[内容简介]

This textbook provides the student of aerospace, civil, or mechanical engineering with all the fundamentals of linear structural dynamics analysis and scattered discussions of non-linear structural dynamics, it is designed to be used primarily for a first-year graduate course. This textbook is a departure from the usual presentation of this material in two important respects. First, descriptions of system dynamics throughout are based on the simpler-to-use Lagrange equations of motion. Second, no organizational distinction is made between single- and multiple-degree-of-freedom systems. In support of these two choices, the first three chapters review the needed skills in dynamics and finite element structural analysis. The remainder of the textbook is organized mostly on the basis of first writing structural system equations of motion, and then solving those equations. The modal method of solution is emphasized, but other approaches are also considered. This textbook covers more material than can reasonably be taught in one semester. Topics that can be put off for later study are generally placed in sections designated by double asterisks or in endnotes. The final two chapters can also be deferred for later study. The textbook contains numerous example problems and end-of-chapter exercises.

[目录]

Preface for the Student     xi
Preface for the Instructor     xv
Acknowledgments     xvii
List of Symbols     xix
The Lagrange Equations of Motion     1
Introduction     1
Newton's Laws of Motion     2
Newton's Equations for Rotations     5
Simplifications for Rotations     8
Conservation Laws     12
Generalized Coordinates     12
Virtual Quantities and the Variational Operator     15
The Lagrange Equations     19
Kinetic Energy     25
Summary     29
Exercises     33
Further Explanation of the Variational Operator     37
Kinetic Energy and Energy Dissipation     41
A Rigid Body Dynamics Example Problem     42
Mechanical Vibrations: Practice Using the Lagrange Equations     46
Introduction     46
Techniques of Analysis for Pendulum Systems     47
Example Problems     53
Interpreting Solutions to Pendulum Equations     66
Linearizing Differential Equations for Small Deflections     71
Summary     72
**Conservation of Energy versus the Lagrange Equations**     73
**Nasty Equations of Motion**     80
**Stability of Vibratory Systems**     82
Exercises     85
The Large-Deflection, Simple Pendulum Solution     93
Divergence and Flutter in Multidegree of Freedom, Force Free Systems     94
Review of the Basics of the Finite Element Method for Simple Elements     99
Introduction     99
Generalized Coordinates for Deformable Bodies     100
Element and Global Stiffness Matrices     103
More Beam Element Stiffness Matrices     112
Summary     123
Exercises     133
A Simple Two-Dimensional Finite Element     138
The Curved Beam Finite Element     146
FEM Equations of Motion for Elastic Systems     157
Introduction     157
Structural Dynamic Modeling     158
Isolating Dynamic from Static Loads     163
Finite Element Equations of Motion for Structures     165
Finite Element Example Problems     172
Summary     186
**Offset Elastic Elements**     193
Exercises     195
Mass Refinement Natural Frequency Results     205
The Rayleigh Quotient     206
The Matrix Form of the Lagrange Equations     210
The Consistent Mass Matrix     210
A Beam Cross Section with Equal Bending and Twisting Stiffness Coefficients     211
Damped Structural Systems     213
Introduction     213
Descriptions of Damping Forces     213
The Response of a Viscously Damped Oscillator to a Harmonic Loading     230
Equivalent Viscous Damping     239
Measuring Damping     242
Example Problems     243
Harmonic Excitation of Multidegree of Freedom Systems     247
Summary     248
Exercises     253
A Real Function Solution to a Harmonic Input     260
Natural Frequencies and Mode Shapes     263
Introduction     263
Natural Frequencies by the Determinant Method     265
Mode Shapes by Use of the Determinant Method     273
**Repeated Natural Frequencies**     279
Orthogonality and the Expansion Theorem     289
The Matrix Iteration Method     293
**Higher Modes by Matrix Iteration**     300
Other Eigenvalue Problem Procedures     307
Summary     311
**Modal Tuning**     315
Exercises      320
Linearly Independent Quantities     323
The Cholesky Decomposition     324
Constant Momentum Transformations     326
Illustration of Jacobi's Method     329
The Gram-Schmidt Process for Creating Orthogonal Vectors     332
The Modal Transformation     334
Introduction     334
Initial Conditions     334
The Modal Transformation     337
Harmonic Loading Revisited     340
Impulsive and Sudden Loadings     342
The Modal Solution for a General Type of Loading     351
Example Problems     353
Random Vibration Analyses     363
Selecting Mode Shapes and Solution Convergence     366
Summary     371
**Aeroelasticity**     373
**Response Spectrums**     388
Exercises     391
Verification of the Duhamel Integral Solution     396
A Rayleigh Analysis Example     398
An Example of the Accuracy of Basic Strip Theory     399
Nonlinear Vibrations     400
Continuous Dynamic Models     402
Introduction     402
Derivation of the Beam Bending Equation     402
Modal Frequencies and Mode Shapes for Continuous Models     406
Conclusion     431
Exercises     438
The Long Beam and Thin Plate Differential Equations     439
Derivation of the Beam Equation of Motion Using Hamilton's Principle     442
Sturm-Liouvilie Problems     445
The Bessel Equation and Its Solutions     445
Nonhomogeneous Boundary Conditions     449
Numerical Integration of the Equations of Motion     451
Introduction     451
The Finite Difference Method     452
Assumed Acceleration Techniques     460
Predictor-Corrector Methods     463
The Runge-Kutta Method     468
Summary     474
**Matrix Function Solutions**     475
Exercises     480
Answers to Exercises     483
Solutions     483
Solutions     486
Solutions     494
Solutions     498
Solutions     509
Solutions     516
Solutions     519
Solutions     525
Solutions     529
Fourier Transform Pairs     531
Introduction to Fourier Transforms     531
Index      537