Mechanical Vibrations: Theory and Applications, SI Edition

MECHANICAL VIBRATIONS: THEORY AND APPLICATIONS takes an applications-based approach at teaching students to apply previously learned engineering principles while laying a foundation for engineering design. This text provides a brief review of the principles of dynamics so that terminology and notation are consistent and applies these principles to derive mathematical models of dynamic mechanical systems. The methods of application of these principles are consistent with popular Dynamics texts. Numerous pedagogical features have been included in the text in order to aid the student with comprehension and retention. These include the development of three benchmark problems which are revisited in each chapter, creating a coherent chain linking all chapters in the book. Also included are learning outcomes, summaries of key concepts including important equations and formulae, fully solved examples with an emphasis on real world examples, as well as an extensive exercise set including objective-type questions. Cover Title Page Copyright About the Author Preface to the SI Edition Preface Contents Ch 1: Introduction 1.1 The Study of Vibrations 1.2 Mathematical Modeling 1.3 Generalized Coordinates 1.4 Classification of Vibration 1.5 Dimensional Analysis 1.6 Simple Harmonic Motion 1.7 Review of Dynamics 1.8 Two Benchmark Examples 1.9 Further Examples 1.10 Summary Problems Ch 2: Modeling of SDOF Systems 2.1 Introduction 2.2 Springs 2.3 Springs in Combination 2.4 Other Sources of Potential Energy 2.5 Viscous Damping 2.6 Energy Dissipated by Viscous Damping 2.7 Inertia Elements 2.8 External Sources 2.9 Free-Body Diagram Method 2.10 Static Deflections and Gravity 2.11 Small Angle or Displacement Assumption 2.12 Equivalent Systems Method 2.13 Benchmark Examples 2.14 Further Examples 2.15 Chapter Summary Problems Ch 3: Free Vibrations of SDOF Systems 3.1 Introduction 3.2 Standard Form of Differential Equation 3.3 Free Vibrations of an Undamped System 3.4 Underdamped Free Vibrations 3.5 Critically Damped Free Vibrations 3.6 Overdamped Free Vibrations 3.7 Coulomb Damping 3.8 Hysteretic Damping 3.9 Other Forms of Damping 3.10 Benchmark Examples 3.11 Further Examples 3.12 Chapter Summary Problems Ch 4: Harmonic Excitation of SDOF Systems 4.1 Introduction 4.2 Forced Response of an Undamped System Due to a Single-Frequency Excitation 4.3 Forced Response of a Viscously Damped System Subject to a Single-Frequency Harmonic Excitation 4.4 Frequency-Squared Excitations 4.5 Response due to Harmonic Excitation of Support 4.6 Vibration Isolation 4.7 Vibration Isolation from Frequency-Squared Excitations 4.8 Practical Aspects of Vibration Isolation 4.9 Multifrequency Excitations 4.10 General Periodic Excitations 4.11 Seismic Vibration Measuring Instruments 4.12 Complex Representations 4.13 Systems with Coulomb Damping 4.14 Systems with Hysteretic Damping 4.15 Energy Harvesting 4.16 Benchmark Examples 4.17 Further Examples 4.18 Chapter Summary Problems Ch 5: Transient Vibrations of SDOF Systems 5.1 Introduction 5.2 Derivation of Convolution Integral 5.3 Response due to a General Excitation 5.4 Excitations Whose Forms Change at Discrete Times 5.5 Transient Motion due to Base Excitation 5.6 Laplace Transform Solutions 5.7 Transfer Functions 5.8 Numerical Methods 5.9 Shock Spectrum 5.10 Vibration Isolation for Short Duration Pulses 5.11 Benchmark Examples 5.12 Further Examples 5.13 Chapter Summary Problems Ch 6: Two Degree-Of-Freedom Systems 6.1 Introduction 6.2 Derivation of the Equations of Motion 6.3 Natural Frequencies and Mode Shapes 6.4 Free Response of Undamped Systems 6.5 Free Vibrations of a System with Viscous Damping 6.6 Principal Coordinates 6.7 Harmonic Response of Two Degree-Of-Freedom Systems 6.8 Transfer Functions 6.9 Sinusoidal Transfer Function 6.10 Frequency Response 6.11 Dynamic Vibration Absorbers 6.12 Damped Vibration Absorbers 6.13 Vibration Dampers 6.14 Benchmark Examples 6.15 Further Examples 6.16 Chapter Summary Problems Ch 7: Modeling of MDOF Systems 7.1 Introduction 7.2 Derivation of Differential Equations Using the Free-Body Diagram Method 7.3 Lagrange's Equations 7.4 Matrix Formulation of Differential Equations for Linear Systems 7.5 Stiffness Influence Coefficients 7.6 Flexibility Influence Coefficients 7.7 Inertia Influence Coefficients 7.8 Lumped-Mass Modeling of Continuous Systems 7.9 Benchmark Examples 7.10 Further Examples 7.11 Summary Problems Ch 8: Free Vibrations of MDOF Systems 8.1 Introduction 8.2 Normal-Mode Solution 8.3 Natural Frequencies and Mode Shapes 8.4 General Solution 8.5 Special Cases 8.6 Energy Scalar Products 8.7 Properties of Natural Frequencies and Mode Shapes 8.8 Normalized Mode Shapes 8.9 Rayleigh's Quotient 8.10 Principal Coordinates 8.11 Determination of Natural Frequencies and Mode Shapes 8.12 Proportional Damping 8.13 General Viscous Damping 8.14 Benchmark Examples 8.15 Further Examples 8.16 Summary Problems Ch 9: Forced Vibrations of MDOF Systems 9.1 Introduction 9.2 Harmonic Excitations 9.3 Laplace Transform Solutions 9.4 Modal Analysis for Undamped Systems and Systems with Proportional Damping 9.5 Modal Analysis for Systems with General Damping 9.6 Numerical Solutions 9.7 Benchmark Examples 9.8 Further Examples 9.9 Chapter Summary Problems Ch 10: Vibrations of Continuous Systems 10.1 Introduction 10.2 General Method 10.3 Second-Order Systems: Torsional Oscillations of a Circular Shaft 10.4 Transverse Beam Vibrations 10.5 Energy Methods 10.6 Benchmark Examples 10.7 Chapter Summary Problems Ch 11: Finite-Element Method 11.1 Introduction 11.2 Assumed Modes Method 11.3 General Method 11.4 The Bar Element 11.5 Beam Element 11.6 Global Matrices 11.7 Benchmark Example 11.8 Further Examples 11.9 Summary Problems Ch 12: Nonlinear Vibrations 12.1 Introduction 12.2 Sources of Nonlinearity 12.3 Qualitative Analysis of Nonlinear Systems 12.4 Quantitative Methods of Analysis 12.5 Free Vibrations of SDOF Systems 12.6 Forced Vibrations of SDOF Systems with Cubic Nonlinearities 12.7 MDOF Systems 12.8 Continuous Systems 12.9 Chaos 12.10 Chapter Summary Problems Ch 13: Random Vibrations 13.1 Introduction 13.2 Behavior of a Random Variable 13.3 Functions of a Random Variable 13.4 Joint Probability Distributions 13.5 Fourier Transforms 13.6 Power Spectral Density 13.7 Mean Square Value of the Response 13.8 Benchmark Example 13.9 Summary Problems Appendix A Unit Impulse Function and Unit Step Function Appendix B Laplace Transforms Appendix C Linear Algebra Appendix D Deflection of Beams Subject to Concentrated Loads Appendix E Integrals Used in Random Vibrations Appendix F Vibes References Index Takes an applications-based approach at teaching students to apply previously learned engineering principles while laying a foundation for engineering design. This text offers a review of the principles of dynamics so that terminology and notation are consistent and applies them to derive mathematical models of dynamic mechanical systems.