VIBRATION PROBLEMS IN ENGINEERING
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1 VIBRATION PROBLEMS IN ENGINEERING FIFTH EDITION W. WEAVER, JR. Professor Emeritus of Structural Engineering The Late S. P. TIMOSHENKO Professor Emeritus of Engineering Mechanics The Late D. H. YOUNG Professor Emeritus of Civil Engineering WILEY A WILEY-INTERSC1ENCE PUBLICATION JOHN WILEY & SONS New York / Chichester / Brisbane / Toronto / Singapore
2 CONTENTS PREFACE xi 1 SYSTEMS WITH ONE DEGREE OF FREEDOM Examples of One-Degree Systems / Undamped Free Translational Vibrations / Rotational Vibrations / Energy Method / Rayleigh's Method / Forced Vibrations: Steady State / Forced Vibrations: Transient State / Free Vibrations with Viscous Damping / Forced Vibrations with Viscous Damping / Equivalent Viscous Damping / General Periodic Forcing Functions / Arbitrary Forcing Functions / Arbitrary Support Motions / Response Spectra / 99. ** 1.15 Step-by-Step Response Calculations / 107 References / 113 Problems / SYSTEMS WITH NONLINEAR CHARACTERISTICS Examples of Nonlinear Systems / Direct Integration for Velocity and Period / Approximate Methods for Free Vibrations / 157 vii
3 viii CONTENTS 2.4 Forced Nonlinear Vibrations / Piecewise-Linear Systems / Numerical Solutions for Nonlinear Systems / 190 References / 207 Problems / SYSTEMS WITH TWO DEGREES OF FREEDOM Examples of Two-Degree Systems / Action Equations: Stiffness Coefficients / Displacement Equations: Flexibility Coefficients / Inertial and Gravitational Coupling / Undamped Free Vibrations / Undamped Forced Vibrations / Free Vibrations with Viscous Dampling / Forced Vibrations with Viscous Damping / 265 References / 267 Problems / SYSTEMS WITH MULTIPLE DEGREES OF FREEDOM Introduction / 275 ' 4.2 Frequencies and Mode Shapes for Undamped Systems / Principal and Normal Coordinates / Normal-Mode Response to Initial Conditions / Normal-Mode Response to Applied Actions / Normal-Mode Response to Support Motions / Iteration Method for Frequencies and Mode Shapes / Damping in Multidegree Systems / Damped Response to Periodic Forcing Functions / Transient Response of Damped Systems / Step-by-Step Response Calculations / 347 References / 352 Problems / CONTINUA WITH INFINITE DEGREES OF FREEDOM Introduction / Free Longitudinal Vibrations of Prismatic Bars / Forced Longitudinal Response of Prismatic Bars / Normal-Mode Method for Prismatic Bars / Prismatic Bar with a Mass or Spring at the End / Bars Subjected to Longitudinal Support Motions / Torsional Vibrations of Circular Shafts / Transverse Vibrations of Stretched Wires / 409
4 CONTENTS ix 5.9 Transverse Vibrations of Prismatic Beams / Transverse Vibrations of a Simple Beam / Vibrations of Beams with Other End Conditions / Effects of Rotary Inertia and Shearing Deformations / Forced Response of a Simple Beam / Forced Response of Beams with Other End Conditions / Beams Subjected to Support Motions / Beams Traversed by Moving Loads / Effect of Axial Force on Vibrations of Beams / Beams on Eastic Supports or Elastic Foundations / Ritz Method for Calculating Frequencies / Vibrations of Nonprismatic Beams / Coupled Flexural and Torsional Vibrations of Beams / Vibrations of Circular Rings / Transverse Vibrations of Membranes / Transverse Vibrations of Plates / 495 References / 505 Problems / FINITE-ELEMENT METHOD FOR DISCRETIZED CONTINUA Introduction / Stresses and Strains in Continua / Equations of Motion for Finite Elements / One-Dimensional Elements / Vibrations of Beams by Finite Elements / 534 References / 542 Problems / 543 BIBLIOGRAPHY 551 APPENDIX A SYSTEMS OF UNITS AND MATERIAL PROPERTIES 553 A.I Systems of Units / 553 A.2 Material Properties / 555 ^ APPENDIX B COMPUTER PROGRAMS 557 B.I Introduction / 557 B.2 Step-by-Step Solutions for Linear One-Degree Systems / 558 B.3 Numerical Solutions for Nonlinear One- Degree Systems / 561
5 x CONTENTS B.4 Iteration of Eigenvalues and Eigenvectors / 562 B.5 Step-By-Step Solutions for Linear Multidegree Systems / 565 B.6 Program Notation / 567 Flowcharts for Programs / 569 ANSWERS TO PROBLEMS 587 INDEX 603
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