| Description |
1 online resource |
| Contents |
880-01 Title Page; Copyright; About the Author; Preface; Chapter 1: Introduction to Structural Vibrations; 1.1 Terminology; 1.2 Types of Vibration; 1.3 Objectives of Vibration Analyses; 1.4 Global and Local Vibrations; 1.5 Theoretical Approaches to Structural Vibrations; References; Chapter 2: Analytical Solutions for Uniform Continuous Systems; 2.1 Methods for Obtaining Equations of Motion of a Vibrating System; 2.2 Vibration of a Stretched String; 2.3 Longitudinal Vibration of a Continuous Rod; 2.4 Torsional Vibration of a Continuous Shaft |
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880-01/(S Contents note continued: 7.4.5. Determination of Natural Frequencies and Mode Shapes -- 7.4.6. Classical and Non-Classical Boundary Conditions -- 7.4.7. Numerical Examples -- 7.5. Out-of-Plane Vibration of a Curved Beam by Finite Element Method with Curved Beam Elements -- 7.5.1. Displacement Functions and Shape Functions -- 7.5.2. Stiffness Matrix for Curved Beam Element -- 7.5.3. Mass Matrix for Curved Beam Element -- 7.5.4. Numerical Example -- 7.6. In-Plane Vibration of a Curved Beam by Finite Element Method with Curved Beam Elements -- 7.6.1. Displacement Functions -- 7.6.2. Element Stiffness Matrix -- 7.6.3. Element Mass Matrix -- 7.6.4. Boundary Conditions of the Curved and Straight Finite Element Methods -- 7.6.5. Numerical Examples -- 7.7. Finite Element Method with Straight Beam Elements for Out-of-Plane Vibration of a Curved Beam -- 7.7.1. Property Matrices of Straight Beam Element for Out-of-Plane Vibrations -- 7.7.2. Transformation Matrix for Out-of-Plane Straight Beam Element -- 7.8. Finite Element Method with Straight Beam Elements for In-Plane Vibration of a Curved Beam -- 7.8.1. Property Matrices of Straight Beam Element for In-Plane Vibrations -- 7.8.2. Transformation Matrix for the In-Plane Straight Beam Element -- References -- 8.1. Free Vibration Response of an SDOF System -- 8.2. Response of an Undamped SDOF System Due to Arbitrary Loading -- 8.3. Response of a Damped SDOF System Due to Arbitrary Loading -- 8.4. Numerical Method for the Duhamel Integral -- 8.4.1. General Summation Techniques -- 8.4.2. Linear Loading Method -- 8.5. Exact Solution for the Duhamel Integral -- 8.6. Exact Solution for a Damped SDOF System Using the Classical Method -- 8.7. Exact Solution for an Undamped SDOF System Using the Classical Method -- 8.8. Approximate Solution for an SDOF Damped System by the Central Difference Method -- 8.9. Solution for the Equations of Motion of an MDOF System -- 8.9.1. Direct Integration Methods -- 8.9.2. Mode Superposition Method -- 8.10. Determination of Forced Vibration Response Amplitudes -- 8.10.1. Total and Steady Response Amplitudes of an SDOF System -- 8.10.2. Determination of Steady Response Amplitudes of an MDOF System -- 8.11. Numerical Examples for Forced Vibration Response Amplitudes -- 8.11.1. Frequency-Response Curves of an SDOF System -- 8.11.2. Frequency-Response Curves of an MDOF System -- References -- A.1. List of Integrals -- A.2. Theory of Modified Half-Interval (or Bisection) Method -- A.3. Determinations of Influence Coefficients -- A.3.1. Determination of Influence Coefficients aiYM and aiψM -- A.3.2. Determination of Influence Coefficients aiYQ and aiψQ -- A.4. Exact Solution of a Cubic Equation -- A.5. Solution of a Cubic Equation Associated with Its Complex Roots -- A.6. Coefficients of Matrix [H] Defined by Equation (7.387) -- A.7. Coefficients of Matrix [H] Defined by Equation (7.439) -- A.8. Exact Solution for a Simply Supported Euler Arch -- References |
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2.5 Flexural Vibration of a Continuous Euler-Bernoulli Beam2.6 Vibration of Axial-Loaded Uniform Euler-Bernoulli Beam; 2.7 Vibration of an Euler-Bernoulli Beam on the Elastic Foundation; 2.8 Vibration of an Axial-Loaded Euler Beam on the Elastic Foundation; 2.9 Flexural Vibration of a Continuous Timoshenko Beam; 2.10 Vibrations of a Shear Beam and a Rotary Beam; 2.11 Vibration of an Axial-Loaded Timoshenko Beam; 2.12 Vibration of a Timoshenko Beam on the Elastic Foundation; 2.13 Vibration of an Axial-Loaded Timoshenko Beam on the Elastic Foundation; 2.14 Vibration of Membranes |
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2.15 Vibration of Flat PlatesReferences; Chapter 3: Analytical Solutions for Non-Uniform Continuous Systems: Tapered Beams; 3.1 Longitudinal Vibration of a Conical Rod; 3.2 Torsional Vibration of a Conical Shaft; 3.3 Displacement Function for Free Bending Vibration of a Tapered Beam; 3.4 Bending Vibration of a Single-Tapered Beam; 3.5 Bending Vibration of a Double-Tapered Beam; 3.6 Bending Vibration of a Nonlinearly Tapered Beam; References; Chapter 4: Transfer Matrix Methods for Discrete and Continuous Systems; 4.1 Torsional Vibrations of Multi-Degrees-of-Freedom Systems |
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4.2 Lumped-Mass Model Transfer Matrix Method for Flexural Vibrations4.3 Continuous-Mass Model Transfer Matrix Method for Flexural Vibrations; 4.4 Flexural Vibrations of Beams with In-Span Rigid (Pinned) Supports; References; Chapter 5: Eigenproblem and Jacobi Method; 5.1 Eigenproblem; 5.2 Natural Frequencies, Natural Mode Shapes and Unit-Amplitude Mode Shapes; 5.3 Determination of Normal Mode Shapes; 5.4 Solution of Standard Eigenproblem with Standard Jacobi Method; 5.5 Solution of Generalized Eigenproblem with Generalized Jacobi Method |
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5.6 Solution of Semi-Definite System with Generalized Jacobi Method5.7 Solution of Damped Eigenproblem; References; Chapter 6: Vibration Analysis by Finite Element Method; 6.1 Equation of Motion and Property Matrices; 6.2 Longitudinal (Axial) Vibration of a Rod; 6.4 Flexural Vibration of an Euler-Bernoulli Beam; 6.5 Shape Functions for a Three-Dimensional Timoshenko Beam Element; 6.6 Property Matrices of a Three-Dimensional Timoshenko Beam Element; 6.7 Transformation Matrix for a Two-Dimensional Beam Element; 6.8 Transformations of Element Stiffness Matrix and Mass Matrix |
| Summary |
"This book illustrates theories and associated mathematical expressions with numerical examples using various methods, leading to exact solutions, more accurate results, and more computationally efficient techniques. It presents the derivations of the equations of motion for all structure foundations using either the continuous model or the discrete model. It discusses applications for students taking courses including vibration mechanics, dynamics of structures, and finite element analyses of structures, the transfer matrix method, and Jacobi method"-- Provided by publisher |
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"A book to introduce the theories or methods presented in some of the author's publications appearing in the international journals"-- Provided by publisher |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record and CIP data provided by publisher |
| Subject |
Vibration -- Mathematical models
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Structural analysis (Engineering) -- Mathematical models
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TECHNOLOGY & ENGINEERING -- Engineering (General)
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TECHNOLOGY & ENGINEERING -- Reference.
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Structural analysis (Engineering) -- Mathematical models
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Vibration -- Mathematical models
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| Form |
Electronic book
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| LC no. |
2013017916 |
| ISBN |
9781119137207 |
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1119137209 |
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111863215X |
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9781118632154 |
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