Mechanical Vibrations

Mechanical Vibrations: Theory and Application to Structural
Dynamics, Third Edition is a comprehensively updated new
edition of the popular textbook. It presents the theory of
vibrations in the context of structural analysis and covers
applications in mechanical and aerospace engineering.

Key features include:

• A systematic approach to dynamic reduction and substructuring,
  based on duality between mechanical and admittance concepts

• An introduction to experimental modal analysis and
  identification methods

• An improved, more physical presentation of wave propagation
  phenomena

• A comprehensive presentation of current practice for solving
  large eigenproblems, focusing on the efficient linear solution of
  large, sparse and possibly singular systems

• A deeply revised description of time integration schemes,
  providing framework for the rigorous accuracy/stability analysis of
  now widely used algorithms such as HHT and Generalized-alpha

• Solved exercises and end of chapter homework problems

• A companion website hosting supplementary material

Auteur

Michel Géradin holds an Engineering Degree in Physics and a PhD from ULg (University of Liège, Belgium). Successively he has been a research fellow from the Belgian FNRS (19681979), Professor of Structural Dynamics at ULg (19792010) and Unit Head of the European Laboratory for Structural Assessment (ELSA) of the JRC (European Commission Ispra, Italy) (19972010). He has also been a Visiting Scholar at Stanford University (1973-1974) and Visiting Professor at the University of Colorado (1986-1987).

He developed research activity in finite element methodology, computational methods in structural dynamics and multibody dynamics. He has been a co-author of the finite element software SAMCEF and co-founding member of Samtech SA in 1986.

He is Doctor Honoris Causa at the Technical University of Lisbon (1996) and École Centrale de Nantes (2007), and an Associate Member of the Royal Academy of Sciences of Belgium (2000).

He is the co-author of Flexible Multibody Dynamics. A Finite Element Approach (Wiley, 2000).

Daniel Rixen holds an MSc in Aerospace Vehicle Design from the College of Aeronautics in Cranfield (UK) and received his Mechanical Engineering and Doctorate degree from the University of Liège (Belgium) supported by the Belgium National Research Fund. After having spent two years as researcher at the Center for Aerospace Structures (University of Colorado, Boulder) between 2000 and 2012 he chaired the Engineering Dynamic group at the Delft University of Technology (The Netherlands). Since 2012 he heads the Institute for Applied Mechanics at the Technische Universität München (Germany). Next to teaching, his passion comprises research on numerical and simulation methods as well as experimental techniques, involving structural and multiphysical applications in e.g. aerospace, automotive, mechatronics, biodynamics and wind energy. A recurring aspect in his investigation is the interaction between system components such as in domain decomposition for parallel computing or component synthesis in dynamic model reduction and in experimental substructuring.

Texte du rabat

Mechanical Vibrations: Theory and Application to Structural Dynamics, Third Edition is a comprehensively updated new edition of the popular textbook. It presents the theory of vibrations in the context of structural analysis and covers applications in mechanical and aerospace engineering. Although keeping the same overall structure, the content of this new edition has been significantly revised in order to cover new topics, enhance focus on selected important issues, provide sets of exercises and improve the quality of presentation.

Without being exhaustive (see the Introduction for a comprehensive list), some key features include:

• A systematic approach to dynamic reduction and substructuring, based on duality between mechanical and admittance concepts
• An introduction to experimental modal analysis and identification methods
• An improved, more physical presentation of wave propagation phenomena
• A comprehensive presentation of current practice for solving large eigenproblems, focusing on the efficient linear solution of large, sparse and possibly singular systems
• A deeply revised description of time integration schemes, providing framework for the rigorous accuracy/stability analysis of now widely used algorithms such as HHT and Generalized-
• Solved exercises and end of chapter homework problems
• A companion website hosting supplementary material
  With revised, coherent and uniform notation, Mechanical Vibrations: Theory and Application to Structural Dynamics, Third Edition is a must-have textbook for graduate students working with vibration in mechanical, aerospace and civil engineering, and is also an excellent reference for researchers and industry practitioners.

Contenu

Foreword xiii

Preface xv

Introduction 1

Suggested Bibliography 7

1 Analytical Dynamics of Discrete Systems 13

1.1 Principle of Virtual Work for a Particle 14

1.1.1 Nonconstrained Particle 14

1.1.2 Constrained Particle 15

1.2 Extension to a System of Particles 17

1.2.1 Virtual Work Principle for N Particles 17

1.2.2 The Kinematic Constraints 18

1.2.3 Concept of Generalized Displacements 20

1.3 Hamilton's Principle for Conservative Systems and Lagrange Equations 23

1.3.1 Structure of Kinetic Energy and Classification of Inertia Forces 27

1.3.2 Energy Conservation in a System with Scleronomic Constraints 29

1.3.3 Classification of Generalized Forces 32

1.4 Lagrange Equations in the General Case 36

1.5 Lagrange Equations for Impulsive Loading 39

1.5.1 Impulsive Loading of a Mass Particle 39

1.5.2 Impulsive Loading for a System of Particles 42

1.6 Dynamics of Constrained Systems 44

1.7 Exercises 46

1.7.1 Solved Exercises 46

1.7.2 Selected Exercises 53

References 54

2 Undamped Vibrations of n-Degree-of-Freedom Systems 57

2.1 Linear Vibrations about an Equilibrium Configuration 59

2.1.1 Vibrations about a Stable Equilibrium Position 59

2.1.2 Free Vibrations about an Equilibrium Configuration Corresponding to Steady Motion 63

2.1.3 Vibrations about a Neutrally Stable Equilibrium Position 66

2.2 Normal Modes of Vibration 67

2.2.1 Systems with a Stable Equilibrium Configuration 68

2.2.2 Systems with a Neutrally Stable Equilibrium Position 69

2.3 Orthogonality of Vibration Eigenmodes 70

2.3.1 Orthogonality of Elastic Modes with Distinct Frequencies 70

2.3.2 Degeneracy Theorem and Generalized Orthogonality Relationships 72

2.3.3 Orthogonality Relationships Including Rigid-body Modes 75

2.4 Vector and Matrix Spectral Expansions Using Eigenmodes 76

2.5 Free Vibrations Induced by Nonzero Initial Conditions 77

2.5.1 Systems with a Stable Equilibrium Position 77

2.5.2 Systems with Neutrally Stable Equilibrium Position 82

2.6 Response to Applied Forces: Forced Harmonic Response 83

2.6.1 Harmonic Response, Impedance and Admittance Matrices 84

2.6.2 Mode Superposition and Spectral Expansion of the Admittance Matrix 84

2.6.3 Statically Exact Expansion of the Admittance Matrix 88

2.6.4 Pseudo-resonance and Resonance 89

2.6.5 Normal Excitation Modes 90

2.7 Response to Applied Forces: Response in the Time Domain 91

2.7.1 Mode Superposition and Normal Equations 91

2.7.2 Impulse Response and Time Integration of the Normal Equations 92

2.7.3 Step Response and Time Integration of the Normal Equations 94

2.7.4 Direct Integration of the Transient Response 95

2.8 Modal Approximations of Dynamic Responses 95

2.8.1 Response Truncation and Mode Displacement Method 96

2.8.2 Mode Acceleration Method 97

2.8.3 Mode Acceleration and Model Reduction on Sele…