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Dynamics of Structures available in Hardcover
- ISBN-10:
- 0132220687
- ISBN-13:
- 9780132220682
- Pub. Date:
- 09/01/1989
- Publisher:
- Prentice Hall Professional Technical Reference
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Product Details
| ISBN-13: | 9780132220682 |
|---|---|
| Publisher: | Prentice Hall Professional Technical Reference |
| Publication date: | 09/01/1989 |
| Series: | Prentice Hall International Series in Civil Engineering and Engineering Mechanics |
| Pages: | 672 |
| Product dimensions: | 6.50(w) x 1.50(h) x 9.50(d) |
Table of Contents
| Preface | XV | |
| List of Symbols | XIX | |
| 1 | Introduction | 1 |
| 1.1 | Objectives of the study of structural dynamics | 1 |
| 1.2 | Importance of vibration analysis | 2 |
| 1.3 | Nature of exciting forces | 3 |
| 1.4 | Mathematical modeling of dynamic systems | 9 |
| 1.5 | Systems of units | 12 |
| 1.6 | Organization of the text | 13 |
| Part 1 | ||
| 2 | Formulation of the Equations of Motion: Single-Degree-of-Freedom Systems | 21 |
| 2.1 | Introduction | 21 |
| 2.2 | Inertia forces | 21 |
| 2.3 | Resultants of inertia forces on a rigid body | 23 |
| 2.4 | Spring forces | 29 |
| 2.5 | Damping forces | 32 |
| 2.6 | Principle of virtual displacement | 33 |
| 2.7 | Formulation of the equations of motion | 38 |
| 2.8 | Modeling of multi-degree-of-freedom discrete parameter system | 54 |
| 2.9 | Effect of gravity load | 57 |
| 2.10 | Axial force effect | 60 |
| 2.11 | Effect of support motion | 65 |
| 3 | Formulation of the Equations of Motion: Multi-Degree-of-Freedom Systems | 73 |
| 3.1 | Introduction | 73 |
| 3.2 | Principal forces in multi-degree-of-freedom dynamic system | 75 |
| 3.3 | Formulation of the equations of motion | 84 |
| 3.4 | Transformation of coordinates | 107 |
| 3.5 | Finite element method | 111 |
| 3.6 | Finite element formulation of the flexural vibrations of a beam | 123 |
| 3.7 | Static condensation of stiffness matrix | 136 |
| 3.8 | Application of the Ritz method to discrete systems | 139 |
| 4 | Principles of Analytical Mechanics | 151 |
| 4.1 | Introduction | 151 |
| 4.2 | Generalized coordinates | 151 |
| 4.3 | Constraints | 156 |
| 4.4 | Virtual work | 159 |
| 4.5 | Generalized forces | 165 |
| 4.6 | Conservative forces and potential energy | 170 |
| 4.7 | Work function | 174 |
| 4.8 | Lagrangian multipliers | 178 |
| 4.9 | Virtual work equation for dynamical systems | 181 |
| 4.10 | Hamilton's equation | 186 |
| 4.11 | Lagrange's equation | 188 |
| 4.12 | Constraint conditions and lagrangian multipliers | 194 |
| 4.13 | Lagrange's equations for discrete multi-degree-of-freedom systems | 196 |
| 4.14 | Rayleigh's dissipation function | 198 |
| Part 2 | ||
| 5 | Free Vibration Response: Single-Degree-of-Freedom System | 209 |
| 5.1 | Introduction | 209 |
| 5.2 | Undamped free vibration | 210 |
| 5.3 | Free vibrations with viscous damping | 220 |
| 5.4 | Damped free vibration with hysteretic damping | 231 |
| 5.5 | Damped free vibration with Coulomb damping | 233 |
| 6 | Forced Harmonic Vibrations: Single-Degree-of-Freedom System | 245 |
| 6.1 | Introduction | 245 |
| 6.2 | Procedures for the solution of the forced vibration equation | 246 |
| 6.3 | Undamped harmonic vibration | 248 |
| 6.4 | Resonant response of an undamped system | 253 |
| 6.5 | Damped harmonic vibration | 254 |
| 6.6 | Complex frequency response | 267 |
| 6.7 | Resonant response of a damped system | 272 |
| 6.8 | Rotating unbalanced force | 273 |
| 6.9 | Transmitted motion due to support movement | 279 |
| 6.10 | Transmissibility and vibration isolation | 284 |
| 6.11 | Vibration measuring instruments | 288 |
| 6.12 | Energy dissipated in viscous damping | 293 |
| 6.13 | Hysteretic damping | 297 |
| 6.14 | Complex stiffness | 301 |
| 6.15 | Coulomb damping | 301 |
| 6.16 | Measurement of damping | 304 |
| 7 | Response to General Dynamic Loading and Transient Response | 317 |
| 7.1 | Introduction | 317 |
| 7.2 | Response to an impulsive force | 317 |
| 7.3 | Response to general dynamic loading | 319 |
| 7.4 | REsponse to a step function load | 320 |
| 7.5 | Response to a ramp function load | 323 |
| 7.6 | Response to a step function load with rise time | 324 |
| 7.7 | Response to shock loading | 330 |
| 7.8 | Response to ground motion | 344 |
| 7.9 | Analysis of response by the phase plane diagram | 354 |
| 8 | Analysis of Single-Degree-of-Freedom Systems: Approximate and Numerical Methods | 361 |
| 8.1 | Introduction | 361 |
| 8.2 | Conservation of energy | 363 |
| 8.3 | Application of Rayleigh method to multi-degree-of-freedom systems | 368 |
| 8.4 | Improved Rayleigh method | 377 |
| 8.5 | Selection of an appropriate vibration shape | 383 |
| 8.6 | Systems with distributed mass and stiffness: Analysis of internal forces | 387 |
| 8.7 | Numerical evaluation of Duhamel's integral | 390 |
| 8.8 | Direct integration of the equations of motion | 399 |
| 8.9 | Integration based on piece-wise linear representation of the excitation | 399 |
| 8.10 | Derivation of general formulae | 404 |
| 8.11 | Constant-acceleration method | 405 |
| 8.12 | Newmark's [beta] method | 408 |
| 8.13 | Wilson-[theta] method | 416 |
| 8.14 | Methods based on difference expressions | 418 |
| 8.15 | Errors involved in numerical integration | 422 |
| 8.16 | Stability of the integration method | 423 |
| 8.17 | Selection of a numerical integration method | 431 |
| 8.18 | Selection of time step | 433 |
| 8.19 | Analysis of nonlinear response | 435 |
| 8.20 | Errors involved in numerical integration of nonlinear systems | 441 |
| 9 | Analysis of Response in the Frequency Domain | 453 |
| 9.1 | Transform methods of analysis | 453 |
| 9.2 | Fourier series representation of a periodic function | 454 |
| 9.3 | Response to a periodically applied load | 456 |
| 9.4 | Exponential form of fourier series | 460 |
| 9.5 | Complex frequency response function | 461 |
| 9.6 | Fourier integral representation of a nonperiodic load | 462 |
| 9.7 | Response to a nonperiodic load | 464 |
| 9.8 | Convolution integral and convolution theorem | 465 |
| 9.9 | Discrete Fourier transform | 468 |
| 9.10 | Discrete convolution and discrete convolution theorem | 471 |
| 9.11 | Comparison of continuous and discrete Fourier transforms | 473 |
| 9.12 | Application of discrete inverse transform | 481 |
| 9.13 | Comparison between continuous and discrete convolution | 487 |
| 9.14 | Discrete convolution of an infinite- and a finite-duration waveform | 492 |
| 9.15 | Corrective response superposition methods | 497 |
| 9.16 | Exponential window method | 515 |
| 9.17 | The fast Fourier transform | 520 |
| 9.18 | Theoretical background to fast Fourier transform | 521 |
| 9.19 | Computing speed of FFT convolution | 525 |
| Part 3 | ||
| 10 | Free-Vibration Response: Multi-Degree-of-Freedom Systems | 533 |
| 10.1 | Introduction | 533 |
| 10.2 | Standard eigenvalue problem | 534 |
| 10.3 | Linearized eigenvalue problem and its properties | 535 |
| 10.4 | Expansion theorem | 540 |
| 10.5 | Rayleigh quotient | 541 |
| 10.6 | Solution of the undamped free-vibration problem | 545 |
| 10.7 | Mode superposition analysis of free-vibration response | 547 |
| 10.8 | Solution of the damped free-vibration problem | 553 |
| 10.9 | Additional orthogonality conditions | 564 |
| 10.10 | Damping orthogonality | 566 |
| 11 | Numerical Solution of the Eigenproblem | 581 |
| 11.1 | Introduction | 581 |
| 11.2 | Properties of standard eigenvalues and eigenvectors | 583 |
| 11.3 | Transformation of a linearized eigenvalue problem to the standard form | 584 |
| 11.4 | Transformation methods | 586 |
| 11.5 | Iteration methods | 602 |
| 11.6 | Determinant search method | 633 |
| 11.7 | Numerical solution of complex eigenvalue problem | 638 |
| 11.8 | Semi-definite or unrestrained systems | 648 |
| 11.9 | Selection of a method for the determination of eigenvalues | 658 |
| 12 | Forced Dynamic Response: Multi-Degree-of-Freedom Systems | 665 |
| 12.1 | Introduction | 665 |
| 12.2 | Normal coordinate transformation | 665 |
| 12.3 | Summary of mode superposition method | 668 |
| 12.4 | Complex frequency response | 673 |
| 12.5 | Vibration absorbers | 679 |
| 12.6 | Effect of support excitation | 681 |
| 12.7 | Forced vibration of unrestrained system | 691 |
| 13 | Analysis of Multi-Degree-of-Freedom Systems: Approximate and Numerical Methods | 701 |
| 13.1 | Introduction | 701 |
| 13.2 | Rayleigh-Ritz method | 702 |
| 13.3 | Application of Ritz method to forced vibration response | 720 |
| 13.4 | Direct integration of the equations of motion | 748 |
| 13.5 | Analysis in the frequency domain | 773 |
| 13.6 | Analysis of nonlinear response | 784 |
| Part 4 | ||
| 14 | Formulation of the Equations of Motion: Continuous Systems | 795 |
| 14.1 | Introduction | 795 |
| 14.2 | Transverse vibrations of a beam | 796 |
| 14.3 | Transverse vibrations of a beam: variational formulation | 799 |
| 14.4 | Effect of damping resistance on transverse vibrations of a beam | 806 |
| 14.5 | Effect of shear deformation and rotatory inertia on the flexural vibrations of a beam | 807 |
| 14.6 | Axial vibrations of a bar | 810 |
| 14.7 | Torsional vibrations of a bar | 813 |
| 14.8 | Transverse vibrations of a string | 814 |
| 14.9 | Transverse vibrations of a shear beam | 815 |
| 14.10 | Transverse vibrations of a beam excited by support motion | 818 |
| 14.11 | Effect of axial force on transverse vibrations of a beam | 822 |
| 15 | Continuous Systems: Free Vibration Response | 829 |
| 15.1 | Introduction | 829 |
| 15.2 | Eigenvalue problem for the transverse vibrations of a beam | 830 |
| 15.3 | General eigenvalue problem for a continuous system | 834 |
| 15.4 | Expansion theorem | 838 |
| 15.5 | Frequencies and mode shapes for lateral vibrations of a beam | 839 |
| 15.6 | Effect of shear deformation and rotatory inertia on the frequencies of flexural vibrations | 848 |
| 15.7 | Frequencies and mode shapes for the axial vibrations of a bar | 852 |
| 15.8 | Frequencies and mode shapes for the transverse vibration of a string | 863 |
| 15.9 | Boundary conditions containing the eigenvalue | 865 |
| 15.10 | Free-vibration response of a continuous system | 871 |
| 15.11 | Undamped free transverse vibrations of a beam | 873 |
| 15.12 | Damped free transverse vibrations of a beam | 876 |
| 16 | Continuous Systems: Forced-Vibration Response | 879 |
| 16.1 | Introduction | 879 |
| 16.2 | Normal coordinate transformation: general case of an undamped system | 880 |
| 16.3 | Forced lateral vibration of a beam | 883 |
| 16.4 | Transverse vibrations of a beam under traveling load | 886 |
| 16.5 | Forced axial vibrations of a uniform bar | 889 |
| 16.6 | Normal coordinate transformation, damped case | 899 |
| 17 | Wave Propagation Analysis | 907 |
| 17.1 | Introduction | 907 |
| 17.2 | The phenomenon of wave propagation | 908 |
| 17.3 | Harmonic waves | 910 |
| 17.4 | One-dimensional wave equation and its solution | 914 |
| 17.5 | Propagation of waves in systems of finite extent | 919 |
| 17.6 | Reflection and refraction of waves at a discontinuity in the system properties | 928 |
| 17.7 | Characteristics of the wave equation | 933 |
| 17.8 | Wave dispersion | 935 |
| Answers to Selected Problems | 945 | |
| Index | 959 |