Fundamentals of mechanical vibrations. ([2016])

• Record Type: Book
• Further Information: Note: Liang-Wu Cai, Kansas State University, USA.
• Authors: Cai, Liang-Wu
• Contents: Preface v 1 A Crash Course on Lagrangian Dynamics 1 1.1 Objectives 1 1.2 Concept of “Equation of Motion” 1 1.3 Generalized Coordinates 5 1.4 Admissible Variations 14 1.5 Degrees of Freedom 17 1.6 Virtual Work and Generalized Forces 19 1.7 Lagrangian 27 1.8 Lagrange’s Equation 27 1.9 Procedure for Deriving Equation(s) of Motion 28 1.10 Worked Examples 28 1.10.1 Systems Containing Only Particles 28 1.10.2 Systems Containing Rigid Bodies 43 1.11 Linearization of Equations of Motion 63 1.11.1 Equilibrium Position(s) 63 1.11.2 Linearization 65 1.11.3 Observations and Further Discussions 68 1.12 Chapter Summary 70 2 Vibrations of Single-DOF Systems 89 2.1 Objectives 89 2.2 Types of Vibration Analyses 89 2.3 Free Vibrations of Undamped System 91 2.3.1 General Solution for Homogeneous Differential Equation . 92 2.3.2 Basic Vibration Terminologies 94 2.3.3 Determining Constants via Initial Conditions 96 2.4 Free Vibrations of Damped Systems 103 2.5 Using Normalized Equation of Motion 105 2.5.1 Normalization of Equation of Motion 105 2.5.2 Classification of Vibration Systems 106 2.5.3 Free Vibration of Underdamped Systems 107 2.5.4 Free Vibration of Critically Damped System 111 2.5.5 Free Vibration of Overdamped System 113 2.6 Forced Vibrations I: Steady-State Responses 120 2.6.1 Harmonic Loading 120 2.6.2 Mechanical Significance of Steady-State Solution 122 2.6.3 Other Examples of Harmonic Loading 128 2.6.4 General Periodic Loading 137 2.7 Forced Vibrations II: Transient Responses 147 2.7.1 Transient Response to Periodic Loading 148 2.7.2 General Loading: Direct Analytical Method 153 2.7.3 Laplace Transform Method 161 2.7.4 Decomposition Method 166 . 2.7.5 Convolution Integral Method 176 2.8 Chapter Summary 190 2.8.1 Free Vibrations of Single-DOF Systems 190 2.8.2 Steady-State Responses for Single-DOF Systems 191 2.8.3 Transient Responses of Single-DOF Systems 192 3 Lumped-Parameter Modeling 205 3.1 Objectives 205 3.2 Modeling 205 3.3 Idealized Elements 206 3.3.1 Mass Elements 206 3.3.2 Spring Elements 207 3.3.3 Damping Elements 209 3.4 Lumped-Parameter Modeling of Simple Components and Structures 210 3.4.1 Equivalent Spring Constants 211 3.4.2 Equivalent Masses 225 3.4.3 Damping Models 234 3.5 Alternative Methods 240 3.5.1 Castigliano Method for Equivalent Spring Constants 241 3.5.2 Rayleigh-Ritz Method for Equivalent Masses 246 3.5.3 Rayleigh-Ritz Method for Equivalent Spring Constants 251 3.5.4 Rayleigh-Ritz Method for Natural Frequencies 253 3.5.5 Determining Lumped . Parameters Through Experimental Measurements 255 3.6 Examples with Lumped-Parameter Models 258 3.7 Chapter Summary 277 4 Vibrations of Multi-DOF Systems 295 4.1 Objectives 295 4.2 Matrix Equation of Motion 295 4.3 Modal Analysis: Natural Frequencies and Mode Shapes 299 4.4 Free Vibrations 312 4.5 Eigenvalues and Eigenvectors 334 4.5.1 Standard Eigenvalue Problem 335 4.5.2 Generalized Eigenvalue Problem 336 4.6 Coupling, . Decoupling and Principal Coordinates 337 4.6.1 Types of Coupling 337 4.6.2 Principal Coordinates 337 4.6.3 Decoupling Method for Free-Vibration Analysis 340 4.7 Forced Vibrations I: Steady-State Responses 350 4.8 Forced Vibrations II: Transient Responses 360 4.8.1 Direct Analytical Method 360 4.8.2 Decoupling Method 363 4.8.3 Laplace Transform Method 380 4.8.4 Convolution Integral Method 383 4.9 Chapter Summary 390 4.9.1 Modal Analyses 390 4.9.2 Free Vibrations of Multi-DOF Systems 391 4.9.3 Steady-State Responses of Multi-DOF Systems 393 4.9.4 Transient Responses of Multi-DOF Systems 393 5 Vibration Analyses Using Finite Element Method 407 5.1 Objectives 407 5.2 Introduction to Finite Element Method 407 5.2.1 Lagrangian Dynamics Formulation of FEM Model 408 5.2.2 Matrix Formulation 412 5.3 Finite Element Analyses of Beams 417 5.3.1 . Formulation of Beam Element 417 5.3.2 Implementation Using MATLAB 422 5.3.3 Generalization: Large-Scale Finite Element Simulations 430 5.3.4 Damping Models in Finite Element Modeling 433 5.4 Vibration Analyses Using ANSYS 434 5.4.1 Introduction to ANSYS Workbench 435 5.4.2 Static Analysis 435 5.4.3 Modal Analysis 454 5.4.4 Harmonic Vibration Analysis 458 5.4.5 Transient Vibration Analysis 464 5.5 Vibration Analyses Using SOLIDWORKS 470 5.5.1 Introduction to SOLIDWORKS Simulation 470 5.5.2 Static Analysis 473 5.5.3 Modal Analysis 489 5.5.4 Harmonic Vibration Analysis 493 5.5.5 Transient Vibration Analysis 498 5.6 Chapter Summary 502 5.6.1 Finite Element Formulation 502 5.6.2 Using Commercial Finite Element Analysis Software 502 A Review of Newtonian Dynamics 507 A.1 Kinematics 507 A.1.1 Kinematics of a Point or a Particle 507 . A.1.2 Relative Motions 509 A.1.3 Kinematics of a Rigid Body 510 A.2 Kinetics 511 A.2.1 Newton-Euler Equations 511 A.2.2 Energy Principles 513 A.2.3 Momentum Principles 514 B A Primer on MATLAB 515 B.1 Matrix Computations 515 B.1.1 Commands and Statements 515 B.1.2 Matrix Generation 516 B.1.3 Accessing Matrix Elements and Sub-Matrices 518 B.1.4 Operators and Elementary Functions 519 B.1.5 Flow Controls 521 B.1.6 M-Files, Scripts and Functions 524 B.1.7 Linear Algebra 528 B.2 Plotting 529 B.2.1 Two-Dimensional Curve Plots 530 B.2.2 Three-Dimensional Curve Plots 532 B.2.3 Three-Dimensional Surface Plots 532 C Tables of Laplace Transform 537 C.1 Properties of Laplace Transform 537 C.2 Function Transformations 538 .
• Publisher Details: Chichester, West Sussex, UK : Wiley ASME Press
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white, and colour)
• Subjects: 621.811; Machinery -- Vibration; Vibration -- Mathematical models
• Languages: English
• ISBNs: 9781119050223
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.