Mechanical Vibration: Analysis, Uncertainties and Control, Second Edition (Mechanical Engineering)

An effective text must be well balanced and thorough in its approach to a topic as expansive as vibration, and Mechanical Vibration is just such a textbook. Written for both senior undergraduate and graduate course levels, this updated and expanded second edition integrates uncertainty and control into the discussion of vibration, outlining basic concepts before delving into the mathematical rigors of modeling and analysis. Mechanical Vibration: Analysis, Uncertainties, and Control, Second Edition provides example problems, end-of-chapter exercises, and an up-to-date set of mini-projects to enhance students' computational abilities and includes abundant references for further study or more in-depth information. The author provides a MATLAB® primer on an accompanying CD-ROM, which contains original programs that can be used to solve complex problems and test solutions. The book is self-contained, covering both basic and more advanced topics such as stochastic processes and variational approaches. It concludes with a completely new chapter on nonlinear vibration and stability. Professors will find that the logical sequence of material is ideal for tailoring individualized syllabi, and students will benefit from the abundance of problems and MATLAB programs provided in the text and on the accompanying CD-ROM, respectively. A solutions manual is also available with qualifying course adoptions.

Introduction and Background
Qualitative Systems Concepts
Qualitative Probability Concepts
Qualitative Vibration, Uncertainties, and Control
Analysis and Design: Interrelationships
Computational Modeling and Design
Modeling for Vibration
Newton's Second Law of Motion
Units
Some Mathematics
Taylor Series and Linearization
Ordinary Differential Equations
Matrices
Transition
Single Degree of Freedom Vibration: An Introduction to Discrete Models
Example Problems and Motivation
Mathematical Modeling: Deterministic
Free Vibration with No Damping
Harmonic Forced Vibration with No Damping
Concepts Summary
Problems
Single Degree of Freedom Vibration: Discrete Models with Damping
Damping
Free Vibration with Damping
Forced Vibration with Damping
Harmonic Excitation and Damped Response
Periodic But Not Harmonic Excitation
Arbitrary Loading: Laplace Transform
Step Loading
Impulsive Excitation
Arbitrary Loading: Convolution
Concepts Summary
Problems
Single Degree of Freedom Vibration: Advanced Topics
Introduction to Lagrange's Equation
Notions of Randomness
Notions of Control
The Inverse Problem
A Self-Excited System and Stability
Solution Analysis and Design Techniques
Concepts Summary
Problems
Mini-Projects
Single Degree of Freedom Vibration: Probabilistic Forces
Introduction
Example Problems and Motivation
Random Variables
Mathematical Expectation
Probability Densities Useful in Applications
Two Random Variables
Random Processes
Random Vibration
Concepts Summary
Problems
Mini-Projects
Vibration Control
Introduction
Feedback Control
Performance of Feedback Control Systems
Automatic Control of Transient Response
Sensitivity to Parameter Variations
State Variable Models
Concepts Summary
Problems
Mini-Projects
Variational Principles
Introduction
Virtual Work
Lagrange's Equation
Hamilton's Principle
Lagrange's Equation with Damping
Concepts Summary
Problems
Additional Readings
Multi Degree of Freedom Vibration
Example Problems and Motivation
Stiffness and Flexibility
Derivation of Equations of Motion
Undamped Vibration
Direct Method: Free Vibration with Damping
Modal Analysis
Concepts Summary
Problems
Mini-Projects
Multi Degree of Freedom Vibration: Advanced Topics
Overview
Generalization to n Degrees of Freedom
Unrestrained Systems
The Geometry of the Eigenvalue Problem
Periodic Structures
Inverse Vibration: Estimate Mass and Stiffness
Sloshing of Fluids in Containers
Stability of Motion
Stochastic Response of a Linear MDOF System
Rayleigh's Quotient
Monte Carlo Simulation
Concepts Summary
Problems
Mini-Projects
Continuous Models for Vibration
Continuous Limit of a Discrete Formulation
Vibration of Strings
Longitudinal (Axial) Vibration of Beams
Torsional Vibration of Shafts
Transverse Vibration of Beams
Beam Vibration: Special Problems
Concepts Summary
Problems
Mini-Projects
Continuous Models for Vibration: Advanced Models
Vibration of Membranes
Vibration of Plates
Random Vibration of Continuous Structures
Approximate Methods
Where Variables Do Not Separate
Concepts Summary
Problems
Mini-Projects
Nonlinear Oscillation
Examples of Nonlinear Vibration
Fundamental Nonlinear Equations
The Phase Plane
Perturbation Methods
Subharmonic and Superharmonic Oscillations
The Mathieu Equation
The van der Pol Equation
Motion in the Large
Advanced Topics
Concluding Summary
Problems
Mini-Projects
Index