Kelly Advanced Vibration Analysis

1. Auflage 2006
ISBN: 978-1-4200-1532-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 664 Seiten

Reihe: Dekker Mechanical Engineering

Delineating a comprehensive theory, Advanced Vibration Analysis provides the bedrock for building a general mathematical framework for the analysis of a model of a physical system undergoing vibration. The book illustrates how the physics of a problem is used to develop a more specific framework for the analysis of that problem. The author elucidates a general theory applicable to both discrete and continuous systems and includes proofs of important results, especially proofs that are themselves instructive for a thorough understanding of the result.

The book begins with a discussion of the physics of dynamic systems comprised of particles, rigid bodies, and deformable bodies and the physics and mathematics for the analysis of a system with a single-degree-of-freedom. It develops mathematical models using energy methods and presents the mathematical foundation for the framework. The author illustrates the development and analysis of linear operators used in various problems and the formulation of the differential equations governing the response of a conservative linear system in terms of self-adjoint linear operators, the inertia operator, and the stiffness operator. The author focuses on the free response of linear conservative systems and the free response of non-self-adjoint systems. He explores three method for determining the forced response and approximate methods of solution for continuous systems.

The use of the mathematical foundation and the application of the physics to build a framework for the modeling and development of the response is emphasized throughout the book. The presence of the framework becomes more important as the complexity of the system increases. The text builds the foundation, formalizes it, and uses it in a consistent fashion including application to contemporary research using linear vibrations.

Zielgruppe

Graduate students and professionals in mechanical engineering, civil engineering, aerospace engineering, and applied mathematics.

Autoren/Hrsg.

Kelly, S. Graham

Fachgebiete

• Naturwissenschaften Physik Mechanik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau

Inhaltsverzeichnis

INTRODUCTION AND VIBRATION OF SINGLE-DEGREE-OF-FREEDOM SYSTEMS
Introduction
Newton's Second Law, Angular Momentum, and Kinetic Energy
Components of Vibrating Systems
Modeling of One-Degree-of-Freedom Systems
Qualitative Aspects of One-Degree-of-Freedom Systems
Free Vibrations of Linear Single-Degree-of-Freedom Systems
Response of a Single-Degree-of-Freedom System Due to Harmonic Excitation
Transient Response of a Single-Degree-of-Freedom System

DERIVATION OF DIFFERENTIAL EQUATIONS USING VARIATIONAL METHODS
Functionals
Variations
Euler-Lagrange Equation
Hamilton's Principle
Lagrange's Equations for Conservative Discrete Systems
Lagrange's Equations for Non-Conservative Discrete Systems
Linear Discrete Systems
Gyroscopic Systems
Continuous Systems
Bars, Strings, and Shafts
Euler-Bernoulli Beams
Timoshenko Beams
Membranes

LINEAR ALGEBRA
Introduction
Three-Dimensional Space
Vector Spaces
Linear Independence
Basis and Dimension
Inner Products
Norms
Gram-Schmidt Orthonormalization Method
Orthogonal Expansions
Linear Operators
Adjoint Operators
Positive Definite Operators
Energy Inner Products

OPERATORS USED IN VIBRATION PROBLEMS
Summary of Basic Theory
Differential Equations for Discrete Systems
Stiffness Matrix
Mass Matrix
Flexibility Matrix
M -1 K and AM
Formulation of Partial Differential Equations for Continuous Systems
Second-Order Problems
Euler-Bernoulli Beam
Timoshenko Beams
Systems with Multiple Deformable Bodies
Continuous Systems with Attached Inertia Elements
Combined Continuous and Discrete Systems
Membranes

FREE VIBRATIONS OF CONSERVATIVE SYSTEMS
Normal Mode Solution
Properties of Eigenvalues and Eigenvectors
Rayleigh's Quotient
Solvability Conditions
Free Response Using the Normal Mode Solution
Discrete Systems
Natural Frequency Calculations Using Flexibility Matrix
Matrix Iteration
Continuous Systems
Second-Order Problems (Wave Equation)
Euler-Bernoulli Beams
Repeated Structures
Timoshenko Beams
Combined Continuous and Discrete Systems
Membranes
Green's Functions

NON-SELF-ADJOINT SYSTEMS
Non-Self-Adjoint Operators
Discrete Systems with Proportional Damping
Discrete Systems with General Damping
Discrete Gyroscopic Systems
Continuous Systems with Viscous Damping

FORCED RESPONSE
Response of Discrete Systems for Harmonic Excitations
Harmonic Excitation of Continuous Systems
Laplace Transform Solutions
Modal Analysis for Undamped Discrete Systems
Modal Analysis for Undamped Continuous Systems
Discrete Systems with Damping

RAYLEIGH-RITZ AND FINITE ELEMENT METHODS
Fourier Best Approximation Theorem
Rayleigh-Ritz Method
Galerkin Method
Rayleigh-Ritz Method for Natural Frequencies and Mode Shapes
Rayleigh-Ritz Methods for Forced Response
Admissible Functions
Assumed Modes Method
Finite Element Method
Assumed Modes Development of Finite Element Method
Bar Element
Beam Element

Exercises
References
Index