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Elements of Structural Dynamics: A New Perspective [Kõva köide]

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(Engineering Consultant), (Indian Institute of Science, Bangalore, India)
  • Formaat: Hardback, 438 pages, kõrgus x laius x paksus: 254x178x26 mm, kaal: 807 g
  • Ilmumisaeg: 14-Sep-2012
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1118339622
  • ISBN-13: 9781118339626
Teised raamatud teemal:
Elements of Structural Dynamics: A New PerspectiveSuurem pilt
  • Formaat: Hardback, 438 pages, kõrgus x laius x paksus: 254x178x26 mm, kaal: 807 g
  • Ilmumisaeg: 14-Sep-2012
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1118339622
  • ISBN-13: 9781118339626
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781118339626.html
Märksõnad:
Structural dynamics is a subset of structural analysis which covers the behavior of structures subjected to dynamic loading. The subject has seen rapid growth and also change in how the basic concepts can be interpreted. For instance, the classical notions of discretizing the operator of a dynamic structural model have given way to a set-theoretic, function-space based framework, which is more conducive to implementation with a computer. This modern perspective, as adopted in this book, is also helpful in putting together the various tools and ideas in a more integrated style. 

Elements of Structural Dynamics: A New Perspective is devoted to covering the basic concepts in linear structural dynamics, whilst emphasizing their mathematical moorings and the associated computational aspects that make their implementation in software possible. 

Key features:





Employs a novel top down approach to structural dynamics. Contains an insightful treatment of the  computational aspects, including the finite element method, that translate into numerical solutions of the dynamic equations of motion. Consistently touches upon the modern mathematical basis for the theories and approximations involved.

Elements of Structural Dynamics: A New Perspective is a holistic treatise on structural dynamics and is an ideal textbook for senior undergraduate and graduate students in Mechanical, Aerospace and Civil engineering departments. This book also forms a useful reference for researchers and engineers in industry.
Preface xi
Acknowledgements xv
Introduction xvii
General Notations xxi
1 Structural Dynamics and Mathematical Modelling
1(20)
1.1 Introduction
1(1)
1.2 System of Rigid Bodies and Dynamic Equations of Motion
2(4)
1.2.1 Principle of Virtual Work
2(1)
1.2.2 Hamilton's Principle
3(1)
1.2.3 Lagrangian Equations of Motion
4(2)
1.3 Continuous Dynamical Systems and Equations of Motion from Hamilton's Principle
6(5)
1.3.1 Strain and Stress Tensors and Strain Energy
7(4)
1.4 Dynamic Equilibrium Equations from Newton's Force Balance
11(2)
1.4.1 Displacement-Strain Relationships
11(2)
1.4.1 Stress-Strain Relationships
13(1)
1.5 Equations of Motion by Reynolds Transport Theorem
13(4)
1.5.1 Mass Conservation
15(1)
1.5.2 Linear Momentum Conservation
16(1)
1.6 Conclusions
17(4)
Exercises
17(1)
Notations
18(1)
References
19(1)
Bibliography
19(2)
2 Continuous Systems-PDES and Solution
21(58)
2.1 Introduction
21(1)
2.2 Some Continuous Systems and PDES
22(14)
2.2.1 A Taut String-the One-Dimensional Wave Equation
22(1)
2.2.2 An Euler-Bernoulli Beam-the One-Dimensional Biharmonic Wave Equation
23(4)
2.2.3 Beam Equation with Rotary Inertia and Shear Deformation Effects
27(2)
2.2.4 Equations of Motion for 2D Plate by Classical Plate Theory (Kirchhoff Theory)
29(7)
2.3 PDES and General Solution
36(4)
2.3.1 PDES and Canonical Transformations
36(2)
2.3.2 General Solution to the Wave Equation
38(1)
2.3.3 Particular Solution (D'Alembert's Solution) to the Wave Equation
38(2)
2.4 Solution to Linear Homogeneous PDES-Method of Separation of Variables
40(16)
2.4.1 Homogeneous PDE with Homogeneous Boundary Conditions
41(1)
2.4.2 Stunn-Liouville Boundary-Value Problem (BVP) for the Wave Equation
42(1)
2.4.3 Adjoint Operator and Self-Adjoint Property
42(3)
2.4.4 Eigenvalues and Eigenfunctions of the Wave Equation
45(1)
2.4.5 Series Solution to the Wave Equation
45(1)
2.4.6 Mixed Boundary Conditions and Wave Equation
46(2)
2.4.7 Stunn-Liouville Boundary-Value Problem for the Biharmonic Wave Equation
48(5)
2.4.8 Thin Rectangular Plates-Free Vibration Solution
53(3)
2.5 Orthonormal Basis and Eigenfunction Expansion
56(3)
2.5.1 Best Approximation to f(x)
57(2)
2.6 Solutions of Inhomogeneous PDES by Eigenlunction-Expansion Method
59(5)
2.7 Solutions of Inhomogeneous PDES by Green's Function Method
64(4)
2.8 Solution of PDES with Inhomogeneous Boundary Conditions
68(1)
2.9 Solution to Nonself-adjoint Continuous Systems
69(5)
2.9.1 Eigensolution of Nonself-adjoint System
69(1)
2.9.2 Biorthogonality Relationship between L and L*
70(3)
2.9.3 Eigensolutions of L and L*
73(1)
2.10 Conclusions
74(5)
Exercises
75(1)
Notations
75(2)
References
77(1)
Bibliography
77(2)
3 Classical Methods for Solving the Equations of Motion
79(20)
3.1 Introduction
79(1)
3.2 Rayleigh-Ritz Method
80(5)
3.2.1 Rayleigh's Principle
84(1)
3.3 Weighted Residuals Method
85(10)
3.3.1 Galerkin Method
86(5)
3.3.2 Collocation Method
91(2)
3.3.3 Subdomain Method
93(1)
3.3.4 Least Squares Method
94(1)
3.4 Conclusions
95(4)
Exercises
95(1)
Notations
96(1)
References
97(1)
Bibliography
97(2)
4 Finite Element Method and Structural Dynamics
99(32)
4.1 Introduction
99(2)
4.2 Weak Formulation of PDES
101(10)
4.2.1 Well-Posedness of the Weak Form
103(1)
4.2.2 Uniqueness and Stability of Solution to Weak Form
104(3)
4.2.3 Numerical Integration by Gauss Quadrature
107(4)
4.3 Element-Wise Representation of the Weak Form and the Fem
111(2)
4.4 Application of the Fem to 2D Problems
113(5)
4.4.1 Membrane Vibrations and Fem
113(2)
4.4.2 Plane (2D) Elasticity Problems-Plane Stress and Plane Strain
115(3)
4.5 Higher Order Polynomial Basis Functions
118(3)
4.5.1 Beam Vibrations and Fem
118(2)
4.5.2 Plate Vibrations and Fem
120(1)
4.6 Some Computational Issues in Fem
121(3)
4.6.1 Element Shape Functions in Natural Coordinates
122(2)
4.7 Fem and Error Estimates
124(2)
4.7.1 A-Priori Error Estimate
124(2)
4.8 Conclusions
126(5)
Exercises
126(1)
Notations
127(2)
References
129(1)
Bibliography
129(2)
5 MDOF Systems and Eigenvalue Problems
131(48)
5.1 Introduction
131(1)
5.2 Discrete Systems through a Lumped Parameter Approach
132(3)
5.2.7 Positive Definite and Semi-Definite Systems
134(1)
5.3 Coupled Linear ODEs and the Linear Differential Operator
135(1)
5.4 Coupled Linear ODEs and Eigensolution
136(6)
5.5 First Order Equations and Uncoupling
142(1)
5.6 First Order versus Second Order ODE and Eigensolutions
143(2)
5.7 MDOF Systems and Modal Dynamics
145(11)
5.7.1 SDOF Oscillator and Modal Solution
146(7)
5.7.2 Rayleigh Quotient
153(2)
5.7.3 Rayleigh-Ritz Method for MDOF Systems
155(1)
5.8 Damped MDOF Systems
156(17)
5.8.1 Damped System and Quadratic Eigenvalue Problem
157(1)
5.8.2 Damped System and Unsymmetric Eigenvalue Problem
158(1)
5.8.3 Proportional Damping and Uncoupling MDOF Systems
159(1)
5.8.4 Damped Systems and Impulse Response
160(1)
5.8.5 Response under General Loading
161(1)
5.8.6 Response under Harmonic Input
161(2)
5.8.7 Complex Frequency Response
163(2)
5.8.8 Force Transmissibility
165(2)
5.8.9 System Response and Measurement of Damping
167(6)
5.9 Conclusions
173(6)
Exercises
173(2)
Notations
175(2)
References
177(1)
Bibliography
177(2)
6 Structures under Support Excitations
179(30)
6.1 Introduction
179(2)
6.2 Continuous Systems and Base Excitations
181(4)
6.3 MDOF Systems under Support Excitation
185(6)
6.4 SDOF Systems under Base Excitation
191(5)
6.4.1 Frequency Response of SDOF System under Base Motion
192(4)
6.5 Support Excitation and Response Spectra
196(2)
6.5.1 Peak Response Estimates of an MDOF System Using Response Spectra
197(1)
6.6 Structures under multi-support excitation
198(5)
6.6.1 Continuous system under multi-support excitation
199(3)
6.6.2 MDOF systems under multi-support excitation
202(1)
6.7 Conclusions
203(6)
Exercises
204(1)
Notations
205(1)
References
206(1)
Bibliography
206(3)
7 Eigensolution Procedures
209(66)
7.1 Introduction
209(1)
7.2 Power and Inverse Iteration Methods and Eigensolutions
210(10)
7.2.1 Order and Rate of Convergence-Distinct Eigenvalues
212(1)
7.2.2 Shifting and Convergence
213(2)
7.2.3 Multiple Eigenvalues
215(1)
7.2.4 Eigenvalues within an Interval-Shifting Scheme with Gram-Schmidt Orthogonalisation and Sturm Sequence Property
216(4)
7.3 Jacobi, Householder, QR Transformation Methods and Eigensolutions
220(11)
7.3.1 Jacobi Method
220(4)
7.3.2 Householder and QR Transformation Methods
224(7)
7.4 Subspace Iteration
231(2)
7.4.1 Convergence in Subspace Iteration
232(1)
7.5 Lanczos Transformation Method
233(4)
7.5.7 Lanczos Method and Error Analysis
235(2)
7.6 Systems with Unsymmetric Matrices
237(23)
7.6.1 Skew-Symmetric Matrices and Eigensolution
245(1)
7.6.2 Unsymmetric Matrices-A Rotor Bearing System
246(7)
7.6.3 Unsymmetric Systems and Eigensolutions
253(7)
7.7 Dynamic Condensation and Eigensolution
260(8)
7.7.1 Symmetric Systems and Dynamic Condensation
262(2)
7.7.2 Unsymmetric Systems and Dynamic Condensation
264(4)
7.8 Conclusions
268(7)
Exercises
268(1)
Notations
269(3)
References
272(1)
Bibliography
273(2)
8 Direct Integration Methods
275(34)
8.1 Introduction
275(6)
8.2 Forward and Backward Euler Methods
281(5)
8.2.1 Forward Euler Method
281(3)
8.2.2 Backward (Implicit) Euler Method
284(2)
8.3 Central Difference Method
286(3)
8.4 Newmark-β Method-a Single-Step Implicit Method
289(8)
8.4.1 Some Degenerate Cases of the Newmark-β Method and Stability
292(3)
8.4.2 Undamped Case-Amplitude and Periodicity Errors
295(1)
8.4.3 Amplitude and Periodicity Errors
295(2)
8.5 HHT-α and Generalized-α Methods
297(6)
8.6 Conclusions
303(6)
Exercises
305(1)
Notations
305(1)
References
306(1)
Bibliography
307(2)
9 Stochastic Structural Dynamics
309(58)
9.1 Introduction
309(2)
9.2 Probability Theory and Basic Concepts
311(1)
9.3 Random Variables
312(5)
9.3.1 Joint Random Variables, Distributions and Density Functions
314(1)
9.3.2 Expected (Average) Values of a Random Variable
315(2)
9.3.3 Characteristic and Moment-Generating Functions
317(1)
9.4 Conditional Probability, Independence and Conditional Expectation
317(2)
9.4.1 Conditional Expectation
319(1)
9.5 Some oft-Used Probability Distributions
319(4)
9.5.7 Binomial Distribution
320(1)
9.5.2 Poisson Distribution
320(1)
9.5.3 Normal Distribution
321(1)
9.5.4 Uniform Distribution
322(1)
9.5.5 Rayleigh Distribution
322(1)
9.6 Stochastic Processes
323(8)
9.6.7 Stationarity of a Stochastic Process
323(2)
9.6.2 Properties of Autocovariance/Autocorrelation Functions of Stationary Processes
325(1)
9.6.3 Spectral Representation of a Stochastic Process
325(2)
9.6.4 Sxx(λ) as the Mean Energy Density of X(t)
327(1)
9.6.5 Some Basic Stochastic Processes
328(3)
9.7 Stochastic Dynamics of Linear Structural Systems
331(7)
9.7.1 Continuous Systems under Stochastic Input
331(6)
9.7.2 Discrete Systems under Stochastic Input-Modal Superposition Method
337(1)
9.8 An Introduction to Ito Calculus
338(22)
9.8.7 Brownian Filtration
340(1)
9.8.2 Measurability
340(1)
9.8.3 An Adapted Stochastic Process
340(1)
9.8.4 Ito Integral
341(1)
9.8.5 Martingale
342(1)
9.8.6 Ito Process
343(9)
9.8.7 Computing the Response Moments
352(5)
9.8.8 Time Integration of SDEs
357(3)
9.9 Conclusions
360(7)
Exercises
361(2)
Notations
363(2)
References
365(1)
Bibliography
366(1)
Appendix A 367(2)
Appendix B 369(6)
Appendix C 375(4)
Appendix D 379(8)
Appendix E 387(4)
Appendix F 391(2)
Appendix G 393(6)
Appendix H 399(8)
Appendix I 407(6)
Index 413
Debasish Roy, Indian Institute of Science, Bangalore, India Debasish Roy is a professor in the Department of Civil Engineering at the Indian Institute of Science. He is a member of the editorial board for seven journals and has published circa 80 journal articles. His current research interests include Nonlinear and Stochastic Structural Dynamics, Linearization Techniques in Non-linear Dynamics, and Mesh-free and Finite Element Methods.

G. V. Rao, Vasthu Shilpa Associates, Bangalore, India Dr. Rao obtained his Ph. D in civil engineering from the Indian Institute of Science and has since been employed in industry. He has many years experience in experimental testing and research in structural engineering and also in research and software development in the area of structural dynamics using FEM. He is currently employed as an engineering consultant at Vasthu Shilpa Associates in India.