Introduction to Structural Dynamics

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Hardcover | 23 October 2006

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566 Pages

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25.4 x 17.78 x 3.18

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This textbook, first published in 2006, provides the student of aerospace, civil and mechanical engineering with all the fundamentals of linear structural dynamics analysis. It is designed for an advanced undergraduate or first-year graduate course. This textbook is a departure from the usual presentation in two important respects. First, descriptions of system dynamics are based on the simpler to use Lagrange equations. Second, no organizational distinctions are made between multi-degree of freedom systems and single-degree of freedom systems. The textbook is organized on the basis of first writing structural equation systems of motion, and then solving those equations mostly by means of a modal transformation. The text contains more material than is commonly taught in one semester so advanced topics are designated by an asterisk. The final two chapters can also be deferred for later studies. The text contains numerous examples and end-of-chapter exercises.

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Non-Fiction Engineering & Technology Civil Engineering Structural Engineering Technology in General Engineering in General Transport Technology & Trades Aerospace & Aviation Technology Mechanical Engineering & Materials Mechanical Engineering

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

Introduction to Structural Dynamics

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Hardcover

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