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Fundamentals of Mechanical Vibrations

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This introductory book covers the most fundamental aspects of linear vibration analysis for mechanical engineering students and e... Weiterlesen
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Beschreibung

This introductory book covers the most fundamental aspects of linear vibration analysis for mechanical engineering students and engineers. Consisting of five major topics, each has its own chapter and is aligned with five major objectives of the book. It starts from a concise, rigorous and yet accessible introduction to Lagrangian dynamics as a tool for obtaining the governing equation(s) for a system, the starting point of vibration analysis. The second topic introduces mathematical tools for vibration analyses for single degree-of-freedom systems. In the process, every example includes a section Exploring the Solution with MATLAB. This is intended to develop student's affinity to symbolic calculations, and to encourage curiosity-driven explorations. The third topic introduces the lumped-parameter modeling to convert simple engineering structures into models of equivalent masses and springs. The fourth topic introduces mathematical tools for general multiple degrees of freedom systems, with many examples suitable for hand calculation, and a few computer-aided examples that bridges the lumped-parameter models and continuous systems. The last topic introduces the finite element method as a jumping point for students to understand the theory and the use of commercial software for vibration analysis of real-world structures.



Autorentext

Dr Liang-Wu Cai, Kansas State University, USA, is Fellow of ASME.



Klappentext

Fundamentals of Mechanical Vibrations

This introductory book covers the most fundamental aspects of linear vibration analysis for mechanical engineering students and engineers. Consisting of five major topics, each has its own chapter and is aligned with five major objectives of the book. It starts from a concise, rigorous, and yet accessible introduction to Lagrangian dynamics as a tool for obtaining the governing equation(s) for a system, the starting point of vibration analysis. The second topic introduces mathematical tools for vibration analyses for single degree-of-freedom systems. In the process, every example includes a section Exploring the Solution with MATLAB. This is intended to develop student's affinity to symbolic calculations and to encourage curiosity-driven explorations. The third topic introduces the lumped-parameter modeling to convert simple engineering structures into models of equivalent masses and springs. The fourth topic introduces mathematical tools for general multiple degrees of freedom systems, with many examples suitable for hand calculation, and a few computer-aided examples that bridges the lumped-parameter models and continuous systems. The last topic introduces the finite element method as a jumping point for students to understand the theory and the use of commercial software for vibration analysis of real-world structures.

  • Thorough and clear explanation of the fundamental concepts and theories without straying into more advanced topics
  • Rigorous and yet accessible treatment of Lagrangian dynamics to arrive at the starting point of vibration analysis with confidence
  • Expanding the horizon by exploring the capabilities of MATLAB for examples of many degrees of freedom and even complete finite element code
  • Instilling the philosophy that, as an engineer, having a solution means the beginning of an exploration


Inhalt

Series Preface ix

Preface xi

1 A Crash Course on Lagrangian Dynamics 1

1.1 Objectives 1

1.2 Concept of "Equation of Motion" 1

1.3 Generalized Coordinates 5

1.4 Admissible Variations 13

1.5 Degrees of Freedom 16

1.6 Virtual Work and Generalized Forces 17

1.7 Lagrangian 24

1.8 Lagrange's Equation 24

1.9 Procedure for Deriving Equation(s) of Motion 24

1.10 Worked Examples 25

1.10.1 Systems Containing Only Particles 25

1.10.2 Systems Containing Rigid Bodies 38

1.11 Linearization of Equations of Motion 57

1.11.1 Equilibrium Position(s) 58

1.11.2 Linearization 59

1.11.3 Observations and Further Discussions 62

1.12 Chapter Summary 63

2 Vibrations of Single-DOF Systems 81

2.1 Objectives 81

2.2 Types of Vibration Analyses 81

2.3 Free Vibrations of Undamped System 83

2.3.1 General Solution for Homogeneous Differential Equation 83

2.3.2 Basic Vibration Terminologies 85

2.3.3 Determining Constants via Initial Conditions 87

2.4 Free Vibrations of Damped Systems 93

2.5 Using Normalized Equation of Motion 94

2.5.1 Normalization of Equation of Motion 94

2.5.2 Classification of Vibration Systems 95

2.5.3 Free Vibration of Underdamped Systems 96

2.5.4 Free Vibration of Critically Damped System 100

2.5.5 Free Vibration of Overdamped System 102

2.6 Forced Vibrations I: Steady-State Responses 108

2.6.1 Harmonic Loading 108

2.6.2 Mechanical Significance of Steady-State Solution 110

2.6.3 Other Examples of Harmonic Loading 115

2.6.4 General Periodic Loading 124

2.7 Forced Vibrations II: Transient Responses 133

2.7.1 Transient Response to Periodic Loading 134

2.7.2 General Loading: Direct Analytical Method 139

2.7.3 Laplace Transform Method 146

2.7.4 Decomposition Method 150

2.7.5 Convolution Integral Method 158

2.8 Chapter Summary 172

2.8.1 Free Vibrations of Single-DOF Systems 172

2.8.2 Steady-State Responses of Single-DOF Systems 173

2.8.3 Transient Responses of Single-DOF Systems 174

3 Lumped-Parameter Modeling 186

3.1 Objectives 186

3.2 Modeling 186

3.3 Idealized Elements 187

3.3.1 Mass Elements 187

3.3.2 Spring Elements 188

3.3.3 Damping Elements 189

3.4 Lumped-Parameter Modeling of Simple Components and Structures 190

3.4.1 Equivalent Spring Constants 191

3.4.2 Equivalent Masses 204

3.4.3 Damping Models 212

3.5 Alternative Methods 218

3.5.1 Castigliano Method for Equivalent Spring Constants 218

3.5.2 RayleighRitz Method for Equivalent Masses 223

3.5.3 RayleighRitz Method for Equivalent Spring Constants 227

3.5.4 RayleighRitz Method for Natural Frequencies 230

3.5.5 Determining Lumped Parameters Through Experimental Measurements 231

3.6 Examples with Lumped-Parameter Models 233

3.7 Chapter Summary 252

4 Vibrations of Multi-DOF Systems 269

4.1 Objectives 269

4.2 Matrix Equation of Motion 269

4.3 Modal Analysis: Natural Frequencies and Mode Shapes 273

4.4 Free Vibrations 284

4.4.1 Free Vibrations of Undamped Systems 284

4.4.2 Free Vibrations of Undamped Unconstrained Systems 293

4.4.3 Free Vibrations of Systems of Many DOFs 296

4.5 Eigenvalues and Eigenvectors 305

4.5.1 Standard Eigenvalue Problem 305

4.5.2 Generalized Eigenvalue Problem 306

4.6 Coupling, Decoupling, and Principal Coordinates 307

4.6.1 Types of Coupling 307

4.6.2 Principal Coordinates 307

4.6.3 Decoupling Method for Free-Vibration Analysis 310

4.7 Forced Vibrations I: Steady-State Responses 319

4.8 Forced ...

Produktinformationen

Titel: Fundamentals of Mechanical Vibrations
Autor:
EAN: 9781119050230
ISBN: 978-1-119-05023-0
Format: E-Book (pdf)
Hersteller: Wiley-ASME Press Series
Herausgeber: Wiley-Asme Press Series
Genre: Maschinenbau, Fertigungstechnik
Veröffentlichung: 25.04.2016
Digitaler Kopierschutz: Adobe-DRM
Dateigrösse: 15.52 MB
Anzahl Seiten: 480
Jahr: 2016