Vibrations, Dynamics and Structural Systems 2nd edition

by Mukhopadhyay,Madhujit

• ISBN13: 9789058092212
• ISBN10: 9058092216
• Edition: Student
• Format: Nonspecific Binding
• Copyright: 2000-01-01
• Publisher: CRC Press

Summary

This textbook is the student edition of the work on vibrations, dynamics and structural systems. There are exercises included at the end of each chapter.

Table of Contents

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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