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Elements of Structural Dynamics
A New Perspective
ISBN/EAN: 9781118339626
Umbreit-Nr.: 3839979
Sprache:
Englisch
Umfang: 438 S.
Format in cm:
Einband:
gebundenes Buch
Erschienen am 14.09.2012
Auflage: 1/2012
- Zusatztext
- 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.
- Kurztext
- 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.
- Autorenportrait
- InhaltsangabePreface xi Acknowledgements xv Introduction xvii General Notations xxi 1 Structural Dynamics and Mathematical Modelling 1 1.1 Introduction 1 1.2 System of Rigid Bodies and Dynamic Equations of Motion 2 1.2.1 Principle of Virtual Work 2 1.2.2 Hamilton's Principle 3 1.2.3 Lagrangian Equations of Motion 4 1.3 Continuous Dynamical Systems and Equations of Motion from Hamilton's Principle 6 1.3.1 Strain and Stress Tensors and Strain Energy 7 1.4 Dynamic Equilibrium Equations from Newton's Force Balance 11 1.4.1 Displacement-Strain Relationships 11 1.4.2 StressStrain Relationships 13 1.5 Equations of Motion by Reynolds Transport Theorem 13 1.5.1 Mass Conservation 15 1.5.2 Linear Momentum Conservation 16 1.6 Conclusions 17 Exercises 17 Notations 18 References 19 Bibliography 19 2 Continuous Systems - PDEs and Solution 21 2.1 Introduction 21 2.2 Some Continuous Systems and PDEs 22 2.2.1 A Taut String - the One-Dimensional Wave Equation 22 2.2.2 An Euler-Bernoulli Beam - the One-Dimensional Biharmonic Wave Equation 23 2.2.3 Beam Equation with Rotary Inertia and Shear Deformation Effects 27 2.2.4 Equations of Motion for 2D Plate by Classical Plate Theory (Kirchhoff Theory) 29 2.3 PDEs and General Solution 36 2.3.1 PDEs and Canonical Transformations 36 2.3.2 General Solution to the Wave Equation 38 2.3.3 Particular Solution (D'Alembert's Solution) to the Wave Equation 38 2.4 Solution to Linear Homogeneous PDEs - Method of Separation of Variables 40 2.4.1 Homogeneous PDE with Homogeneous Boundary Conditions 41 2.4.2 SturmLiouville BoundaryValue Problem (BVP) for the Wave Equation 42 2.4.3 Adjoint Operator and Self-Adjoint Property 42 2.4.4 Eigenvalues and Eigenfunctions of the Wave Equation 45 2.4.5 Series Solution to the Wave Equation 45 2.4.6 Mixed Boundary Conditions and Wave Equation 46 2.4.7 SturmLiouville BoundaryValue Problem for the Biharmonic Wave Equation 48 2.4.8 Thin Rectangular Plates - Free Vibration Solution 53 2.5 Orthonormal Basis and Eigenfunction Expansion 56 2.5.1 Best Approximation to f(x) 57 2.6 Solutions of Inhomogeneous PDEs by Eigenfunction-Expansion Method 59 2.7 Solutions of Inhomogeneous PDEs by Green's Function Method 64 2.8 Solution of PDEs with Inhomogeneous Boundary Conditions 68 2.9 Solution to Nonself-adjoint Continuous Systems 69 2.9.1 Eigensolution of Nonself-adjoint System 69 2.9.2 Biorthogonality Relationship between L and L* 70 2.9.3 Eigensolutions of L and L* 73 2.10 Conclusions 74 Exercises 75 Notations 75 References 77 Bibliography 77 3 Classical Methods for Solving the Equations of Motion 79 3.1 Introduction 79 3.2 RayleighRitz Method 80 3.2.1 Rayleigh's Principle 84 3.3 Weighted Residuals Method 85 3.3.1 Galerkin Method 86 3.3.2 Collocation Method 91 3.3.3 Subdomain Method 93 3.3.4 Least Squares Method 94 3.4 Conclusions 95 Exercises 95 Notations 96 References 97 Bibliography 97 4 Finite Element Method and Structural Dynamics 99 4.1 Introduction 99 4.2 Weak Formulation of PDEs 101 4.2.1 WellPosedness of the Weak Form 103 4.2.2 Uniqueness and Stability of Solution to Weak Form 104 4.2.3 Numerical Integration by Gauss Quadrature 107 4.3 ElementWise Representation of the Weak Form and the FEM 111 4.4 Application of the FEM to 2D Problems 113 4.4.1 Membrane Vibrations and FEM 113 4.4.2 Plane (2D) Elasticity Problems - Plane Stress and Plane Strain 115 4.5 Higher Order Polynomial Basis Functions 118 4.5.1 Beam Vibrations and FEM 118 4.5.2 Plate Vibrations and FEM 120 4.6 Some Computational Issues in FEM 121 4.6.1 Element Shape Functions in Natural Coordinates 122 4.7 FEM and Error Estimates 124 4.7.1 APriori Error Estimate 124 4.8 Conclusions 126 Exercises 126 Notations 127 References 129 Bibliography 129 5 MDOF Syste