| 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 |
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