Fundamentals of Mechanical Vibrations

Inbunden, Engelska, 2016

AvLiang-Wu Cai,USA) Cai, Liang-Wu (Kansas State University,Liang-Wu Cal

1 789 kr

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This introductory book covers the most fundamental aspects of linear vibration analysis for mechanical engineering students and engineers. Consisting of five major topics, each has its own chapter and is aligned with five major objectives of the book. It starts from a concise, rigorous and yet accessible introduction to Lagrangian dynamics as a tool for obtaining the governing equation(s) for a system, the starting point of vibration analysis. The second topic introduces mathematical tools for vibration analyses for single degree-of-freedom systems. In the process, every example includes a section Exploring the Solution with MATLAB. This is intended to develop student's affinity to symbolic calculations, and to encourage curiosity-driven explorations. The third topic introduces the lumped-parameter modeling to convert simple engineering structures into models of equivalent masses and springs. The fourth topic introduces mathematical tools for general multiple degrees of freedom systems, with many examples suitable for hand calculation, and a few computer-aided examples that bridges the lumped-parameter models and continuous systems. The last topic introduces the finite element method as a jumping point for students to understand the theory and the use of commercial software for vibration analysis of real-world structures.

Produktinformation

Utgivningsdatum2016-06-03
Mått175 x 249 x 28 mm
Vikt875 g
FormatInbunden
SpråkEngelska
SerieWiley-ASME Press Series
Antal sidor480
FörlagJohn Wiley & Sons Inc
ISBN9781119050124

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Series Preface ixPreface xi1 A Crash Course on Lagrangian Dynamics 11.1 Objectives 11.2 Concept of "Equation of Motion" 11.3 Generalized Coordinates 51.4 Admissible Variations 131.5 Degrees of Freedom 161.6 Virtual Work and Generalized Forces 171.7 Lagrangian 241.8 Lagrange’s Equation 241.9 Procedure for Deriving Equation(s) of Motion 241.10 Worked Examples 251.10.1 Systems Containing Only Particles 251.10.2 Systems Containing Rigid Bodies 381.11 Linearization of Equations of Motion 571.11.1 Equilibrium Position(s) 581.11.2 Linearization 591.11.3 Observations and Further Discussions 621.12 Chapter Summary 632 Vibrations of Single-DOF Systems 812.1 Objectives 812.2 Types of Vibration Analyses 812.3 Free Vibrations of Undamped System 832.3.1 General Solution for Homogeneous Differential Equation 832.3.2 Basic Vibration Terminologies 852.3.3 Determining Constants via Initial Conditions 872.4 Free Vibrations of Damped Systems 932.5 Using Normalized Equation of Motion 942.5.1 Normalization of Equation of Motion 942.5.2 Classification of Vibration Systems 952.5.3 Free Vibration of Underdamped Systems 962.5.4 Free Vibration of Critically Damped System 1002.5.5 Free Vibration of Overdamped System 1022.6 Forced Vibrations I: Steady-State Responses 1082.6.1 Harmonic Loading 1082.6.2 Mechanical Significance of Steady-State Solution 1102.6.3 Other Examples of Harmonic Loading 1152.6.4 General Periodic Loading 1242.7 Forced Vibrations II: Transient Responses 1332.7.1 Transient Response to Periodic Loading 1342.7.2 General Loading: Direct Analytical Method 1392.7.3 Laplace Transform Method 1462.7.4 Decomposition Method 1502.7.5 Convolution Integral Method 1582.8 Chapter Summary 1722.8.1 Free Vibrations of Single-DOF Systems 1722.8.2 Steady-State Responses of Single-DOF Systems 1732.8.3 Transient Responses of Single-DOF Systems 1743 Lumped-Parameter Modeling 1863.1 Objectives 1863.2 Modeling 1863.3 Idealized Elements 1873.3.1 Mass Elements 1873.3.2 Spring Elements 1883.3.3 Damping Elements 1893.4 Lumped-Parameter Modeling of Simple Components and Structures 1903.4.1 Equivalent Spring Constants 1913.4.2 Equivalent Masses 2043.4.3 Damping Models 2123.5 Alternative Methods 2183.5.1 Castigliano Method for Equivalent Spring Constants 2183.5.2 Rayleigh–Ritz Method for Equivalent Masses 2233.5.3 Rayleigh–Ritz Method for Equivalent Spring Constants 2273.5.4 Rayleigh–Ritz Method for Natural Frequencies 2303.5.5 Determining Lumped Parameters Through Experimental Measurements 2313.6 Examples with Lumped-Parameter Models 2333.7 Chapter Summary 2524 Vibrations of Multi-DOF Systems 2694.1 Objectives 2694.2 Matrix Equation of Motion 2694.3 Modal Analysis: Natural Frequencies and Mode Shapes 2734.4 Free Vibrations 2844.4.1 Free Vibrations of Undamped Systems 2844.4.2 Free Vibrations of Undamped Unconstrained Systems 2934.4.3 Free Vibrations of Systems of Many DOFs 2964.5 Eigenvalues and Eigenvectors 3054.5.1 Standard Eigenvalue Problem 3054.5.2 Generalized Eigenvalue Problem 3064.6 Coupling, Decoupling, and Principal Coordinates 3074.6.1 Types of Coupling 3074.6.2 Principal Coordinates 3074.6.3 Decoupling Method for Free-Vibration Analysis 3104.7 Forced Vibrations I: Steady-State Responses 3194.8 Forced Vibrations II: Transient Responses 3284.8.1 Direct Analytical Method 3284.8.2 Decoupling Method 3314.8.3 Laplace Transform Method 3474.8.4 Convolution Integral Method 3494.9 Chapter Summary 3574.9.1 Modal Analyses 3574.9.2 Free Vibrations of Multi-DOF Systems 3574.9.3 Steady-State Responses of Multi-DOF Systems 3594.9.4 Transient Responses of Multi-DOF Systems 3595 Vibration Analyses Using Finite Element Method 3705.1 Objectives 3705.2 Introduction to Finite Element Method 3705.2.1 Lagrangian Dynamics Formulation of FEM Model 3715.2.2 Matrix Formulation 3745.3 Finite Element Analyses of Beams 3785.3.1 Formulation of Beam Element 3795.3.2 Implementation Using MATLAB 3835.3.3 Generalization: Large-Scale Finite Element Simulations 3925.3.4 Damping Models in Finite Element Modeling 3945.4 Vibration Analyses Using SOLIDWORKS 3955.4.1 Introduction to SOLIDWORKS Simulation 3965.4.2 Static Analysis 3985.4.3 Modal Analysis 4155.4.4 Harmonic Vibration Analysis 4195.4.5 Transient Vibration Analysis 4255.5 Chapter Summary 4285.5.1 Finite Element Formulation 4285.5.2 Using Commercial Finite Element Analysis Software 429Appendix A Review of Newtonian Dynamics 433A.1 Kinematics 433A.1.1 Kinematics of a Point or a Particle 433A.1.2 Relative Motions 435A.1.3 Kinematics of a Rigid Body 436A.2 Kinetics 437A.2.1 Newton–Euler Equations 437A.2.2 Energy Principles 438A.2.3 Momentum Principles 439Appendix B A Primer on MATLAB 440B.1 Matrix Computations 440B.1.1 Commands and Statements 440B.1.2 Matrix Generation 441B.1.3 Accessing Matrix Elements and Submatrices 442B.1.4 Operators and Elementary Functions 444B.1.5 Flow Controls 446B.1.6 M-Files, Scripts, and Functions 449B.1.7 Linear Algebra 452B.2 Plotting 454B.2.1 Two-Dimensional Curve Plots 454B.2.2 Three-Dimensional Curve Plots 456B.2.3 Three-Dimensional Surface Plots 457Appendix C Tables of Laplace Transform 459C.1 Properties of Laplace Transform 459C.2 Function Transformations 459Index 461