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Analytical and numerical methods for vibration analyses /
"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 found...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, NJ :
John Wiley & Sons Inc.,
2013.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Wu, Jong-Shyong. | |
| 245 | 1 | 0 | |a Analytical and numerical methods for vibration analyses / |c Jong-Shyong Wu. |
| 264 | 1 | |a Hoboken, NJ : |b John Wiley & Sons Inc., |c 2013. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 520 | |a "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"-- |c Provided by publisher. | ||
| 520 | |a "A book to introduce the theories or methods presented in some of the author's publications appearing in the international journals"-- |c Provided by publisher. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record and CIP data provided by publisher. | |
| 505 | 0 | |6 880-01 |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Vibration |x Mathematical models. | |
| 650 | 0 | |a Structural analysis (Engineering) |x Mathematical models. | |
| 650 | 6 | |a Vibration |x Modèles mathématiques. | |
| 650 | 6 | |a Théorie des constructions |x Modèles mathématiques. | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Engineering (General) |2 bisacsh | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Reference. |2 bisacsh | |
| 650 | 7 | |a Structural analysis (Engineering) |x Mathematical models |2 fast | |
| 650 | 7 | |a Vibration |x Mathematical models |2 fast | |
| 758 | |i has work: |a Analytical and Numerical Methods for Vibration Analyses [electronic resource] (Text) |1 https://id.oclc.org/worldcat/entity/E39PCYgTwJdYmhh7DBcDTTVFqP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Wu, Jong-Shyong. |t Analytical and numerical methods for vibration analyses. |d Hoboken, NJ : John Wiley & Sons Inc., 2013 |z 9781118632154 |w (DLC) 2013008893 |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1332524 |z Texto completo |
| 880 | 0 | 0 | |6 505-00/(S |g Machine generated contents note: |g 1.1. |t Terminology -- |g 1.2. |t Types of Vibration -- |g 1.3. |t Objectives of Vibration Analyses -- |g 1.3.1. |t Free Vibration Analysis -- |g 1.3.2. |t Forced Vibration Analysis -- |g 1.4. |t Global and Local Vibrations -- |g 1.5. |t Theoretical Approaches to Structural Vibrations -- |t References -- |g 2.1. |t Methods for Obtaining Equations of Motion of a Vibrating System -- |g 2.2. |t Vibration of a Stretched String -- |g 2.2.1. |t Equation of Motion -- |g 2.2.2. |t Free Vibration of a Uniform Clamped[--]Clamped String -- |g 2.3. |t Longitudinal Vibration of a Continuous Rod -- |g 2.3.1. |t Equation of Motion -- |g 2.3.2. |t Free Vibration of a Uniform Rod -- |g 2.4. |t Torsional Vibration of a Continuous Shaft -- |g 2.4.1. |t Equation of Motion -- |g 2.4.2. |t Free Vibration of a Uniform Shaft -- |g 2.5. |t Flexural Vibration of a Continuous Euler[--]Bernoulli Beam -- |g 2.5.1. |t Equation of Motion -- |g 2.5.2. |t Free Vibration of a Uniform Euler[--]Bernoulli Beam -- |g 2.5.3. |t Numerical Example -- |g 2.6. |t Vibration of Axial-Loaded Uniform Euler[--]Bernoulli Beam -- |g 2.6.1. |t Equation of Motion -- |g 2.6.2. |t Free Vibration of an Axial-Loaded Uniform Beam -- |g 2.6.3. |t Numerical Example -- |g 2.6.4. |t Critical Buckling Load of a Uniform Euler[--]Bernoulli Beam -- |g 2.7. |t Vibration of an Euler[--]Bernoulli Beam on the Elastic Foundation -- |g 2.7.1. |t Influence of Stiffness Ratio and Total Beam Length -- |g 2.7.2. |t Influence of Supporting Conditions of the Beam -- |g 2.8. |t Vibration of an Axial-Loaded Euler Beam on the Elastic Foundation -- |g 2.8.1. |t Equation of Motion -- |g 2.8.2. |t Free Vibration of a Uniform Beam -- |g 2.8.3. |t Numerical Example -- |g 2.9. |t Flexural Vibration of a Continuous Timoshenko Beam -- |g 2.9.1. |t Equation of Motion -- |g 2.9.2. |t Free Vibration of a Uniform Timoshenko Beam -- |g 2.9.3. |t Numerical Example -- |g 2.10. |t Vibrations of a Shear Beam and a Rotary Beam -- |g 2.10.1. |t Free Vibration of a Shear Beam -- |g 2.10.2. |t Free Vibration of a Rotary Beam -- |g 2.11. |t Vibration of an Axial-Loaded Timoshenko Beam -- |g 2.11.1. |t Equation of Motion -- |g 2.11.2. |t Free Vibration of an Axial-Loaded Uniform Timoshenko Beam -- |g 2.11.3. |t Numerical Example -- |g 2.12. |t Vibration of a Timoshenko Beam on the Elastic Foundation -- |g 2.12.1. |t Equation of Motion -- |g 2.12.2. |t Free Vibration of a Uniform Beam on the Elastic Foundation -- |g 2.12.3. |t Numerical Example -- |g 2.13. |t Vibration of an Axial-Loaded Timoshenko Beam on the Elastic Foundation -- |g 2.13.1. |t Equation of Motion -- |g 2.13.2. |t Free Vibration of a Uniform Timoshenko Beam -- |g 2.13.3. |t Numerical Example -- |g 2.14. |t Vibration of Membranes -- |g 2.14.1. |t Free Vibration of a Rectangular Membrane -- |g 2.14.2. |t Free Vibration of a Circular Membrane -- |g 2.15. |t Vibration of Flat Plates -- |g 2.15.1. |t Free Vibration of a Rectangular Plate -- |g 2.15.2. |t Free Vibration of a Circular Plate -- |t References -- |g 3.1. |t Longitudinal Vibration of a Conical Rod -- |g 3.1.1. |t Determination of Natural Frequencies and Natural Mode Shapes -- |g 3.1.2. |t Determination of Normal Mode Shapes -- |g 3.1.3. |t Numerical Examples -- |g 3.2. |t Torsional Vibration of a Conical Shaft -- |g 3.2.1. |t Determination of Natural Frequencies and Natural Mode Shapes -- |g 3.2.2. |t Determination of Normal Mode Shapes -- |g 3.2.3. |t Numerical Example -- |g 3.3. |t Displacement Function for Free Bending Vibration of a Tapered Beam -- |g 3.4. |t Bending Vibration of a Single-Tapered Beam -- |g 3.4.1. |t Determination of Natural Frequencies and Natural Mode Shapes -- |g 3.4.2. |t Determination of Normal Mode Shapes -- |g 3.4.3. |t Finite Element Model of a Single-Tapered Beam -- |g 3.4.4. |t Numerical Example -- |g 3.5. |t Bending Vibration of a Double-Tapered Beam -- |g 3.5.1. |t Determination of Natural Frequencies and Natural Mode Shapes -- |g 3.5.2. |t Determination of Normal Mode Shapes -- |g 3.5.3. |t Finite Element Model of a Double-Tapered Beam -- |g 3.5.4. |t Numerical Example -- |g 3.6. |t Bending Vibration of a Nonlinearly Tapered Beam -- |g 3.6.1. |t Equation of Motion and Boundary Conditions -- |g 3.6.2. |t Natural Frequencies and Mode Shapes for Various Supporting Conditions -- |g 3.6.3. |t Finite Element Model of a Non-Uniform Beam -- |g 3.6.4. |t Numerical Example -- |t References -- |g 4.1. |t Torsional Vibrations of Multi-Degrees-of-Freedom Systems -- |g 4.1.1. |t Holzer Method for Torsional Vibrations -- |g 4.1.2. |t Transfer Matrix Method for Torsional Vibrations -- |g 4.2. |t Lumped-Mass Model Transfer Matrix Method for Flexural Vibrations -- |g 4.2.1. |t Transfer Matrices for a Station and a Field -- |g 4.2.2. |t Free Vibration of a Flexural Beam -- |g 4.2.3. |t Discretization of a Continuous Beam -- |g 4.2.4. |t Transfer Matrices for a Timoshenko Beam -- |g 4.2.5. |t Numerical Example -- |g 4.2.6. |t Timoshenko Beam Carrying Multiple Various Concentrated Elements -- |g 4.2.7. |t Transfer Matrix for Axial-Loaded Euler Beam and Timoshenko Beam -- |g 4.3. |t Continuous-Mass Model Transfer Matrix Method for Flexural Vibrations -- |g 4.3.1. |t Flexural Vibration of an Euler[--]Bernoulli Beam -- |g 4.3.2. |t Flexural Vibration of a Timoshenko Beam with Axial Load -- |g 4.4. |t Flexural Vibrations of Beams with In-Span Rigid (Pinned) Supports -- |g 4.4.1. |t Transfer Matrix of a Station Located at an In-Span Rigid (Pinned) Support -- |g 4.4.2. |t Natural Frequencies and Mode Shapes of a Multi-Span Beam -- |g 4.4.3. |t Numerical Examples -- |t References -- |g 5.1. |t Eigenproblem -- |g 5.2. |t Natural Frequencies, Natural Mode Shapes and Unit-Amplitude Mode Shapes -- |g 5.3. |t Determination of Normal Mode Shapes -- |g 5.3.1. |t Normal Mode Shapes Obtained From Natural Ones -- |g 5.3.2. |t Normal Mode Shapes Obtained From Unit-Amplitude Ones -- |g 5.4. |t Solution of Standard Eigenproblem with Standard Jacobi Method -- |g 5.4.1. |t Formulation Based on Forward Multiplication -- |g 5.4.2. |t Formulation Based on Backward Multiplication -- |g 5.4.3. |t Convergence of Iterations -- |g 5.5. |t Solution of Generalized Eigenproblem with Generalized Jacobi Method -- |g 5.5.1. |t Standard Jacobi Method -- |g 5.5.2. |t Generalized Jacobi Method -- |g 5.5.3. |t Formulation Based on Forward Multiplication -- |g 5.5.4. |t Determination of Elements of Rotation Matrix (α and γ) -- |g 5.5.5. |t Convergence of Iterations -- |g 5.5.6. |t Formulation Based on Backward Multiplication -- |g 5.6. |t Solution of Semi-Definite System with Generalized Jacobi Method -- |g 5.7. |t Solution of Damped Eigenproblem -- |t References -- |g 6.1. |t Equation of Motion and Property Matrices -- |g 6.2. |t Longitudinal (Axial) Vibration of a Rod -- |g 6.3. |t Property Matrices of a Torsional Shaft -- |g 6.4. |t Flexural Vibration of an Euler[--]Bernoulli Beam -- |g 6.5. |t Shape Functions for a Three-Dimensional Timoshenko Beam Element -- |g 6.5.1. |t Assumptions for the Formulations -- |g 6.5.2. |t Shear Deformations Due to Translational Nodal Displacements V1 and V3 -- |g 6.5.3. |t Shear Deformations Due to Rotational Nodal Displacements V2 and V4 -- |g 6.5.4. |t Determination of Shape Functions φyi(ξ) (i = 1-4) -- |g 6.5.5. |t Determination of Shape Functions φxi(ξ) (i = 1-4) -- |g 6.5.6. |t Determination of Shape Functions φzi(ξ) (i = 1-4) -- |g 6.5.7. |t Determination of Shape Functions φxi(ξ) (i = 1-4) -- |g 6.5.8. |t Shape Functions for a 3D Beam Element -- |g 6.6. |t Property Matrices of a Three-Dimensional Timoshenko Beam Element -- |g 6.6.1. |t Stiffness Matrix of a 3D Timoshenko Beam Element -- |g 6.6.2. |t Mass Matrix of a 3D Timoshenko Beam Element -- |g 6.7. |t Transformation Matrix for a Two-Dimensional Beam Element -- |g 6.8. |t Transformations of Element Stiffness Matrix and Mass Matrix -- |g 6.9. |t Transformation Matrix for a Three-Dimensional Beam Element -- |g 6.10. |t Property Matrices of a Beam Element with Concentrated Elements -- |g 6.11. |t Property Matrices of Rigid[--]Pinned and Pinned[--]Rigid Beam Elements -- |g 6.11.1. |t Property Matrices of the R-P Beam Element -- |g 6.11.2. |t Property Matrices of the P-R Beam Element -- |g 6.12. |t Geometric Stiffness Matrix of a Beam Element Due to Axial Load -- |g 6.13. |t Stiffness Matrix of a Beam Element Due to Elastic Foundation -- |t References -- |g 7.1. |t Analytical Solution for Out-of-Plane Vibration of a Curved Euler Beam -- |g 7.1.1. |t Differential Equations for Displacement Functions -- |g 7.1.2. |t Determination of Displacement Functions -- |g 7.1.3. |t Internal Forces and Moments -- |g 7.1.4. |t Equilibrium and Continuity Conditions -- |g 7.1.5. |t Determination of Natural Frequencies and Mode Shapes -- |g 7.1.6. |t Classical and Non-Classical Boundary Conditions -- |g 7.1.7. |t Numerical Examples -- |g 7.2. |t Analytical Solution for Out-of-Plane |
| 880 | 0 | 0 | |t Vibration of a Curved Timoshenko Beam -- |g 7.2.1. |t Coupled Equations of Motion and Boundary Conditions -- |g 7.2.2. |t Uncoupled Equation of Motion for uy -- |g 7.2.3. |t Relationships Between ψx, ψθ and uy -- |g 7.2.4. |t Determination of Displacement Functions Uy(θ), ψx(θ) and ψθ(θ) -- |g 7.2.5. |t Internal Forces and Moments -- |g 7.2.6. |t Classical Boundary Conditions -- |g 7.2.7. |t Equilibrium and Compatibility Conditions -- |g 7.2.8. |t Determination of Natural Frequencies and Mode Shapes -- |g 7.2.9. |t Numerical Examples -- |g 7.3. |t Analytical Solution for In-Plane Vibration of a Curved Euler Beam -- |g 7.3.1. |t Differential Equations for Displacement Functions -- |g 7.3.2. |t Determination of Displacement Functions -- |g 7.3.3. |t Internal Forces and Moments -- |g 7.3.4. |t Continuity and Equilibrium Conditions -- |g 7.3.5. |t Determination of Natural Frequencies and Mode Shapes -- |g 7.3.6. |t Classical Boundary Conditions -- |g 7.3.7. |t Mode Shapes Obtained From Finite Element Method and Analytical (Exact) Method -- |g 7.3.8. |t Numerical Examples -- |g 7.4. |t Analytical Solution for In-Plane Vibration of a Curved Timoshenko Beam -- |g 7.4.1. |t Differential Equations for Displacement Functions -- |g 7.4.2. |t Determination of Displacement Functions -- |g 7.4.3. |t Internal Forces and Moments -- |g 7.4.4. |t Equilibrium and Compatibility Conditions. |
| 880 | 0 | 0 | |6 505-01/(S |g Contents note continued: |g 7.4.5. |t Determination of Natural Frequencies and Mode Shapes -- |g 7.4.6. |t Classical and Non-Classical Boundary Conditions -- |g 7.4.7. |t Numerical Examples -- |g 7.5. |t Out-of-Plane Vibration of a Curved Beam by Finite Element Method with Curved Beam Elements -- |g 7.5.1. |t Displacement Functions and Shape Functions -- |g 7.5.2. |t Stiffness Matrix for Curved Beam Element -- |g 7.5.3. |t Mass Matrix for Curved Beam Element -- |g 7.5.4. |t Numerical Example -- |g 7.6. |t In-Plane Vibration of a Curved Beam by Finite Element Method with Curved Beam Elements -- |g 7.6.1. |t Displacement Functions -- |g 7.6.2. |t Element Stiffness Matrix -- |g 7.6.3. |t Element Mass Matrix -- |g 7.6.4. |t Boundary Conditions of the Curved and Straight Finite Element Methods -- |g 7.6.5. |t Numerical Examples -- |g 7.7. |t Finite Element Method with Straight Beam Elements for Out-of-Plane Vibration of a Curved Beam -- |g 7.7.1. |t Property Matrices of Straight Beam Element for Out-of-Plane Vibrations -- |g 7.7.2. |t Transformation Matrix for Out-of-Plane Straight Beam Element -- |g 7.8. |t Finite Element Method with Straight Beam Elements for In-Plane Vibration of a Curved Beam -- |g 7.8.1. |t Property Matrices of Straight Beam Element for In-Plane Vibrations -- |g 7.8.2. |t Transformation Matrix for the In-Plane Straight Beam Element -- |t References -- |g 8.1. |t Free Vibration Response of an SDOF System -- |g 8.2. |t Response of an Undamped SDOF System Due to Arbitrary Loading -- |g 8.3. |t Response of a Damped SDOF System Due to Arbitrary Loading -- |g 8.4. |t Numerical Method for the Duhamel Integral -- |g 8.4.1. |t General Summation Techniques -- |g 8.4.2. |t Linear Loading Method -- |g 8.5. |t Exact Solution for the Duhamel Integral -- |g 8.6. |t Exact Solution for a Damped SDOF System Using the Classical Method -- |g 8.7. |t Exact Solution for an Undamped SDOF System Using the Classical Method -- |g 8.8. |t Approximate Solution for an SDOF Damped System by the Central Difference Method -- |g 8.9. |t Solution for the Equations of Motion of an MDOF System -- |g 8.9.1. |t Direct Integration Methods -- |g 8.9.2. |t Mode Superposition Method -- |g 8.10. |t Determination of Forced Vibration Response Amplitudes -- |g 8.10.1. |t Total and Steady Response Amplitudes of an SDOF System -- |g 8.10.2. |t Determination of Steady Response Amplitudes of an MDOF System -- |g 8.11. |t Numerical Examples for Forced Vibration Response Amplitudes -- |g 8.11.1. |t Frequency-Response Curves of an SDOF System -- |g 8.11.2. |t Frequency-Response Curves of an MDOF System -- |t References -- |g A.1. |t List of Integrals -- |g A.2. |t Theory of Modified Half-Interval (or Bisection) Method -- |g A.3. |t Determinations of Influence Coefficients -- |g A.3.1. |t Determination of Influence Coefficients aiYM and aiψM -- |g A.3.2. |t Determination of Influence Coefficients aiYQ and aiψQ -- |g A.4. |t Exact Solution of a Cubic Equation -- |g A.5. |t Solution of a Cubic Equation Associated with Its Complex Roots -- |g A.6. |t Coefficients of Matrix [H] Defined by Equation (7.387) -- |g A.7. |t Coefficients of Matrix [H] Defined by Equation (7.439) -- |g A.8. |t Exact Solution for a Simply Supported Euler Arch -- |t References. |
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