| Preface to second edition | p. vii |
| Preface to first edition | p. ix |
| Introduction | |
| Introduction | p. 1 |
| Brief History of Vibrations | p. 2 |
| Comparison between Static and Dynamic Analysis | p. 4 |
| D'Alembert's Principle | p. 5 |
| Some Basic Definitions | p. 5 |
| Dynamic Loading | p. 9 |
| Finite Element Discretization | p. 10 |
| Response of the System | p. 11 |
| Types of Analysis | p. 11 |
| Linear and Nonlinear Vibration | p. 12 |
| References | p. 12 |
| Free Vibration of Single Degree of Freedom System | |
| Introduction | p. 14 |
| Equation of Motion of Single Degree of Freedom (SDF) System | p. 14 |
| Free Undamped Vibration of the SDF System | p. 17 |
| Free Damped Vibration of SDF System | p. 26 |
| Free Vibration with Coulomb Damping | p. 33 |
| Energy Method and Free Torsional Vibration | p. 35 |
| Logarithmic Decrement | p. 43 |
| References | p. 47 |
| Exercise 2 | p. 48 |
| Forced Vibration of Single Degree of Freedom System | |
| Introduction | p. 56 |
| Response of Damped Systems to Harmonic Loading | p. 56 |
| Rotating Unbalance | p. 65 |
| Reciprocating unbalance | p. 67 |
| Whirling of Rotating Shafts | p. 69 |
| Vibration Isolation and Transmissibility | p. 70 |
| Energy Dissipation by Damping | p. 74 |
| Equivalent Viscous Damping | p. 78 |
| Self-excited Vibrations | p. 79 |
| Vibration Measuring Seismic Instruments | p. 82 |
| Response of Structures due to Transient Vibration | p. 86 |
| Response of the SDF System to a General Type of Forcing Function | p. 89 |
| Dynamic Load Factor and Response Spectrum | p. 92 |
| Response due to Periodic Forces | p. 93 |
| Response due to Nonperiodic Excitation | p. 101 |
| Relationship between Complex Frequency Response Function and Unit Impluse Response Function | p. 104 |
| Support Motion | p. 105 |
| Response of SDF Systems Related to Earthquakes | p. 107 |
| Techniques for Analysing Earthquake Response | p. 110 |
| References | p. 114 |
| Exercise 3 | p. 115 |
| Numerical Methods in Structural Analysis: Applied to SDF Systems | |
| Introduction | p. 124 |
| Direct Integral Techniques | p. 124 |
| Numerical Evaluation of Duhamel's Integral | p. 137 |
| Numerical Computation in Frequency Domain | p. 142 |
| References | p. 146 |
| Exercise 4 | p. 147 |
| Vibration of Two Degrees of Freedom System | |
| Introduction | p. 150 |
| Free Vibration of Undamped Two Degrees of Freedom Systems | p. 150 |
| Torsional Vibration of Two Degrees of Freedom System | p. 154 |
| Forced Vibration of Two Degrees of Freedom Undamped System | p. 155 |
| Vibration Absorber | p. 156 |
| Free Vibration of Two Degrees of Freedom System with Viscous Damping | p. 161 |
| Coordinate Coupling | p. 162 |
| Free Vibration of Damped Two Degrees of Freedom System | p. 164 |
| References | p. 169 |
| Exercise 5 | p. 169 |
| Free Vibration of Multiple Degrees of Freedom System | |
| Introduction | p. 174 |
| Equations of Motion of MDF Systems | p. 174 |
| Free Undamped Vibration Analysis of MDF systems | p. 177 |
| Orthogonality Relationship | p. 178 |
| Eigenvalue Problem | p. 180 |
| Determination of Absolute Displacement of Free Vibration of MDF Systems | p. 181 |
| Eigenvalue Solution Techniques | p. 186 |
| Dunkerley's Equation | p. 187 |
| Holzer Method | p. 190 |
| Transfer Matrix Method | p. 194 |
| Myklestad Method | p. 201 |
| Stodola's Method | p. 206 |
| Matrix Deflation Procedure | p. 214 |
| Rayleigh's Method | p. 217 |
| Rayleigh-Ritz Method | p. 219 |
| Subspace Iteration Method | p. 221 |
| Simultaneous Iteration Method and Algorithm | p. 222 |
| Geared Systems | p. 223 |
| Branched Systems | p. 224 |
| Reduction Methods for Dynamic Analysis | p. 226 |
| Component Mode Synthesis Method | p. 231 |
| Lagrange's Equation | p. 237 |
| References | p. 239 |
| Exercise 6 | p. 240 |
| Forced Vibration Analysis of Multiple Degrees of Freedom System | |
| Introduction | p. 246 |
| Mode Superposition Method for the Determination of Response of MDF System | p. 246 |
| Mode Acceleration Method for the Determination of Response of MDF System | p. 250 |
| Response of MDF Systems under the Action of Transient Forces | p. 252 |
| Damping in MDF Systems | p. 257 |
| Response of MDF Systems to Support Motion | p. 266 |
| Earthquake Spectrum Analysis of Structures having MDF Systems | p. 269 |
| Use of Response Spectra for Designing MDF Systems | p. 271 |
| Direct Integration for Determining Response of MDF Systems | p. 275 |
| Complex Matrix Inversion Method for Forced Vibration Analysis of MDF Systems | p. 279 |
| Frequency Domain Analysis of MDF Systems by Modal Superposition for Harmonic Loads | p. 280 |
| Frequency Domain Analysis of Direct Frequency Response Method | p. 282 |
| References | p. 284 |
| Exercise 7 | p. 284 |
| Free Vibration Analysis of Continuous Systems | |
| Introduction | p. 289 |
| Vibration of Strings | p. 289 |
| Free Longitudinal Vibration of a Bar | p. 295 |
| Free Torsional Vibration of the Shaft | p. 299 |
| Free Flexural Vibration of Beams | p. 302 |
| Free Flexural Vibration of Simply Supported Beam | p. 304 |
| Free Flexural Vibration of Beams with Other End Conditions | p. 306 |
| Free Flexural Vibration of Beams with General End Conditions | p. 308 |
| Orthogonality Properties of Normal Modes | p. 314 |
| Effect of Rotary Inertia on the Free Flexural Vibration of Beams | p. 317 |
| Free Vibration of the Shear Beam | p. 320 |
| Effect of Axial Force on the Free Flexural Vibration of Beams | p. 322 |
| Free Vibration of Beams Including Shear Deformation and Rotary Inertia Effects | p. 324 |
| Collocation Method for Obtaining Normal Modes of Vibration of a Continuous Systems | p. 327 |
| Rayleigh's Quotient for Fundamental Frequency | p. 331 |
| Rayleigh-Ritz Method for Determining Natural Frequencies for Continuous Systems | p. 333 |
| Vibration of Membranes | p. 336 |
| Transverse Vibration of Rectangular Thin Plates | p. 339 |
| References | p. 345 |
| Exercise 8 | p. 345 |
| Forced Vibration of Continuous Systems | |
| Introduction | p. 349 |
| Forced Axial Vibration of Bars | p. 349 |
| Forced Vibration of the Shear Beam under Ground Motion Excitation | p. 352 |
| Forced Vibration of Flexural Member | p. 355 |
| Forced Transverse Vibration of Uniform Damped Beam | p. 359 |
| Forced Vibration of Flexural Member subjected to Ground Motion Excitation | p. 360 |
| Response of Beams due to Moving Loads | p. 362 |
| References | p. 365 |
| Exercise 9 | p. 366 |
| Dynamic Direct Stiffness Method | |
| Introduction | p. 371 |
| Continuous Beam | p. 371 |
| Method Analogous to Classical Methods in Statical Analysis | p. 374 |
| Dynamic Stiffness Matrix in Bending | p. 376 |
| Dynamic Stiffness Matrix for Flexural and Rigid Axial Displacements | p. 382 |
| Dynamic Stiffness Matrix of a Bar Undergoing Axial Deformation | p. 385 |
| Dynamic Stiffness Matrix of a Bar subjected to Axial and Bending Deformation | p. 386 |
| Beam Segments with Distributed Mass Having Shear Deformation and Rotary Inertia | p. 390 |
| References | p. 395 |
| Exercise 10 | p. 395 |
| Vibration of Ship and Aircraft as a Beam | |
| Introduction | p. 397 |
| Shift in Stiffness Matrix | p. 397 |
| Added Mass of a Ship | p. 398 |
| Flexibility Matrix Method for Determining Natural Frequencies of a Free-free Beam in Vertical Vibration | p. 400 |
| Flexibility Matrix Method for the Analysis of Coupled Horizontal and Torsional Vibration | p. 405 |
| Numerical Examples | p. 409 |
| References | p. 412 |
| Exercise 11 | p. 412 |
| Finite Element Method in Vibration Analysis | |
| Introduction to the Finite Element Method | p. 414 |
| Torsional Vibration of Shafts | p. 414 |
| Axial Vibration of Rods | p. 418 |
| Flexural Vibration of Beams | p. 421 |
| Vibration of Timoshenko Beams | p. 424 |
| Inplane Vibration of Plates | p. 429 |
| Flexural Vibration of Plates | p. 436 |
| Flexural Vibrations of Plates using Isoparametric Elements | p. 438 |
| Periodic Structures | p. 446 |
| References | p. 457 |
| Exercise 12 | p. 459 |
| Finite Difference Method for the Vibration Analysis of Beams and Plates | |
| Introduction to the Finite Difference Method | p. 462 |
| Central Difference Method | p. 462 |
| Free Vibration of Beams | p. 464 |
| Free Vibration of Rectangular Plates | p. 466 |
| Semianalytic Finite Difference Method for Free Vibration Analysis of Rectangular Plates | p. 468 |
| Semianalytic Finite Difference Method for Forced Vibration Analysis of Plates | p. 471 |
| Spline Finite Strip Method of Analysis of Plate Vibration | p. 474 |
| References | p. 484 |
| Exercise 13 | p. 485 |
| Nonlinear Vibration | |
| Introduction | p. 486 |
| Perturbation Method | p. 487 |
| Step-by-Step Integration | p. 490 |
| References | p. 495 |
| Random Vibrations | |
| Introduction | p. 496 |
| Random Process | p. 496 |
| Probability Distributions | p. 497 |
| Ensemble Averages, Mean and Autocorrelation | p. 501 |
| Stationary Process, Ergodic Process and Temporal Averages | p. 504 |
| Power Spectral Density | p. 507 |
| Relationship between Autocorrelation Function and Power Spectral Density | p. 508 |
| Random Response of SDF Systems | p. 511 |
| Random Response of MDF Systems | p. 514 |
| Response of Flexural Beams under Random Loading | p. 519 |
| Finite Element Random Response of Plates | p. 521 |
| References | p. 525 |
| Exercise 15 | p. 526 |
| Computer Programme in Vibration Analysis | |
| Introduction | p. 529 |
| Computer Programme for Forced Vibration Analysis | p. 529 |
| Computer Programme for Random Vibration Analysis | p. 530 |
| Computer Programme for Free Vibration Analysis of Framed Structures | p. 532 |
| Computer Programme for Free Vibration Analysis of Ships by Flexibility Matrix Method | p. 552 |
| Computer Programme for the Free Vibration Analysis of Plates | p. 559 |
| References | p. 572 |
| The Stiffness Matrix | |
| Stiffness Matrix | p. 573 |
| Direct Stiffness Method | p. 574 |
| Table for Spring Stiffness | p. 581 |
| Index | p. 582 |
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