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    Fundamentals of Structural Dynamics Second Edition Roy R. Craig, Jr. Andrew J. Kurdila WILEY JOHN WILEY & SONS, INC.
    Copyright © 2006 by John Wiley & Sons. Inc. All rights reserved. Published by John Wiley & Sons. Inc.. Hoboken. New Jersey Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive. Danvers. MA 01923, 978-750-8400, fax 978-646-8600. or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc.. 111 River Street, Hoboken, NJ 07030, (201) 748-6011. fax (201) 748-6008. Limit of Liability /Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not iimited to special, incidental, consequential, or other damages. For general information on our other products and services piease contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993 or fax 317-572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic format. Library of Congress Cataloging-in-Pnblication Data: Craig, Roy R., 1934- p. cm. Fundamentals of structural dynamics / by Roy R. Craig, Jr. and Andrew J. Kurdila.— 2nd ed. Rev. ed. of: Structural dynamics. cl981. Includes bibliographical references and index. ISBN 13: 978-0-471-43044-5 ISBN 10: 0-471-43044-7 (cloth) 1. Structural dynamics— Data processing. 2. Structural dynamics— Mathematical models. I. Kurdila, Andrew. II. Craig, Roy R.. 1934-. Structural dynamics. III. Title. TA654.C72 2006 624.L71 — dc22 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1 2005043679
    The first author dedicates his work on this edition to his grandchildren: Talia, Kyle, and Hart Barron, and Alex, Brandon, and Chase Lemens. The second author dedicates his work to his wife, Jeannie, and to his children: Patrick, Hannah, and Justin.
    viii Contents 5.6 System Response by the Laplace Transform Method: System Transfer Function 136 References Problems 142 143 References Problems 240 241 9 Vibration of Undamped 2-DOF Systems 248 6 Numerical Evaluation of the Dynamic Response of SDOF Systems 147 6.1 6.2 6.3 148 Integration of Second-Order Ordinary Differential Equations Integration of First-Order Ordinary Differential Equations Nonlinear SDOF Systems References Problems 181 182 159 171 7 Response of SDOF Systems to Periodic Excita­ tion: Frequency-Domain Analysis 184 7.1 7.2 7.3 7.4 7.5 184 189 Response to Periodic Excitation: Real Fourier Series Response to Periodic Excitation: Complex Fourier Series Response to Nonperiodic Excitation: Fourier Integral Relationship Between Complex Frequency Response and Unit Impulse Response Discrete Fourier Transform and Fast Fourier Transform References Problems 200 205 205 195 199 Part II Multiple-Degree-of-Freedom Systems— Basic Topics 209 8 Mathematical Models of MDOF Systems 211 8.1 8.2 8.3 8.4 8.5 218 Application of Newton’s Laws to Lumped-Parameter Models 212 introduction to Analytical Dynamics: Hamilton’s Principle and Lagrange’s Equations Application of Lagrange’s Equations to Lumped-Parameter Models Application of Lagrange’s Equations to Continuous Models: Assumed-Modes Method Constrained Coordinates and Lagrange Multipliers 238 228 223 9.1 9.2 9.3 9.4 9.5 9.6 249 254 Free Vibration of 2-DOF Systems: Natural Frequencies and Mode Shapes Beat Phenomenon Additional Examples of Modes and Frequencies of 2-DOF Systems: Assumed-Modes Models 258 Free Vibration of Systems with Rigid-Body Modes Introduction to Mode Superposition: Frequency Response of an Undamped 2-DOF System Undamped Vibration Absorber Reference Problems 275 275 266 268 272 10 Vibration Properties of MDOF Systems: Modes, Frequencies, and Damping 281 10.1 Some Properties of Natural Frequencies and Natural Modes of Undamped MDOF Systems 282 10.2 Model Reduction: Rayleigh, Rayleigh-Ritz, 10.3 10.4 10.5 302 298 and Assumed-Modes Methods Uncoupled Damping in MDOF Systems Structures with Arbitrary Viscous Damping: Complex Modes Natural Frequencies and Mode Shapes of Damped Structures with Rigid-Body Modes References Problems 322 322 316 307 11 Dynamic Response of MDOF Systems: Mode- Superposition Method 325 11.1 Mode-Superposition Method: Principal Coordinates 325 11.2 Mode-Superposition Solutions for MDOF Systems with Modal Damping: Frequency-Respönse Analysis 330 11.3 Mode-Displacement Solution for the Response of MDOF Systems 342
    Contents Preface to Structural Dynamics— An Introduction to Computer Methods Preface to Fundamentals of Structural Dynamics About the Authors xv xi 3.3 3.4 3.5 xiii 1 The Science and Art of Structural Dynamics 1 1.1 1.2 1.3 1.4 1.5 1.6 1 2 Introduction to Structural Dynamics Modeling of Structural Components and Systems Prototype Spring-Mass Model Vibration Testing of Structures Scope of the Book Computer Simulations; Supplementary Material on the Website References Problems 7 12 12 16 16 15 P a rti Single-Degree-of-Freedom Systems 19 2 Mathematical Models of SDOF Systems 21 2.1 2.2 2.3 2.4 2.5 21 24 Brief Review of the Dynamics of Particles and Rigid Bodies Elements of Lumped-Parameter Models Application of Newton’s Laws to Lumped-Parameter Models 27 Application of the Principle of Virtual Displacements to Lumped-Parameter Models Application of the Principle of Virtual Displacements to Continuous Models: Assumed-Modes Method References Problems 41 34 50 51 3 Free Vibration of SDOF Systems 56 3.1 3.2 Free Vibration of Undamped SDOF Systems Free Vibration of Viscous-Damped SDOF Systems 58 61 66 70 Stability of Motion Free Vibration of an SDOF System with Coulomb Damping Experimental Determination of the Natural Frequency and Damping Factor of an SDOF System References Problems 77 72 78 4 Response of SDOF Systems to Harmonic Excitation 81 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 93 87 96 82 Response of Undamped SDOF Systems to Harmonic Excitation Response of Viscous-Damped SDOF Systems to Harmonic Excitation: Frequency-Response Functions Complex Frequency Response Vibration Isolation: Force Transmissibility and Base Motion Vibration Measuring Instruments: Accelerometers and Vibrometers Use of Frequency-Response Data to Determine the Natural Frequency and Damping Factor of a Lightly Damped SDOF System Equivalent Viscous Damping Structural Damping 111 References 112 113 Problems 107 104 101 5 Response of SDOF Systems to Nonperiodic Excitation 117 5.1 5.2 5.3 5.4 5.5 117 Response of a Viscous-Damped SDOF System to an Ideal Step Input Response of Undamped SDOF Systems to Rectangular Pulse and Ramp Loadings Response of Undamped SDOF Systems to a Short-Duration Impulse: Unit Impulse Response Response of SDOF Systems to General Dynamic Excitation: Convolution Integral Method Response Spectra 125 128 123 119
    11.4 Mode-Acceleration Solution for the Response 11.5 of Undamped MDOF Systems Dynamic Stresses by Mode Superposition 351 349 11.6 Mode Superposition for Undamped Systems with Rigid-Body Modes References Problems 360 359 353 Part III Continuous Systems 365 12 Mathematical Models of Continuous Systems 367 12.1 12.2 12.3 12.4 367 374 Applications of Newton’s Laws: Axial Deformation and Torsion Application of Newton's Laws: Transverse Vibration of Linearly Elastic Beams (Bemoulli-Euler Beam Theory) Application of Hamilton’s Principle: Torsion of a Rod with Circular Cross Section 379 Application of the Extended Hamilton’s Principle: Beam Flexure Including Shear Deformation and Rotatory Inertia (Timoshenko Beam Theory) References Problems 382 385 385 13 Free Vibration of Continuous Systems 388 13.1 13.2 13.3 13.4 13.5 13.6 388 398 392 Free Axial and Torsional Vibration Free Transverse Vibration of Bernoulli-Euler Beams Rayleigh’s Method for Approximating the Fundamental Frequency of a Continuous System Free Transverse Vibration of Beams Including Shear Deformation and Rotatory Inertia Some Properties of Natural Modes of Continuous Systems Free Vibration of Thin Flat Plates References Problems 405 409 409 400 401 Part IV Computational Methods Dynamics 4X5 in Structural Contents ix 14 Introduction Structures to Finite Element Modeling of 417 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 418 438 419 430 Introduction to the Finite Element Method Element Stiffness and Mass Matrices and Element Force Vector Transformation of Element Matrices Assembly of System Matrices: Direct Stiffness Method Boundary Conditions Constraints: Reduction of Degrees of Freedom Systems with Rigid-Body Modes Finite Element Solutions for Natural Frequencies and Mode Shapes References Problems 462 463 453 445 447 451 15 Numerical Evaluation of Modes and Frequencies of MDOF Systems 469 15.1 15.2 15.3 15.4 15.5 15.6 471 469 Introduction to Methods for Solving Algebraic Eigenproblems Vector Iteration Methods Subspace Iteration 480 QR Method for Symmetric Eigenproblems Lanczos Eigensolver Numerical Case Study References Problems 498 498 483 489 496 16 Direct Integration Methods for Dynamic Response of MDOF Systems 500 16.1 16.2 16.3 16.4 16.5 504 510 Damping in MDOF Systems 501 Numerical Integration: Mathematical Framework Integration of Second-Order MDOF Systems Single-Step Methods and Spectral Stability Numerical Case Study References Problems 527 528 516 525
    x Contents 17 Component-Mode Synthesis 531 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 534 539 544 532 Introduction to Component-Mode Synthesis Component Modes: Normal, Constraint, and Rigid-Body Modes Component Modes: Attachment and Inertia-Relief Attachment Modes Flexibility Matrices and Residual Flexibility Substructure Coupling Procedures Component-Mode Synthesis Methods: Fixed-Interface Methods Component-Mode Synthesis Methods: Free-Interface Methods 559 Brief Introduction to Multilevel Substructuring References Problems 571 572 564 557 549 PartV Advanced Topics in Structural Dynamics 577 18 Introduction to Experimental Modal Analysis 579 19.2 19.3 19.4 19.5 19.6 19.7 620 Constitutive Laws of Linear Piezoelectricity Application of Newton's Laws to Piezostructural Systems 624 Application of Extended Hamilton’s Principle to Piezoelectricity 630 Active Truss Models Active Beam Models 637 Active Composite Laminates References Problems 646 647 627 641 20 Introduction to Earthquake Response of Structures 650 20.1 20.2 20.3 20.4 650 Introduction Response of a SDOF System to Earthquake Excitation: Response Spectra Response of MDOF Systems to Earthquake Excitation Further Considerations References Problems 666 660 664 665 652 18.1 18.2 18.3 18.4 18.5 18.6 580 590 Introduction Frequency-Response Function 584 Representations Vibration Test Hardware Fourier Transforms, Digital Signal Processing, and Estimation of FRFs Modal Parameter Estimation 604 Mode Shape Estimation and Model Verification References Problems 612 615 616 594 A Units 667 B Complex Numbers 671 C Elements of Laplace Transforms 674 D Fundamentals of Linear Algebra 682 E Introduction to the Use of Matlab 697 19 Introduction to Active Structures 617 19.1 Introduction to Piezoelectric Materials 617 Index 715
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