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

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Naturwissenschaften Physik Mechanik

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