Vibrations and stability : advanced theory, analysis, and tools / Jon Juel Thomsen.
Thomsen, Jon Juel, 1959-
2021
TA355
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Title Vibrations and stability : advanced theory, analysis, and tools / Jon Juel Thomsen.
Author Thomsen, Jon Juel, 1959-
Edition 3rd ed.
ISBN 9783030680459 (electronic bk.)
3030680452 (electronic bk.)
3030680444
9783030680442
9783030680466 (print)
3030680460
9783030680473 (print)
3030680479
9783030680442
DOI https://doi.org/10.1007/978-3-030-68045-9
Published Cham : Springer, 2021.
Language English
Description 1 online resource (539 pages)
Item Number 10.1007/978-3-030-68045-9 doi
Call Number TA355
Dewey Decimal Classification 620.3
Summary This book ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It is intended for advanced students, university teachers, and researchers in mechanical/structural engineering dynamics, and professional engineers aiming at strengthening their theoretical foundation. Assuming background knowledge in elementary vibrations, it provides a set of useful tools for understanding and analyzing the more complex dynamical phenomena that can be met in engineering and scientific practice. Summarizing first basic linear vibration theory, it progresses over various types of nonlinearity and nonlinear interaction to bifurcation analysis, chaotic vibrations, and special high-frequency effects. It trains the student to analyze simple models, recognize nonlinear phenomena, and work with advanced tools such as perturbation analysis and bifurcation analysis. Focusing attention on a limited number of simple, generic models, the book covers the qualitative behavior of a wide variety of mechanical/structural systems; the key examples dealt with can be fabricated as simple physical models for classroom demonstrations. Explaining theory in terms of relevant examples from real systems, this book is user-friendly and meets the increasing interest in, and significance of, nonlinear dynamics in mechanical/structural engineering. This 3rd edition adds many new topics, sections, figures, exercise problems, literature references, and other updates; it is backed up by a separately available booklet with worked out solutions to exercise problems.
Note 2.7.4 Minimum Properties of the Eigenvalues.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Description based on print version record.
Available in Other Form Vibrations and Stability.
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Intro
Preface
Contents
About the Author
Notations
1 Vibration Basics
1.1 Introduction
1.2 Single Degree of Freedom Systems
1.2.1 Undamped Free Vibrations
1.2.2 Damped Free Vibrations
1.2.3 Harmonic Forcing
1.2.4 Arbitrary Forcing
1.3 Multiple Degree of Freedom Systems
1.3.1 Equations of Motion
1.3.2 Undamped Free Vibrations
1.3.3 Orthogonality of Modes
1.3.4 Damped Free Vibrations
1.3.5 Harmonically Forced Vibrations, No Damping
1.3.6 Harmonically Forced Vibrations, Damping Included
1.3.7 General Periodic Forcing

1.3.8 Arbitrary Forcing, Transients
1.4 Continuous Systems
1.4.1 Equations of Motion
1.4.2 Undamped Free Vibrations
1.4.3 Orthogonality of Modes
1.4.4 Normal Coordinates
1.4.5 Forced Vibrations, No Damping
1.4.6 Forced Vibrations, Damping Included
1.4.7 Complex-Valued Eigenvalues and Mode Shapes
1.4.8 Rayleigh's Method
1.4.9 Ritz Method
1.5 Energy Methods for Setting up Equations of Motion
1.5.1 Lagrange's Equations
1.5.2 Hamilton's Principle
1.5.3 From PDEs to ODEs: Mode Shape Expansion
1.5.4 Using Lagrange's Equations with Continuous Systems

1.6 Nondimensionalized Equations of Motion
1.7 Damping: Types, Measures, Parameter Relations
1.7.1 Damping in Equations of Motion
1.7.2 Damping Models
1.7.3 Damping Measures and Their Relations
1.7.4 Damping Influence on Free Vibration Decay
1.7.5 Damping Influence on Resonance Buildup
1.7.6 Estimating Mass/Stiffness-Proportional Damping Constants
1.7.7 Mass/Stiffness Damping Proportionality Constants for Beams
1.8 The Stiffness and Flexibility Methods for Deriving Equations of Motion
1.8.1 Common Basis
1.8.2 The Flexibility Method
1.8.3 The Stiffness Method

1.8.4 Maxwell's Reciprocity Theorem
1.9 Classification of Forces and Systems
1.9.1 Force Classification
1.9.2 System Classification
1.9.3 Stability Assessment
1.10 Problems
2 Eigenvalue Problems of Vibrations and Stability
2.1 Introduction
2.2 The Algebraic EVP
2.2.1 Mathematical Form
2.2.2 Properties of Eigenvalues and Eigenvectors
2.2.3 Methods of Solution
2.3 The Differential EVP
2.3.1 Mathematical Form
2.4 Stability-Related EVPs
2.4.1 The Clamped-Hinged Euler Column
2.4.2 The Paradox of Follower-Loading
2.4.3 Buckling by Gravity

2.5 Vibration-Related EVPs
2.5.1 Axial Vibrations of Straight Rods
2.5.2 Flexural Vibrations of Beams
2.6 Concepts of Differential EVPs
2.6.1 Multiplicity
2.6.2 Boundary Conditions: Essential or Natural/Suppressible
2.6.3 Function Classes: Eigen-, Test-, and Admissible Functions
2.6.4 Adjointness
2.6.5 Definiteness
2.6.6 Orthogonality
2.6.7 Three Classes of EVPs
2.6.8 The Rayleigh Quotient
2.7 Properties of Eigenvalues and Eigenfunctions
2.7.1 Real-Valueness of Eigenvalues
2.7.2 Sign of the Eigenvalues
2.7.3 Orthogonality of Eigenfunctions

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