Vibration Problems in Engineering

W. Weaver Jr. and S. P. Timoshenko are the authors of Vibration Problems in Engineering, 5th Edition, published by Wiley.

• Preface xi1 Systems with One Degree of Freedom 11.1 Examples of One-Degree Systems 11.2 Undamped Free Translational Vibrations 21.3 Rotational Vibrations 121.4 Energy Method 241.5 Rayleigh’s Method 241.6 Forced Vibrations: Steady State 391.7 Forced Vibrations with Viscous Damping 521.8 Free Vibrations with Viscous Damping 611.9 Forced Vibrations with Viscous Damping 611.10 Equivalent Viscous Damping 691.11 General Periodic Forcing Functions 761.12 Arbitrary Forcing Functions 841.13 Arbitrary Support Motions 931.14 Response Spectra 991.15 Step-by-Step Response Calculations 107References 113Problems 1142 Systems with Nonlinear Characteristics 1392.1 Examples of Nonlinear Systems 1392.2 Direct Integration for Velocity and Period 1492.3 Approximate Methods for Free Vibrations 1572.4 Forced Nonlinear Vibrations 1662.5 Piecewise-Linear Systems 1752.6 Numerical Solutions for Nonlinear Systems 190References 207Problems 2083 Systems with Two Degrees of Freedom 2173.1 Examples of Two-Degree Systems 2173.2 Action Equations: Stiffness Coefficients 2233.3 Displacement Equations: Flexibility Coefficients 2253.4 Inertial and Gravitational Coupling 2333.5 Undamped Free Vibrations 2413.6 Undamped Forced Vibrations 2513.7 Free Vibrations with Viscous Dampling 2603.8 Forced Vibrations with Viscous Dampling 265References 267Problems 2674 Systems with Multiple Degrees of Freedom 2754.1 Introduction 2754.2 Frequencies and Mode Shapes for Undamped Systems 2764.3 Principal and Normal Coordinates 2874.4 Normal-Mode Response to Initial Conditions 2954.5 Normal-Mode Response to Applied Actions 3014.6 Normal-Mode Response to Support Motions 3094.7 Iteration Method for Frequencies and Mode Shapes 3184.8 Damping in Multidegree Systems 3334.9 Damped Response to Periodic Forcing Functions 3374.10 Transient Response of Damped Systems 3434.11 Step-by-Step Response Calculations 347References 352Problems 3525 Continua with Infinite Degrees of Freedom 3635.1 Introduction 3635.2 Free Longitudinal Vibrations of Prismatic Bars 3645.3 Forced Longitudinal Response of Prismatic Bars 3735.4 Normal-Mode Method for Prismatic Bars 3805.5 Prismatic Bar with a Mass or Spring at the End 3875.6 Bars Subjected to Longitudinal Support Motions 3955.7 Torsional Vibrations of Circular Shafts 4015.8 Transverse Vibrations of Stretched Wires 4095.9 Transverse Vibrations of Prismatic Beams 4165.10 Transverse Vibrations of a Simple Beam 4225.11 Vibrations of Beams with Other End Conditions 4255.12 Effects of Rotary Inertia and Shearing Deformations 4335.13 Forced Response of a Simple Beam 4365.14 Forced Response of Beams with Other End Conditions 4425.15 Beams Subjected to Support Motions 4445.16 Beams Traversed by Moving Loads 4485.17 Effect of Axial Force on Vibrations of Beams 4545.18 Beams on Eastic Supports or Elastic Foundations 4565.19 Ritz Method for Calculating Frequencies 4615.20 Vibrations of Nonprismatic Beams 4665.21 Coupled Flexural and Torsional Vibrations of Beams 4745.22 Vibrations of Circular Rings 4785.23 Transverse Vibrations of Membranes 4955.24 Transverse Vibrations of Plates 495References 505Problems 5066 Finite-Element Method for Discretized Continua 5116.1 Introduction 5116.2 Stresses and Strains in Continua 5136.3 Equations of Motion for Finite Elements 5166.4 One-Dimensional Elements 5206.5 Vibrations of Beams by Finite Elements 534References 542Problems 543Bibliography 551Appendix A Systems of Units and Material Properties 553A.1 Systems of Units 553A.2 Material Properties 555Appendix B Computer Programs 557B.1 Introduction 557B.2 Step-by-Step Solutions for Linear One-Degree Systems 558B.3 Numerical Solutions for Nonlinear One-Degree SystemsB.4 Iteration of Eigenvalues and Eigenvectors 562B.5 Step-by-Step Solutions for Linear Multidegree Systems 565B.6 Program Notation 567Flowcharts for Programs 569Answers to Problems 587Index 603