Structural dynamics : vibrations and systems.
Mukhopadhyay, Madhujit
Structural dynamics : vibrations and systems. - New Delhi Ane Books 2006 - xv,556p.
Contents Preface vii Chapter 1 INTRODUCTION 1.1 Introduction 1 1.2 Brief History of Vibrations 1 1.3 Comparison between Static and Dynamic Analyses 3 1.4 D'Alembert's Principle 4 1.5 Some Basic Definitions 5 1.6 Dynamic Loading 7 1.7 Finite Element Discretization 8 1.8 Response of the System 10 1.9 Types of Analysis 10 1.10 Linear and Nonlinear Vibration 10 References 11 Chapter 2 FREE VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEM 2.1 Introduction 13 2.2 Equation of Motion of Single Degree of Freedom (SDF) System 13 2.3 Free Undamped Vibration of the SDF System 16 2.4 Free Damped Vibration of SDF System 24 2.5 Free Vibration with Coulomb Damping 30 2.6 Energy Method and Free Torsional Vibration 32 2.7 Logarithmic Decrement 38 References 43 Exercise 2 44 Chapter 3 FORCED VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEM 3.1 Introduction 51 3.2 Response of Damped Systems to Harmonic Loading 51 3.3 Rotating Unbalance 59 3.4 Reciprocating unbalance 61 3.5 Whirling of Rotating Shafts 62 3.6 Vibration Isolation and Transmissibility 64 3.7 Energy Dissipation by Damping 68 3.8 Equivalent Viscous Damping 71 3.9 Self-excited Vibrations 72 3.10 Vibration Measuring Seismic Instruments 75 3.11 Response of Structures due to Transient Vibration 79 3.12 Response of the SDF System to a General Type of Forcing Function 81 3.13 Dynamic Load Factor and Response Spectrum 83 3.14 Response due to Periodic Forces 84 3.15 Response due to Nonperiodic Excitation 91 3.16 Relationship between Complex Frequency Response Function and Unit Impluse Response Function 3.17 Support Motion 3.18 Response of SDF Systems Related to Earthquakes 3.19 Techniques for Analysing Earthquake Response References Exercise 3 Chapter 4 NUMERICAL METHODS IN STRUCTURAL ANALYSIS : APPLIED TO SDF SYSTEMS 4.1 Introduction 113 4.2 Direct Integration Techniques 113 4.3 Numerical Evaluation of DuhameF s Integral 125 4.4 Numerical Computation in Frequency Domain 129 References 134 Exercise 4 135 Chapter 5VIBRATION OF TWO DEGREES OF FREEDOM SYSTEM 5.1 Introduction 137 5.2 Free Vibration of Undamped Two Degrees of Freedom Systems 137 5.3 Torsional Vibration of Two Degrees of Freedom System 140 5.4 Forced Vibration of Two Degrees of Freedom Undamped System 142 5.5 Vibration Absorber 143 5.6 Free Vibration of Two Degrees of Freedom System with Viscous Damping147 5.7 Coordinate Coupling 147 5.8 Free Vibration of Damped Two Degrees of Freedom System 149 References 155 Exercise 5 156 Chapter 6 FREE VIBRATION OF MULTIPLE DEGREES OF FREEDOM SYSTEM 6.1 Introduction 161 6.2 Equations of Motion of MDF Systems 161 6.3 Free Undamped Vibration Analysis of MDF systems 163 6.4 Orthogonality Relationship 165 6.5 Eigenvalue Problem 167 6.6 Determination of Absolute Displacement of Free Vibration of MDF Systems 167 6.7 Eigenvalue Solution Techniques 171 6.8 Dunkerley's Equation 173 6.9 Holzer Method 175 6.10 Transfer Matrix Method 178 6.11 Myklestad Method 184 6.12 Stodola's Method 189 6.13 Matrix Deflation Procedure 196 6.14 Rayleigh's Method 199 6.15 Rayleigh-Ritz Method 200 6.16 Subspace Iteration Method 202 6.17 Simultaneous Iteration Method and Algorithm203 6.18 Geared Systems 2O4 6.19 Branched Systems 205 6.20 Reduction Methods for Dynamic Analysis 206 6.21 Component Mode Synthesis Method 211 6.22 Lagrange's Equation 217 References 219 Exercise 6 220 Chapter 7 FORCED VIBRATION ANALYSIS OF MULTIPLE DEGREES OF FREEDOM SYSTEM 7.1 Introduction 225 7.2 Mode Superposition Method for the Determination of Response of MDF System 225 7.3 Mode Acceleration Method for the Determination of Response of MDF System 229 7.4 Response of MDF Systems under the Action of Transient Forces 230 7.5 Damping in MDF Systems 235 7.6 Response of MDF Systems to Support Motion 243 7.7 Earthquake Spectrum Analysis of Structures having MDF Systems 246 7.8 Use of Response Spectra for Designing MDF Systems 248 7.9 Direct Integration for Determining Response of MDF Systems 251 7.10 Complex Matrix Inversion Method for Forced Vibration Analysis of MDF Systems 254 7.11 Frequency Domain Analysis of MDF Systems by Modal Superposition for Harmonic Loads 255 7.12 Frequency Domain Analysis of Direct Frequency Response Method 258 References 260 Exercise 7 261 Chapter 8 FREE VIBRATION ANALYSIS OF CONTINUOUS SYSTEMS 8.1 Introduction 265 8.2 Vibration of Strings 265 8.3 Free Longitudinal Vibration of a Bar 271 8.4 Free Torsional Vibration of the Shaft 275 8.5 Free Flexural Vibration of Beams 277 8.6 Free Flexural Vibration of Simply Supported Beam 279 8.7 Free Flexural Vibration of Beams with Other End Conditions 281 8.8 Free Flexural Vibration of Beams with General End Conditions 283 8.9 Orthogonality Properties of Normal Modes 287 8.10 Effect of Rotary Inertia on the Free Flexural Vibration of Beams 291 8.11Free Vibration of the Shear Beam 294 I 8.12 Effect of Axial Force on the Free Flexural Vibration of Beams 296 8.13 Free Vibration of Beams Including Shear Deformation and Rotary Inertia Effects 298 8.14 Collocation Method for Obtaining Normal Modes of Vibration of a Continuous Systems 300 8.15 Rayleigh's Quotient for Fundamental Frequency 304 8.16 Rayleigh-Ritz Method for Determining Natural Frequencies for Continuous Systems 306 8.17 Vibration of Membranes 309 8.18 Transverse Vibration of Rectangular Thin Plates 312 References 318 Exercise 8 M5LJ5I 319 Chapter 9 FORCED VIBRATION OF CONTINUOUS SYSTEMS 9.1 Introduction 321 9.2 Forced Axial Vibration of Bars 321 '9.3 Forced Vibration of the Shear Beam under Ground Motion Excitation 324 9.4 Forced Vibration of Flexural Member 326 9.5 Forced Transverse Vibration of Uniform Damped Beam 330 9.6 Forced Vibration of Flexural Member subjected to Ground Motion Excitation 332 9.7 Response of Beams due to Moving Loads 334 References 337 Exercise 9 338 Chapter 10 DYNAMIC DIRECT STIFFNESS METHOD 10.1Introduction 343 10.2 Continuous Beam 343 10.3 Method Analogous to Classical Methods in Statical Analysis 346 10.4 Dynamic Stiffness Matrix in Bending 348 10.5 Dynamic Stiffness Matrix for Flexural and Rigid Axial Displacements 354 10.6 Dynamic Stiffness Matrix of a Bar Undergoing Axial Deformation 356 10.7 Dynamic Stiffness Matrix of a Bar subjected to Axial and Bending Deformation 358 10.8 Beam Segments with Distributed Mass Having Shear Deformation and Rotary Inertia 361 References 366 Exercise 10 367 Chapter 11 VIBRATION OF SHIP AND AIRCRAFT AS A BEAM 11.1 Introduction 369 11.2 Shift in Stiffness Matrix 369 11.3 Added Mass of a Ship 369 11.4 Flexibility Matrix Method for Determining Natural Frequencies of a Free-free Beam in Vertical Vibration 372 11.5 Flexibility Matrix Method for the Analysis of Coupled Horizontal and Torsional Vibration377 11.6 Numerical Examples 381 References 384 Exercise 11 385 Chapter 12 FINITE ELEMENT METHOD IN VIBRATION ANALYSIS 12.1 Introduction to the Finite Element Method 387 12.2 Torsional Vibration of Shafts 387 12.3 Axial Vibration of Rods 391 12.4 Flexural Vibration of Beams 394 12.5 Vibration of Timoshenko Beams 397 12.6 Inplane Vibration of Plates 402 12.7 Flexural Vibration of Plates 407 12.8 Flexural Vibrations of Plates using Isoparametric Elements 411 12.9 Periodic Structures 418 References 429 Exercise 12 431 Chapter 13 FINITE DIFFERENCE METHOD FOR THE VIBRATION ANALYSIS OF BEAMS AND PLATES 13.1 Introduction to the Finite Difference Method 433 13.2 Central Difference Method 433 13.3 Free Vibration of Beams 435 13.4 Free Vibration of Rectangular Plates 437 13.5 Semianalytic Finite Difference Method for Free Vibration Analysis of Rectangular Plates 439 13.6 Semianalytic Finite Difference Method for Forced Vibration Analysis of Plates 442 13.7 Spline Finite Strip Method of Analysis of Plate Vibration 444 References 454 Exercise 13 455 Chapter 14 NONLINEAR VIBRATION 14.1Introduction 457 14.2 Perturbation Method 458 14.3 Step-by-Step Integration 461 References 466 Chapter 15 RANDOM VIBRATIONS 15.1 Introduction 467 15.2 Random Process 467 15.3 Probability Distributions 468 15.4 Ensemble Averages, Mean and Autocorrelation 472 15.5 Stationary Process, Ergodic Process and Temporal Averages 474 15.6 Power Spectral Density 477 15.7 Relationship between Autocorrelation Function and Power Spectral Density 478 Random Response of SDF Systems 481 Random Response of MDF Systems 484 15.10 Response of Flexural Beams under Random Loading 489 15.11 Finite Element Random Response of Plates 490 References 495 Exercise 15 496 Chapter 16 COMPUTER PROGRAM IN VIBRATION ANALYSIS 16.1Introduction* 499 16.2 Computer Program for Forced Vibration Analysis 499 16.3 Computer Program for Random Vibration Analysis 499 16.4 Computer Program for Free Vibration Analysis of Framed Structures 501 16.5 Computer Program for Free Vibration Analysis of Ships by Flexibility Matrix Method 521 16.6 Computer Program for the Free Vibration Analysis of Plates 527 References 541 Appendix A :THE STIFFNESS MATRIX A. 1 Stiffness Matrix 543 A.2Direct Stiffness Method 544 Appendix B :TABLE FOR SPRING STIFFNESS 551 Index 553
8180520900
624.176 / MUK
Structural dynamics : vibrations and systems. - New Delhi Ane Books 2006 - xv,556p.
Contents Preface vii Chapter 1 INTRODUCTION 1.1 Introduction 1 1.2 Brief History of Vibrations 1 1.3 Comparison between Static and Dynamic Analyses 3 1.4 D'Alembert's Principle 4 1.5 Some Basic Definitions 5 1.6 Dynamic Loading 7 1.7 Finite Element Discretization 8 1.8 Response of the System 10 1.9 Types of Analysis 10 1.10 Linear and Nonlinear Vibration 10 References 11 Chapter 2 FREE VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEM 2.1 Introduction 13 2.2 Equation of Motion of Single Degree of Freedom (SDF) System 13 2.3 Free Undamped Vibration of the SDF System 16 2.4 Free Damped Vibration of SDF System 24 2.5 Free Vibration with Coulomb Damping 30 2.6 Energy Method and Free Torsional Vibration 32 2.7 Logarithmic Decrement 38 References 43 Exercise 2 44 Chapter 3 FORCED VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEM 3.1 Introduction 51 3.2 Response of Damped Systems to Harmonic Loading 51 3.3 Rotating Unbalance 59 3.4 Reciprocating unbalance 61 3.5 Whirling of Rotating Shafts 62 3.6 Vibration Isolation and Transmissibility 64 3.7 Energy Dissipation by Damping 68 3.8 Equivalent Viscous Damping 71 3.9 Self-excited Vibrations 72 3.10 Vibration Measuring Seismic Instruments 75 3.11 Response of Structures due to Transient Vibration 79 3.12 Response of the SDF System to a General Type of Forcing Function 81 3.13 Dynamic Load Factor and Response Spectrum 83 3.14 Response due to Periodic Forces 84 3.15 Response due to Nonperiodic Excitation 91 3.16 Relationship between Complex Frequency Response Function and Unit Impluse Response Function 3.17 Support Motion 3.18 Response of SDF Systems Related to Earthquakes 3.19 Techniques for Analysing Earthquake Response References Exercise 3 Chapter 4 NUMERICAL METHODS IN STRUCTURAL ANALYSIS : APPLIED TO SDF SYSTEMS 4.1 Introduction 113 4.2 Direct Integration Techniques 113 4.3 Numerical Evaluation of DuhameF s Integral 125 4.4 Numerical Computation in Frequency Domain 129 References 134 Exercise 4 135 Chapter 5VIBRATION OF TWO DEGREES OF FREEDOM SYSTEM 5.1 Introduction 137 5.2 Free Vibration of Undamped Two Degrees of Freedom Systems 137 5.3 Torsional Vibration of Two Degrees of Freedom System 140 5.4 Forced Vibration of Two Degrees of Freedom Undamped System 142 5.5 Vibration Absorber 143 5.6 Free Vibration of Two Degrees of Freedom System with Viscous Damping147 5.7 Coordinate Coupling 147 5.8 Free Vibration of Damped Two Degrees of Freedom System 149 References 155 Exercise 5 156 Chapter 6 FREE VIBRATION OF MULTIPLE DEGREES OF FREEDOM SYSTEM 6.1 Introduction 161 6.2 Equations of Motion of MDF Systems 161 6.3 Free Undamped Vibration Analysis of MDF systems 163 6.4 Orthogonality Relationship 165 6.5 Eigenvalue Problem 167 6.6 Determination of Absolute Displacement of Free Vibration of MDF Systems 167 6.7 Eigenvalue Solution Techniques 171 6.8 Dunkerley's Equation 173 6.9 Holzer Method 175 6.10 Transfer Matrix Method 178 6.11 Myklestad Method 184 6.12 Stodola's Method 189 6.13 Matrix Deflation Procedure 196 6.14 Rayleigh's Method 199 6.15 Rayleigh-Ritz Method 200 6.16 Subspace Iteration Method 202 6.17 Simultaneous Iteration Method and Algorithm203 6.18 Geared Systems 2O4 6.19 Branched Systems 205 6.20 Reduction Methods for Dynamic Analysis 206 6.21 Component Mode Synthesis Method 211 6.22 Lagrange's Equation 217 References 219 Exercise 6 220 Chapter 7 FORCED VIBRATION ANALYSIS OF MULTIPLE DEGREES OF FREEDOM SYSTEM 7.1 Introduction 225 7.2 Mode Superposition Method for the Determination of Response of MDF System 225 7.3 Mode Acceleration Method for the Determination of Response of MDF System 229 7.4 Response of MDF Systems under the Action of Transient Forces 230 7.5 Damping in MDF Systems 235 7.6 Response of MDF Systems to Support Motion 243 7.7 Earthquake Spectrum Analysis of Structures having MDF Systems 246 7.8 Use of Response Spectra for Designing MDF Systems 248 7.9 Direct Integration for Determining Response of MDF Systems 251 7.10 Complex Matrix Inversion Method for Forced Vibration Analysis of MDF Systems 254 7.11 Frequency Domain Analysis of MDF Systems by Modal Superposition for Harmonic Loads 255 7.12 Frequency Domain Analysis of Direct Frequency Response Method 258 References 260 Exercise 7 261 Chapter 8 FREE VIBRATION ANALYSIS OF CONTINUOUS SYSTEMS 8.1 Introduction 265 8.2 Vibration of Strings 265 8.3 Free Longitudinal Vibration of a Bar 271 8.4 Free Torsional Vibration of the Shaft 275 8.5 Free Flexural Vibration of Beams 277 8.6 Free Flexural Vibration of Simply Supported Beam 279 8.7 Free Flexural Vibration of Beams with Other End Conditions 281 8.8 Free Flexural Vibration of Beams with General End Conditions 283 8.9 Orthogonality Properties of Normal Modes 287 8.10 Effect of Rotary Inertia on the Free Flexural Vibration of Beams 291 8.11Free Vibration of the Shear Beam 294 I 8.12 Effect of Axial Force on the Free Flexural Vibration of Beams 296 8.13 Free Vibration of Beams Including Shear Deformation and Rotary Inertia Effects 298 8.14 Collocation Method for Obtaining Normal Modes of Vibration of a Continuous Systems 300 8.15 Rayleigh's Quotient for Fundamental Frequency 304 8.16 Rayleigh-Ritz Method for Determining Natural Frequencies for Continuous Systems 306 8.17 Vibration of Membranes 309 8.18 Transverse Vibration of Rectangular Thin Plates 312 References 318 Exercise 8 M5LJ5I 319 Chapter 9 FORCED VIBRATION OF CONTINUOUS SYSTEMS 9.1 Introduction 321 9.2 Forced Axial Vibration of Bars 321 '9.3 Forced Vibration of the Shear Beam under Ground Motion Excitation 324 9.4 Forced Vibration of Flexural Member 326 9.5 Forced Transverse Vibration of Uniform Damped Beam 330 9.6 Forced Vibration of Flexural Member subjected to Ground Motion Excitation 332 9.7 Response of Beams due to Moving Loads 334 References 337 Exercise 9 338 Chapter 10 DYNAMIC DIRECT STIFFNESS METHOD 10.1Introduction 343 10.2 Continuous Beam 343 10.3 Method Analogous to Classical Methods in Statical Analysis 346 10.4 Dynamic Stiffness Matrix in Bending 348 10.5 Dynamic Stiffness Matrix for Flexural and Rigid Axial Displacements 354 10.6 Dynamic Stiffness Matrix of a Bar Undergoing Axial Deformation 356 10.7 Dynamic Stiffness Matrix of a Bar subjected to Axial and Bending Deformation 358 10.8 Beam Segments with Distributed Mass Having Shear Deformation and Rotary Inertia 361 References 366 Exercise 10 367 Chapter 11 VIBRATION OF SHIP AND AIRCRAFT AS A BEAM 11.1 Introduction 369 11.2 Shift in Stiffness Matrix 369 11.3 Added Mass of a Ship 369 11.4 Flexibility Matrix Method for Determining Natural Frequencies of a Free-free Beam in Vertical Vibration 372 11.5 Flexibility Matrix Method for the Analysis of Coupled Horizontal and Torsional Vibration377 11.6 Numerical Examples 381 References 384 Exercise 11 385 Chapter 12 FINITE ELEMENT METHOD IN VIBRATION ANALYSIS 12.1 Introduction to the Finite Element Method 387 12.2 Torsional Vibration of Shafts 387 12.3 Axial Vibration of Rods 391 12.4 Flexural Vibration of Beams 394 12.5 Vibration of Timoshenko Beams 397 12.6 Inplane Vibration of Plates 402 12.7 Flexural Vibration of Plates 407 12.8 Flexural Vibrations of Plates using Isoparametric Elements 411 12.9 Periodic Structures 418 References 429 Exercise 12 431 Chapter 13 FINITE DIFFERENCE METHOD FOR THE VIBRATION ANALYSIS OF BEAMS AND PLATES 13.1 Introduction to the Finite Difference Method 433 13.2 Central Difference Method 433 13.3 Free Vibration of Beams 435 13.4 Free Vibration of Rectangular Plates 437 13.5 Semianalytic Finite Difference Method for Free Vibration Analysis of Rectangular Plates 439 13.6 Semianalytic Finite Difference Method for Forced Vibration Analysis of Plates 442 13.7 Spline Finite Strip Method of Analysis of Plate Vibration 444 References 454 Exercise 13 455 Chapter 14 NONLINEAR VIBRATION 14.1Introduction 457 14.2 Perturbation Method 458 14.3 Step-by-Step Integration 461 References 466 Chapter 15 RANDOM VIBRATIONS 15.1 Introduction 467 15.2 Random Process 467 15.3 Probability Distributions 468 15.4 Ensemble Averages, Mean and Autocorrelation 472 15.5 Stationary Process, Ergodic Process and Temporal Averages 474 15.6 Power Spectral Density 477 15.7 Relationship between Autocorrelation Function and Power Spectral Density 478 Random Response of SDF Systems 481 Random Response of MDF Systems 484 15.10 Response of Flexural Beams under Random Loading 489 15.11 Finite Element Random Response of Plates 490 References 495 Exercise 15 496 Chapter 16 COMPUTER PROGRAM IN VIBRATION ANALYSIS 16.1Introduction* 499 16.2 Computer Program for Forced Vibration Analysis 499 16.3 Computer Program for Random Vibration Analysis 499 16.4 Computer Program for Free Vibration Analysis of Framed Structures 501 16.5 Computer Program for Free Vibration Analysis of Ships by Flexibility Matrix Method 521 16.6 Computer Program for the Free Vibration Analysis of Plates 527 References 541 Appendix A :THE STIFFNESS MATRIX A. 1 Stiffness Matrix 543 A.2Direct Stiffness Method 544 Appendix B :TABLE FOR SPRING STIFFNESS 551 Index 553
8180520900
624.176 / MUK