Vibrations, Dynamics and Structural Systems

by Mukhopadhyay,Ma

• ISBN13: 9789054107286
• ISBN10: 9054107286
• Edition: 2nd
• Format: Hardcover
• Copyright: 2000-09-20
• Publisher: Routledge

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	vii
Preface to first edition	ix
Introduction
Introduction	1	(1)
Brief History of Vibrations	2	(2)
Comparison between Static and Dynamic Analysis	4	(1)
D'Alembert's Principle	5	(1)
Some Basic Definitions	5	(4)
Dynamic Loading	9	(1)
Finite Element Discretization	10	(1)
Response of the System	11	(1)
Types of Analysis	11	(1)
Linear and Nonlinear Vibration	12	(2)
References	12	(2)
Free Vibration of Single Degree of Freedom System
Introduction	14	(1)
Equation of Motion of Single Degree of Freedom (SDF) System	14	(3)
Free Undamped Vibration of the SDF System	17	(9)
Free Damped Vibration of SDF System	26	(7)
Free Vibration with Coulomb Damping	33	(2)
Energy Method and Free Torsional Vibration	35	(8)
Logarithmic Decrement	43	(13)
References	47	(1)
Exercise 2	48	(8)
Forced Vibration of Single Degree of Freedom System
Introduction	56	(1)
Response of Damped Systems to Harmonic Loading	56	(9)
Rotating Unbalance	65	(2)
Reciprocating unbalance	67	(2)
Whirling of Rotating Shafts	69	(1)
Vibration Isolation and Transmissibility	70	(4)
Energy Dissipation by Damping	74	(4)
Equivalent Viscous Damping	78	(1)
Self-excited Vibrations	79	(3)
Vibration Measuring Seismic Instruments	82	(4)
Response of Structures due to Transient Vibration	86	(3)
Response of the SDF System to a General Type of Forcing Function	89	(3)
Dynamic Load Factor and Response Spectrum	92	(1)
Response due to Periodic Forces	93	(8)
Response due to Nonperiodic Excitation	101	(3)
Relationship between Complex Frequency Response Function and Unit Impluse Response Function	104	(1)
Support Motion	105	(2)
Response of SDF Systems Related to Earthquakes	107	(3)
Techniques for Analysing Earthquake Response	110	(14)
References	114	(1)
Exercise 3	115	(9)
Numerical Methods in Structural Analysis: Applied to SDF Systems
Introduction	124	(1)
Direct Integral Techniques	124	(13)
Numerical Evaluation of Duhamel's Integral	137	(5)
Numerical Computation in Frequency Domain	142	(8)
References	146	(1)
Exercise 4	147	(3)
Vibration of Two Degrees of Freedom System
Introduction	150	(1)
Free Vibration of Undamped Two Degrees of Freedom Systems	150	(4)
Torsional Vibration of Two Degrees of Freedom System	154	(1)
Forced Vibration of Two Degrees of Freedom Undamped System	155	(1)
Vibration Absorber	156	(5)
Free Vibration of Two Degrees of Freedom System with Viscous Damping	161	(1)
Coordinate Coupling	162	(2)
Free Vibration of Damped Two Degrees of Freedom System	164	(10)
References	169	(1)
Exercise 5	169	(5)
Free Vibration of Multiple Degrees of Freedom System
Introduction	174	(1)
Equations of Motion of MDF Systems	174	(3)
Free Undamped Vibration Analysis of MDF systems	177	(1)
Orthogonality Relationship	178	(2)
Eigenvalue Problem	180	(1)
Determination of Absolute Displacement of Free Vibration of MDF Systems	181	(5)
Eigenvalue Solution Techniques	186	(1)
Dunkerley's Equation	187	(3)
Holzer Method	190	(4)
Transfer Matrix Method	194	(7)
Myklestad Method	201	(5)
Stodola's Method	206	(8)
Matrix Deflation Procedure	214	(3)
Rayleigh's Method	217	(2)
Rayleigh-Ritz Method	219	(2)
Subspace Iteration Method	221	(1)
Simultaneous Iteration Method and Algorithm	222	(1)
Geared Systems	223	(1)
Branched Systems	224	(2)
Reduction Methods for Dynamic Analysis	226	(5)
Component Mode Synthesis Method	231	(6)
Lagrange's Equation	237	(9)
References	239	(1)
Exercise 6	240	(6)
Forced Vibration Analysis of Multiple Degrees of Freedom System
Introduction	246	(1)
Mode Superposition Method for the Determination of Response of MDF System	246	(4)
Mode Acceleration Method for the Determination of Response of MDF System	250	(2)
Response of MDF Systems under the Action of Transient Forces	252	(5)
Damping in MDF Systems	257	(9)
Response of MDF Systems to Support Motion	266	(3)
Earthquake Spectrum Analysis of Structures having MDF Systems	269	(2)
Use of Response Spectra for Designing MDF Systems	271	(4)
Direct Integration for Determining Response of MDF Systems	275	(4)
Complex Matrix Inversion Method for Forced Vibration Analysis of MDF Systems	279	(1)
Frequency Domain Analysis of MDF Systems by Modal Superposition for Harmonic Loads	280	(2)
Frequency Domain Analysis of Direct Frequency Response Method	282	(7)
References	284	(1)
Exercise 7	284	(5)
Free Vibration Analysis of Continuous Systems
Introduction	289	(1)
Vibration of Strings	289	(6)
Free Longitudinal Vibration of a Bar	295	(4)
Free Torsional Vibration of the Shaft	299	(3)
Free Flexural Vibration of Beams	302	(2)
Free Flexural Vibration of Simply Supported Beam	304	(2)
Free Flexural Vibration of Beams with Other End Conditions	306	(2)
Free Flexural Vibration of Beams with General End Conditions	308	(6)
Orthogonality Properties of Normal Modes	314	(3)
Effect of Rotary Inertia on the Free Flexural Vibration of Beams	317	(3)
Free Vibration of the Shear Beam	320	(2)
Effect of Axial Force on the Free Flexural Vibration of Beams	322	(2)
Free Vibration of Beams Including Shear Deformation and Rotary Inertia Effects	324	(3)
Collocation Method for Obtaining Normal Modes of Vibration of a Continuous Systems	327	(4)
Rayleigh's Quotient for Fundamental Frequency	331	(2)
Rayleigh-Ritz Method for Determining Natural Frequencies for Continuous Systems	333	(3)
Vibration of Membranes	336	(3)
Transverse Vibration of Rectangular Thin Plates	339	(10)
References	345	(1)
Exercise 8	345	(4)
Forced Vibration of Continuous Systems
Introduction	349	(1)
Forced Axial Vibration of Bars	349	(3)
Forced Vibration of the Shear Beam under Ground Motion Excitation	352	(3)
Forced Vibration of Flexural Member	355	(4)
Forced Transverse Vibration of Uniform Damped Beam	359	(1)
Forced Vibration of Flexural Member subjected to Ground Motion Excitation	360	(2)
Response of Beams due to Moving Loads	362	(9)
References	365	(1)
Exercise 9	366	(5)
Dynamic Direct Stiffness Method
Introduction	371	(1)
Continuous Beam	371	(3)
Method Analogous to Classical Methods in Statical Analysis	374	(2)
Dynamic Stiffness Matrix in Bending	376	(6)
Dynamic Stiffness Matrix for Flexural and Rigid Axial Displacements	382	(3)
Dynamic Stiffness Matrix of a Bar Undergoing Axial Deformation	385	(1)
Dynamic Stiffness Matrix of a Bar subjected to Axial and Bending Deformation	386	(4)
Beam Segments with Distributed Mass Having Shear Deformation and Rotary Inertia	390	(7)
References	395	(1)
Exercise 10	395	(2)
Vibration of Ship and Aircraft as A Beam
Introduction	397	(1)
Shift in Stiffness Matrix	397	(1)
Added Mass of a Ship	398	(2)
Flexibility Matrix Method for Determining Natural Frequencies of a Free-free Beam in Vertical Vibration	400	(5)
Flexibility Matrix Method for the Analysis of Coupled Horizontal and Torsional Vibration	405	(4)
Numerical Examples	409	(5)
References	412	(1)
Exercise 11	412	(2)
Finite Element Method in Vibration Analysis
Introduction to the Finite Element Method	414	(1)
Torsional Vibration of Shafts	414	(4)
Axial Vibration of Rods	418	(3)
Flexural Vibration of Beams	421	(3)
Vibration of Timoshenko Beams	424	(5)
Inplane Vibration of Plates	429	(7)
Flexural Vibration of Plates	436	(2)
Flexural Vibrations of Plates using Isoparametric Elements	438	(8)
Periodic Structures	446	(16)
References	457	(2)
Exercise 12	459	(3)
Finite Difference Method for the Vibration Analysis of Beams And Plates
Introduction to the Finite Difference Method	462	(1)
Central Difference Method	462	(2)
Free Vibration of Beams	464	(2)
Free Vibration of Rectangular Plates	466	(2)
Semianalytic Finite Difference Method for Free Vibration Analysis of Rectangular Plates	468	(3)
Semianalytic Finite Difference Method for Forced Vibration Analysis of Plates	471	(3)
Spline Finite Strip Method of Analysis of Plate Vibration	474	(12)
References	484	(1)
Exercise 13	485	(1)
Nonlinear Vibration
Introduction	486	(1)
Perturbation Method	487	(3)
Step-by-Step Integration	490	(6)
References	495	(1)
Random Vibrations
Introduction	496	(1)
Random Process	496	(1)
Probability Distributions	497	(4)
Ensemble Averages, Mean and Autocotrelation	501	(3)
Stationary Process, Ergodic Process and Temporal Averages	504	(3)
Power Spectral Density	507	(1)
Relationship between Autocorrelation Function and Power Spectral Density	508	(3)
Random Response of SDF Systems	511	(3)
Random Response of MDF Systems	514	(5)
Response of Flexural Beams under Random Loading	519	(2)
Finite Element Random Response of Plates	521	(8)
References	525	(1)
Exercise 15	526	(3)
Computer Programme in Vibration Analysis
Introduction	529	(1)
Computer Programme for Forced Vibration Analysis	529	(1)
Computer Programme for Random Vibration Analysis	530	(2)
Computer Programme for Free Vibration Analysis of Framed Structures	532	(20)
Computer Programme for Free Vibration Analysis of Ships by Flexibility Matrix Method	552	(7)
Computer Programme for the Free Vibration Analysis of Plates	559	(14)
References	572	(1)
Appendix A: THE STIFFNESS MATRIX
A.1 Stiffness Matrix	573	(1)
A.2 Direct Stiffness Method	574	(7)
Appendix B: TABLE FOR SPRING STIFFNESS	581	(1)
Index	582