to minimize the maximum amplitude resulting in good shock absorbers; and, the other is to maximize its peak amplitude so that the resulting resonators possesses a minimum loss or high-q performance. 4.2 Shock Absorbers A good shock absorber should have the following characteristics: 3
4 Frequency Response Functions for Different Damping Ratios of a 2-DOF Suspension Model 0 Invariant points Amplitude Frequency (Hz) Fig. 2. Frequency Response Function at Mass (a) The peak amplitude should be insensitive over a wide range of excitation frequencies; (b) The cost for implementing damping should be affordable; (c) The auxiliary mass (m 2 ) should be as light as possible; (d) The response time duration to reach its steady state should be short. We now proceeds with the task of designing a good shock absorber Determination of Undamped Natural Frequencies The natural frequencies are determined by setting c = 0 from the denominator of (4.7): 4
5 [ µf 2 s 2 (s 2 )(s 2 f 2 ) ] = 0 s 4 [ + ( + µ)f 2 ]s 2 + f 2 = 0 (4.8) The two distinct roots of this equation will be designated as s 2 n and s 2 2n Determination of Invariant Points Since the two invariant points would play a key role, it is necessary to find the two coordinates. Of several approaches, we utilize the fact that they are independent of system damping, c. To this end, we rearrange the frequency response function or the magnification factor (4.7) as X (ω) = H(s, c, f, µ) = [ (2 c c c s) 2 A + B (2 c c c s) 2 C + D ] 2, s = ω/ω A = B = (s 2 f 2 ) 2 C = (s 2 + µs 2 ) 2 D = [µf 2 s 2 (s 2 )(s 2 f 2 )] 2 (4.9) The damping-independency of the two invariant points implies that at the invariant points the magnification factor satisfies: A B = C D AD = BC (4.0) for which the amplification factor becomes: X (ω) = H(s, c, f, µ) = ( A C ) 2 (4.) The equation for determining the invariant points yields two 5
6 equations: (s 2 f 2 ) = (s 2 + µs 2 ) [µf 2 s 2 (s 2 )(s 2 f 2 )] (s 2 f 2 ) = (s 2 + µs 2 ) [µf 2 s 2 (s 2 )(s 2 f 2 )] (4.2) The first of the above relation yields the trivial solution, viz., s = ω/ω = 0, (4.3) a static case which is not of interest for the present discussion. The second of (4.2) can be rearranged as (2 + µ)s 4 2( + f 2 + µf 2 )s 2 + 2f 2 = 0 (4.4) The two invariant points, s and s 2 can be shown to satisfy s 2 < + µ < s2 2 (4.5) and the corresponding amplification factors are given by X (ω) = ( + µ)s 2 (,2) (4.6) Determination of Amplification Factor at the Invariant Points The foregoing analysis now supplies the coordinates of the two invariant points as P = (x, y ) = (s, ( + µ)s 2 ), Q = (x 2, y 2 ) = (s 2, (4.7) In order to see succinctly the magnification factor, we arrange as ( + µ)s 2 2 ) µ 2 + µ z2 2 ( + µ)2 f 2 (2 + µ) z = 0, z = s 2 ( + µ) (4.8) 6
7 so that the product of the two roots of the above equation, (z z 2 ), is given by z z 2 = 2 + µ µ = + 2 µ (4.9) which is independent of the frequency ratio f = ω 2 /Ω. It should be noted that for a shock absorber the magnification factor should remain small for a wide range of frequencies, which can be realized if we set the amplification factors to attain their maximum at the two invariant points and at the same time their peaks to be the same. The latter condition can be realized if the coefficient associated with z-terms in (4.8) vanishes: ( + µ) 2 f 2 = 0 f = ω 2 Ω = + µ, µ = m 2/M (4.20) The amplification factor, (X (ω)/ ), for this particular choice at the two invariant points becomes X (ω) = ( + µ)s 2 (,2) = + 2 µ (4.2) Determination of Absorber Damping In the previous section, we imposed the condition on the amplification factor at the two invariant points to be the same. However, it is possible that the amplification factor may be larger at other exciting frequencies. Of several possible choices, we impose that the maximum amplification factors for the frequency ranges of interest would not exceed that at the invariant points. This can be carried out as follows. First, we differentiate (4.9) with respect to s = ω/ω set the resulting expression to zero: ( s ) [X (ω) ] = 0 (4.22) 7
8 for the two invariant points obtained from (4.2.3). For s = s : ζ 2 = ( c c c ) 2 = µ 3 ( µ µ+2 ) 2 8( + µ) 3 For s = s 2 : ζ 2 = ( c c c ) 2 = µ 3 + ( µ µ+2 ) 2 8( + µ) 3 (4.23) In practice, we must have one damping value for all the frequency range. To this end, we take the average value to be: ζ = 3µ 8( + µ) 3 (4.24) Applications First, in order to utilize Matlab capability, we express (4.5) in its transfer function form: X (s) F = (m 2 s 2 + k 2 + cs) [(M s 2 + K )(m 2 s 2 + k 2 ) + m 2 s 2 k 2 ] + sc[k + (M + m 2 )s 2 ] (4.25) where s is now the Laplace Transform variable. The preceding equation can be arranged to read: X (s) = Ω 2 (a 0 s 2 + a s + a 2 ) (b 0 s 4 + b s 3 + b 2 s 2 + b 3 s + b 4 ) a 0 =, a = 2ζΩ, a 2 = ω 2 2 b 0 =, b = 2( + µ)ζω, b 2 = Ω 2 + ( + µ)ω 2 2, b 3 = 2ζΩ 3 (4.26) The amplification factor ( X (s) ) vs. the driving frequency (ω) is illustrated in Fig. 3, with (Ω = 0(Hz), ω 2 = 9.5(Hz), µ = 0.0). Observe the two invariant points at which the amplification factors are different, namely, at s and s 2 points determined by (4.2.3) and its magnitudes given by (4.7). When the amplification factor is optimized to have its peak at the invariant points by selecting the frequency ratio according to 8
9 Proof of two invariant points for den Hartog oscillator Q Amplitude Ratio (X(ω)/xst) 0 Ω =0, ω 2 = 9.5, µ =0.0 Invariant points P 0 0 s s 2 Frequency ( ω ) (Hz) 0 Fig. 3. Invariant Points of a Den Hartog Oscillator Optimized Amplitude for den Hartog oscillator ζ = Amplitude Ratio (X(ω)/xst) 0 ζ = Ω =0, ω 2 =9.5, µ =0.0 ζ = opt 0 0 Frequency ( ω ) (Hz) 0 Fig. 4. Den Hartog suspension model optimized for a wider range of frequencies 9
10 Optimized Amplitude for den Hartog oscillator Amplitude Ratio (X(ω)/xst) 0 Ω =0, ω 2 =9.5, µ = Frequency ( ω ) (Hz) 0 Fig. 5. Den Hartog suspension model optimized for a wider range of frequencies (4.20) and the damping ratio according to (4.24) (ζ = ), its amplification attains its maximum at the invariant points. This is illustrated along with two non-optimal damping coefficients in Fig. 4. Observe that the optimum amplification factor at the invariant points are about 3.5, which may not be acceptable. Figure 5 illustrates the reduction of the peak amplification factor by about half by increasing the small mass from m 2 = 0.0M to five times (m 2 = 0.05M ). In practice, a suspension system is designed to operate far smaller then the invariant points or sufficiently larger then the invariant point frequencies. Under this scenario the infrequent disturbances close to the invariant points can still be bounded. The two-dof suspension model that we have been studying so far is applicable to machinery shock isolation design. For vehicles subject to road roughness conditions, a modified model is more appropriate as shown in Fig. 6. An analysis of this model for achieving an optimum shock isolation is left for an exercise. 0
11 Two-DOF Vehicle Shock Isolation Model m 2 x C x 2 M K /2 K 2 Ground input: x (t) g Fig. 6. A Two-DOF Vehicle Suspension Model
Modeling of Resonators
. 23 Modeling of Resonators 23 1 Chapter 23: MODELING OF RESONATORS 23 2 23.1 A GENERIC RESONATOR A second example where simplified discrete modeling has been found valuable is in the assessment of the
More informationIn this lecture you will learn the following
Module 9 : Forced Vibration with Harmonic Excitation; Undamped Systems and resonance; Viscously Damped Systems; Frequency Response Characteristics and Phase Lag; Systems with Base Excitation; Transmissibility
More informationChapter 5 Design. D. J. Inman 1/51 Mechanical Engineering at Virginia Tech
Chapter 5 Design Acceptable vibration levels (ISO) Vibration isolation Vibration absorbers Effects of damping in absorbers Optimization Viscoelastic damping treatments Critical Speeds Design for vibration
More informationChapter 23: Principles of Passive Vibration Control: Design of absorber
Chapter 23: Principles of Passive Vibration Control: Design of absorber INTRODUCTION The term 'vibration absorber' is used for passive devices attached to the vibrating structure. Such devices are made
More informationSecond Order Systems
Second Order Systems independent energy storage elements => Resonance: inertance & capacitance trade energy, kinetic to potential Example: Automobile Suspension x z vertical motions suspension spring shock
More informationLecture 9: Harmonic Loads (Con t)
Lecture 9: Harmonic Loads (Con t) Reading materials: Sections 3.4, 3.5, 3.6 and 3.7 1. Resonance The dynamic load magnification factor (DLF) The peak dynamic magnification occurs near r=1 for small damping
More informationTuning TMDs to Fix Floors in MDOF Shear Buildings
Tuning TMDs to Fix Floors in MDOF Shear Buildings This is a paper I wrote in my first year of graduate school at Duke University. It applied the TMD tuning methodology I developed in my undergraduate research
More informationModule 4: Dynamic Vibration Absorbers and Vibration Isolator Lecture 19: Active DVA. The Lecture Contains: Development of an Active DVA
The Lecture Contains: Development of an Active DVA Proof Mass Actutor Application of Active DVA file:///d /chitra/vibration_upload/lecture19/19_1.htm[6/25/2012 12:35:51 PM] In this section, we will consider
More informatione jωt = cos(ωt) + jsin(ωt),
This chapter introduces you to the most useful mechanical oscillator model, a mass-spring system with a single degree of freedom. Basic understanding of this system is the gateway to the understanding
More informationChapter a. Spring constant, k : The change in the force per unit length change of the spring. b. Coefficient of subgrade reaction, k:
Principles of Soil Dynamics 3rd Edition Das SOLUTIONS MANUAL Full clear download (no formatting errors) at: https://testbankreal.com/download/principles-soil-dynamics-3rd-editiondas-solutions-manual/ Chapter
More informationModeling and Experimentation: Mass-Spring-Damper System Dynamics
Modeling and Experimentation: Mass-Spring-Damper System Dynamics Prof. R.G. Longoria Department of Mechanical Engineering The University of Texas at Austin July 20, 2014 Overview 1 This lab is meant to
More information2.72 Elements of Mechanical Design
MIT OpenCourseWare http://ocw.mit.edu 2.72 Elements of Mechanical Design Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 2.72 Elements of
More information7.2 Controller tuning from specified characteristic polynomial
192 Finn Haugen: PID Control 7.2 Controller tuning from specified characteristic polynomial 7.2.1 Introduction The subsequent sections explain controller tuning based on specifications of the characteristic
More informationLECTURE 12. STEADY-STATE RESPONSE DUE TO ROTATING IMBALANCE
LECTURE 12. STEADY-STATE RESPONSE DUE TO ROTATING IMBALANCE Figure 3.18 (a) Imbalanced motor with mass supported by a housing mass m, (b) Freebody diagram for, The product is called the imbalance vector.
More informationLaboratory handout 5 Mode shapes and resonance
laboratory handouts, me 34 82 Laboratory handout 5 Mode shapes and resonance In this handout, material and assignments marked as optional can be skipped when preparing for the lab, but may provide a useful
More informationChapter 8: Frequency Domain Analysis
Chapter 8: Frequency Domain Analysis Samantha Ramirez Preview Questions 1. What is the steady-state response of a linear system excited by a cyclic or oscillatory input? 2. How does one characterize the
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 informationThe Effect of Mass Ratio and Air Damper Characteristics on the Resonant Response of an Air Damped Dynamic Vibration Absorber
Modern Mechanical Engineering, 0,, 93-03 doi:0.436/mme.0.0 Published Online November 0 (http://www.scirp.org/journal/mme) The Effect of Mass Ratio and Characteristics on the Resonant Response of an Air
More information1-DOF Forced Harmonic Vibration. MCE371: Vibrations. Prof. Richter. Department of Mechanical Engineering. Handout 8 Fall 2011
MCE371: Vibrations Prof. Richter Department of Mechanical Engineering Handout 8 Fall 2011 Harmonic Forcing Functions Transient vs. Steady Vibration Follow Palm, Sect. 4.1, 4.9 and 4.10 Harmonic forcing
More informationEngineering Structures
Engineering Structures 31 (2009) 715 728 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct Particle swarm optimization of tuned mass dampers
More informationLaboratory notes. Torsional Vibration Absorber
Titurus, Marsico & Wagg Torsional Vibration Absorber UoB/1-11, v1. Laboratory notes Torsional Vibration Absorber Contents 1 Objectives... Apparatus... 3 Theory... 3 3.1 Background information... 3 3. Undamped
More informationMinimax Optimization Of Dynamic Pendulum Absorbers For A Damped Primary System
Minima Optimization Of Dynamic Pendulum Absorbers For A Damped Primary System Mohammed A. Abdel-Hafiz Galal A. Hassaan Abstract In this paper a minima optimization procedure for dynamic vibration pendulum
More informationThe Phasor Analysis Method For Harmonically Forced Linear Systems
The Phasor Analysis Method For Harmonically Forced Linear Systems Daniel S. Stutts, Ph.D. April 4, 1999 Revised: 10-15-010, 9-1-011 1 Introduction One of the most common tasks in vibration analysis is
More information18.12 FORCED-DAMPED VIBRATIONS
8. ORCED-DAMPED VIBRATIONS Vibrations A mass m is attached to a helical spring and is suspended from a fixed support as before. Damping is also provided in the system ith a dashpot (ig. 8.). Before the
More informationDamped Oscillators (revisited)
Damped Oscillators (revisited) We saw that damped oscillators can be modeled using a recursive filter with two coefficients and no feedforward components: Y(k) = - a(1)*y(k-1) - a(2)*y(k-2) We derived
More information6.003 Homework #6 Solutions
6.3 Homework #6 Solutions Problems. Maximum gain For each of the following systems, find the frequency ω m for which the magnitude of the gain is greatest. a. + s + s ω m = w This system has poles at s
More informationA Guide to linear dynamic analysis with Damping
A Guide to linear dynamic analysis with Damping This guide starts from the applications of linear dynamic response and its role in FEA simulation. Fundamental concepts and principles will be introduced
More informationOutline of parts 1 and 2
to Harmonic Loading http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano March, 6 Outline of parts and of an Oscillator
More informationResonant Inerter Based Absorbers for a Selected Global Mode
Downloaded from orbit.dtu.dk on: Jun 3, 208 Resonant Inerter Based Absorbers for a Selected Global Mode Krenk, Steen Published in: Proceedings of the 6th European Conference on Structural Control Publication
More informationCar Dynamics using Quarter Model and Passive Suspension; Part V: Frequency Response Considering Driver-seat
357 Car Dynamics using Quarter Model and Passive Suspension; Part V: Frequency Response Considering Driver-seat Galal Ali Hassaan Emeritus Professor, Department of Mechanical Design & Production, Faculty
More informationDate: _15 April (1) The only reference material you may use is one 8½x11 crib sheet and a calculator.
PH1140: Oscillations and Waves Name: SOLUTIONS Conference: Date: _15 April 2005 EXAM #2: D2005 INSTRUCTIONS: (1) The only reference material you may use is one 8½x11 crib sheet and a calculator. (2) Show
More informationPHYSICS. Chapter 15 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 15 Lecture RANDALL D. KNIGHT Chapter 15 Oscillations IN THIS CHAPTER, you will learn about systems that oscillate in simple harmonic
More informationIntroduction to Feedback Control
Introduction to Feedback Control Control System Design Why Control? Open-Loop vs Closed-Loop (Feedback) Why Use Feedback Control? Closed-Loop Control System Structure Elements of a Feedback Control System
More informationسایت آموزش مهندسی مکانیک
http://www.drshokuhi.com سایت آموزش مهندسی مکانیک 1 Single-degree-of-freedom Systems 1.1 INTRODUCTION In this chapter the vibration of a single-degree-of-freedom system will be analyzed and reviewed. Analysis,
More informationME scope Application Note 28
App Note 8 www.vibetech.com 3/7/17 ME scope Application Note 8 Mathematics of a Mass-Spring-Damper System INTRODUCTION In this note, the capabilities of ME scope will be used to build a model of the mass-spring-damper
More informationExercises Lecture 15
AM1 Mathematical Analysis 1 Oct. 011 Feb. 01 Date: January 7 Exercises Lecture 15 Harmonic Oscillators In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium
More informationTHEORY OF VIBRATION ISOLATION
CHAPTER 30 THEORY OF VIBRATION ISOLATION Charles E. Crede Jerome E. Ruzicka INTRODUCTION Vibration isolation concerns means to bring about a reduction in a vibratory effect. A vibration isolator in its
More informationC. points X and Y only. D. points O, X and Y only. (Total 1 mark)
Grade 11 Physics -- Homework 16 -- Answers on a separate sheet of paper, please 1. A cart, connected to two identical springs, is oscillating with simple harmonic motion between two points X and Y that
More informationVIBRATION ANALYSIS OF E-GLASS FIBRE RESIN MONO LEAF SPRING USED IN LMV
VIBRATION ANALYSIS OF E-GLASS FIBRE RESIN MONO LEAF SPRING USED IN LMV Mohansing R. Pardeshi 1, Dr. (Prof.) P. K. Sharma 2, Prof. Amit Singh 1 M.tech Research Scholar, 2 Guide & Head, 3 Co-guide & Assistant
More information(1) The only reference material you may use is one 8½x11 crib sheet and a calculator.
PH1140: Oscillations and Waves Name: SOLUTIONS AT END Conference: Date: _14 April 2005 EXAM #2: D2006 INSTRUCTIONS: (1) The only reference material you may use is one 8½x11 crib sheet and a calculator.
More informationFinite Element Modules for Demonstrating Critical Concepts in Engineering Vibration Course
Finite Element Modules for Demonstrating Critical Concepts in Engineering Vibration Course Shengyong Zhang Assistant Professor of Mechanical Engineering College of Engineering and Technology Purdue University
More informationDynamics of structures
Dynamics of structures 2.Vibrations: single degree of freedom system Arnaud Deraemaeker (aderaema@ulb.ac.be) 1 One degree of freedom systems in real life 2 1 Reduction of a system to a one dof system Example
More informationImplementation Issues for the Virtual Spring
Implementation Issues for the Virtual Spring J. S. Freudenberg EECS 461 Embedded Control Systems 1 Introduction One of the tasks in Lab 4 is to attach the haptic wheel to a virtual reference position with
More informationSystems Analysis and Control
Systems Analysis and Control Matthew M. Peet Illinois Institute of Technology Lecture 8: Response Characteristics Overview In this Lecture, you will learn: Characteristics of the Response Stability Real
More informationIntroduction to Vibration. Mike Brennan UNESP, Ilha Solteira São Paulo Brazil
Introduction to Vibration Mike Brennan UNESP, Ilha Solteira São Paulo Brazil Vibration Most vibrations are undesirable, but there are many instances where vibrations are useful Ultrasonic (very high
More informationVibration Control Prof. Dr. S. P. Harsha Department of Mechanical & Industrial Engineering Indian Institute of Technology, Roorkee
Vibration Control Prof. Dr. S. P. Harsha Department of Mechanical & Industrial Engineering Indian Institute of Technology, Roorkee Module - 1 Review of Basics of Mechanical Vibrations Lecture - 2 Introduction
More informationTuned mass dampers on damped structures
Downloaded from orbit.dtu.dk on: Jul 15, 2018 Tuned mass dampers on damped structures Krenk, Steen; Høgsberg, Jan Becker Published in: 7th European Conference on Structural Dynamics Publication date: 2008
More informationMATHEMATICAL MODEL OF DYNAMIC VIBRATION ABSORBER-RESPONSE PREDICTION AND REDUCTION
ANNALS of Faculty Engineering Hunedoara International Journal of Engineering Tome XIV [2016] Fascicule 1 [February] ISSN: 1584-2665 [print; online] ISSN: 1584-2673 [CD-Rom; online] a free-access multidisciplinary
More informationUniversity of Alberta ENGM 541: Modeling and Simulation of Engineering Systems Laboratory #7. M.G. Lipsett & M. Mashkournia 2011
ENG M 54 Laboratory #7 University of Alberta ENGM 54: Modeling and Simulation of Engineering Systems Laboratory #7 M.G. Lipsett & M. Mashkournia 2 Mixed Systems Modeling with MATLAB & SIMULINK Mixed systems
More informationLecture 6 mechanical system modeling equivalent mass gears
M2794.25 Mechanical System Analysis 기계시스템해석 lecture 6,7,8 Dongjun Lee ( 이동준 ) Department of Mechanical & Aerospace Engineering Seoul National University Dongjun Lee Lecture 6 mechanical system modeling
More informationThe Behaviour of Simple Non-Linear Tuned Mass Dampers
ctbuh.org/papers Title: Authors: Subject: Keyword: The Behaviour of Simple Non-Linear Tuned Mass Dampers Barry J. Vickery, University of Western Ontario Jon K. Galsworthy, RWDI Rafik Gerges, HSA & Associates
More informationMathematical Physics
Mathematical Physics MP205 Vibrations and Waves Lecturer: Office: Lecture 9-10 Dr. Jiří Vala Room 1.9, Mathema
More informationWEEKS 8-9 Dynamics of Machinery
WEEKS 8-9 Dynamics of Machinery References Theory of Machines and Mechanisms, J.J.Uicker, G.R.Pennock ve J.E. Shigley, 2011 Mechanical Vibrations, Singiresu S. Rao, 2010 Mechanical Vibrations: Theory and
More informationForced Oscillation and Resonance
Chapter Forced Oscillation and Resonance The forced oscillation problem will be crucial to our understanding of wave phenomena Complex exponentials are even more useful for the discussion of damping and
More informationu (t t ) + e ζωn (t tw )
LINEAR CIRCUITS LABORATORY OSCILLATIONS AND DAMPING EFFECT PART I TRANSIENT RESPONSE TO A SQUARE PULSE Transfer Function F(S) = ω n 2 S 2 + 2ζω n S + ω n 2 F(S) = S 2 + 3 RC ( RC) 2 S + 1 RC ( ) 2 where
More informationIntroduction to Vibration. Professor Mike Brennan
Introduction to Vibration Professor Mie Brennan Introduction to Vibration Nature of vibration of mechanical systems Free and forced vibrations Frequency response functions Fundamentals For free vibration
More informationDynamic Analysis on Vibration Isolation of Hypersonic Vehicle Internal Systems
International Journal of Engineering Research and Technology. ISSN 0974-3154 Volume 6, Number 1 (2013), pp. 55-60 International Research Publication House http://www.irphouse.com Dynamic Analysis on Vibration
More informationTHE subject of the analysis is system composed by
MECHANICAL VIBRATION ASSIGNEMENT 1 On 3 DOF system identification Diego Zenari, 182160, M.Sc Mechatronics engineering Abstract The present investigation carries out several analyses on a 3-DOF system.
More information10 Measurement of Acceleration, Vibration and Shock Transducers
Chapter 10: Acceleration, Vibration and Shock Measurement Dr. Lufti Al-Sharif (Revision 1.0, 25/5/2008) 1. Introduction This chapter examines the measurement of acceleration, vibration and shock. It starts
More informationMODEL-BASED ANALYSIS OF WHEEL SPEED VIBRATIONS FOR ROAD FRICTION CLASSIFICATION USING MF-SWIFT. Antoine Schmeitz, Mohsen Alirezaei
MODEL-BASED ANALYSIS OF WHEEL SPEED VIBRATIONS FOR ROAD FRICTION CLASSIFICATION USING MF-SWIFT Antoine Schmeitz, Mohsen Alirezaei CONTENTS Introduction Road friction classification from wheel speed vibrations
More informationStructural Dynamics Lecture 2. Outline of Lecture 2. Single-Degree-of-Freedom Systems (cont.)
Outline of Single-Degree-of-Freedom Systems (cont.) Linear Viscous Damped Eigenvibrations. Logarithmic decrement. Response to Harmonic and Periodic Loads. 1 Single-Degreee-of-Freedom Systems (cont.). Linear
More informationAcoustics-An An Overview. Lecture 1. Vibro-Acoustics. What? Why? How? Lecture 1
Vibro-Acoustics Acoustics-An An Overview 1 Vibro-Acoustics What? Why? How? 2 Linear Non-Linear Force Motion Arbitrary motion Harmonic Motion Mechanical Vibrations Sound (Acoustics) 3 Our heart beat, our
More informationÜbersetzungshilfe / Translation aid (English) To be returned at the end of the exam!
Prüfung Regelungstechnik I (Control Systems I) Prof. Dr. Lino Guzzella 3.. 24 Übersetzungshilfe / Translation aid (English) To be returned at the end of the exam! Do not mark up this translation aid -
More informationProb. 1 SDOF Structure subjected to Ground Shaking
Prob. 1 SDOF Structure subjected to Ground Shaking What is the maximum relative displacement and the amplitude of the total displacement of a SDOF structure subjected to ground shaking? magnitude of ground
More informationDr Ian R. Manchester Dr Ian R. Manchester AMME 3500 : Review
Week Date Content Notes 1 6 Mar Introduction 2 13 Mar Frequency Domain Modelling 3 20 Mar Transient Performance and the s-plane 4 27 Mar Block Diagrams Assign 1 Due 5 3 Apr Feedback System Characteristics
More informationVibrations of Single Degree of Freedom Systems
Vibrations of Single Degree of Freedom Systems CEE 541. Structural Dynamics Department of Civil and Environmental Engineering Duke University Henri P. Gavin Fall, 16 This document describes free and forced
More informationLecture 4: R-L-C Circuits and Resonant Circuits
Lecture 4: R-L-C Circuits and Resonant Circuits RLC series circuit: What's V R? Simplest way to solve for V is to use voltage divider equation in complex notation: V X L X C V R = in R R + X C + X L L
More informationIntroduction to Mechanical Vibration
2103433 Introduction to Mechanical Vibration Nopdanai Ajavakom (NAV) 1 Course Topics Introduction to Vibration What is vibration? Basic concepts of vibration Modeling Linearization Single-Degree-of-Freedom
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 informationOscillator Homework Problems
Oscillator Homework Problems Michael Fowler 3//7 1 Dimensional exercises: use dimensions to find a characteristic time for an undamped simple harmonic oscillator, and a pendulum Why does the dimensional
More informationCALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems
R. M. Murray Fall 2004 CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems CDS 101/110 Homework Set #2 Issued: 4 Oct 04 Due: 11 Oct 04 Note: In the upper left hand corner of the first page
More informationDesign of an Innovative Acoustic Metamaterial
Design of an Innovative Acoustic Metamaterial PAVLOS MAVROMATIDIS a, ANDREAS KANARACHOS b Electrical Engineering Department a, Mechanical Engineering Department b Frederick University 7 Y. Frederickou
More informationDynamics of Structures: Theory and Analysis
1. Free vibrations 2. Forced vibrations 3. Transient response 4. Damping mechanisms Dynamics of Structures: Theory and Analysis Steen Krenk Technical University of Denmark 5. Modal analysis I: Basic idea
More informationMeasurement Techniques for Engineers. Motion and Vibration Measurement
Measurement Techniques for Engineers Motion and Vibration Measurement Introduction Quantities that may need to be measured are velocity, acceleration and vibration amplitude Quantities useful in predicting
More informationRectilinear System. Introduction. Hardware
Rectilinear System Introduction For this lab, there are three separate experiments that will be performed. The first experiment will calculate all the system parameters that will be used in later parts
More informationFrequency Response of Linear Time Invariant Systems
ME 328, Spring 203, Prof. Rajamani, University of Minnesota Frequency Response of Linear Time Invariant Systems Complex Numbers: Recall that every complex number has a magnitude and a phase. Example: z
More informationMINIMAX DESIGN OF PREFILTERS FOR MANEUVERING FLEXIBLE STRUCTURES
MINIMAX DESIGN OF PREFILTERS FOR MANEUVERING FLEXIBLE STRUCTURES Tarunraj Singh Yong-Lin Kuo Department of Mechanical and Aerospace Engineering SUNY at Buffalo, Buffalo, New York 426 ABSTRACT This paper
More informationBroadband Vibration Response Reduction Using FEA and Optimization Techniques
Broadband Vibration Response Reduction Using FEA and Optimization Techniques P.C. Jain Visiting Scholar at Penn State University, University Park, PA 16802 A.D. Belegundu Professor of Mechanical Engineering,
More informationSTRUCTURAL DYNAMICS BASICS:
BASICS: STRUCTURAL DYNAMICS Real-life structures are subjected to loads which vary with time Except self weight of the structure, all other loads vary with time In many cases, this variation of the load
More informationFigure XP3.1 (a) Mass in equilibrium, (b) Freebody diagram, (c) Kinematic constraint relation Example Problem 3.1 Figure XP3.1 illustrates a mass m
LECTURE 7. MORE VIBRATIONS ` Figure XP3.1 (a) Mass in equilibrium, (b) Freebody diagram, (c) Kinematic constraint relation Example Problem 3.1 Figure XP3.1 illustrates a mass m that is in equilibrium and
More informationStructural System Identification (KAIST, Summer 2017) Lecture Coverage:
Structural System Identification (KAIST, Summer 2017) Lecture Coverage: Lecture 1: System Theory-Based Structural Identification Lecture 2: System Elements and Identification Process Lecture 3: Time and
More information1 Pushing your Friend on a Swing
Massachusetts Institute of Technology MITES 017 Physics III Lecture 05: Driven Oscillations In these notes, we derive the properties of both an undamped and damped harmonic oscillator under the influence
More informationCollocated versus non-collocated control [H04Q7]
Collocated versus non-collocated control [H04Q7] Jan Swevers September 2008 0-0 Contents Some concepts of structural dynamics Collocated versus non-collocated control Summary This lecture is based on parts
More informationControls Problems for Qualifying Exam - Spring 2014
Controls Problems for Qualifying Exam - Spring 2014 Problem 1 Consider the system block diagram given in Figure 1. Find the overall transfer function T(s) = C(s)/R(s). Note that this transfer function
More informationTOPIC E: OSCILLATIONS SPRING 2019
TOPIC E: OSCILLATIONS SPRING 2019 1. Introduction 1.1 Overview 1.2 Degrees of freedom 1.3 Simple harmonic motion 2. Undamped free oscillation 2.1 Generalised mass-spring system: simple harmonic motion
More informationMulti Degrees of Freedom Systems
Multi Degrees of Freedom Systems MDOF s http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano March 9, 07 Outline, a System
More informationEngineering Science OUTCOME 2 - TUTORIAL 3 FREE VIBRATIONS
Unit 2: Unit code: QCF Level: 4 Credit value: 5 Engineering Science L/60/404 OUTCOME 2 - TUTORIAL 3 FREE VIBRATIONS UNIT CONTENT OUTCOME 2 Be able to determine the behavioural characteristics of elements
More informationResearch Article Parameters Optimization for a Kind of Dynamic Vibration Absorber with Negative Stiffness
Mathematical Problems in Engineering Volume 6 Article ID 9635 pages http://dx.doi.org/.55/6/9635 Research Article Parameters Optimization for a Kind of Dynamic Vibration Absorber with Negative Stiffness
More informationa) Find the equation of motion of the system and write it in matrix form.
.003 Engineering Dynamics Problem Set Problem : Torsional Oscillator Two disks of radius r and r and mass m and m are mounted in series with steel shafts. The shaft between the base and m has length L
More informationLectures Chapter 10 (Cutnell & Johnson, Physics 7 th edition)
PH 201-4A spring 2007 Simple Harmonic Motion Lectures 24-25 Chapter 10 (Cutnell & Johnson, Physics 7 th edition) 1 The Ideal Spring Springs are objects that exhibit elastic behavior. It will return back
More information2.710: Solutions to Home work 1
.710: Solutions to Home work 1 Problem 1: Optics Buzzwords You will get full credit for this problem if your comments about the topic indicate a certain depth of understanding about what you have written
More informationVTU-NPTEL-NMEICT Project
VTU-NPTEL-NMEICT Project Progress Report The Project on Development of Remaining Three Quadrants to NPTEL Phase-I under grant in aid NMEICT, MHRD, New Delhi SME Name : Course Name: Type of the Course Module
More informationChapter 14 Oscillations
Chapter 14 Oscillations Chapter Goal: To understand systems that oscillate with simple harmonic motion. Slide 14-2 Chapter 14 Preview Slide 14-3 Chapter 14 Preview Slide 14-4 Chapter 14 Preview Slide 14-5
More informationPROJECT 1 DYNAMICS OF MACHINES 41514
PROJECT DYNAMICS OF MACHINES 454 Theoretical and Experimental Modal Analysis and Validation of Mathematical Models in Multibody Dynamics Ilmar Ferreira Santos, Professor Dr.-Ing., Dr.Techn., Livre-Docente
More informationReduction of the effect of floor vibrations in a checkweigher using an electromagnetic force balance system
ACTA IMEKO ISSN: 1 870X July 017, Volume 6 Number, 65 69 Reduction of the effect of floor vibrations in a checkweigher using an electromagnetic force balance system Yuji Yamakawa 1, Takanori Yamazaki 1
More informationVibrations: Second Order Systems with One Degree of Freedom, Free Response
Single Degree of Freedom System 1.003J/1.053J Dynamics and Control I, Spring 007 Professor Thomas Peacock 5//007 Lecture 0 Vibrations: Second Order Systems with One Degree of Freedom, Free Response Single
More informationEMA 545 Final Exam - Prof. M. S. Allen Spring 2011
EMA 545 Final Exam - Prof. M. S. Allen Spring 2011 Honor Pledge: On my honor, I pledge that this exam represents my own work, and that I have neither given nor received inappropriate aid in the preparation
More informationSecond Order Transfer Function Discrete Equations
Second Order Transfer Function Discrete Equations J. Riggs 23 Aug 2017 Transfer Function Equations pg 1 1 Introduction The objective of this paper is to develop the equations for a discrete implementation
More informationarxiv: v1 [physics.class-ph] 3 Jun 2016
A principle of similarity for nonlinear vibration absorbers arxiv:166.144v1 [physics.class-ph] 3 Jun 16 G. Habib, G. Kerschen email: giuseppe.habib@ulg.ac.be Phone: +3 4 36648 Space Structures and Systems
More informationMassachusetts Institute of Technology Department of Mechanical Engineering Dynamics and Control II Design Project
Massachusetts Institute of Technology Department of Mechanical Engineering.4 Dynamics and Control II Design Project ACTIVE DAMPING OF TALL BUILDING VIBRATIONS: CONTINUED Franz Hover, 5 November 7 Review
More information