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Description:

This textbook provides the student of aerospace, civil, and mechanical engineering with all the fundamentals of linear structural dynamics analysis. It is designed for an advanced undergraduate or first year graduate course. This textbook is a departure from the usual presentation in two important respects. First, descriptions of system dynamics are based on the simpler to use Lagrange equations. Second, no organizational distinctions are made between multi-degree of freedom systems and single-degree of freedom systems. The textbook is organized on the basis of first writing structural equation systems of motion, and then solving those equations mostly by means of a modal transformation.… More The text contains more material than is commonly taught in one semester so advanced topics are designated by an asterisk. The final two chapters can also be deferred for later studies. The text contains numerous examples and end-of-chapter exercises.Less

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Book details

List price: $180.00 Copyright year: 2006 Publisher: Cambridge University Press Publication date: 10/23/2006 Binding: Hardcover Pages: 566 Size: 7.00" wide x 10.00" long x 1.25" tall Weight: 2.486 Language: English

AuthorTable of Contents

Martin J. Wiener is the Mary Jones Professor of History at Rice University. His previous books include Between Two Worlds: The Political Thought of Graham Wallas (1971), English Culture and the Decline of the Industrial Spirit (1980), and Reconstructing the Criminal (1990).

Preface for the Student

Preface for the Instructor

Acknowledgments

List of Symbols

The Lagrange Equations of Motion

Introduction

Newton's Laws of Motion

Newton's Equations for Rotations

Simplifications for Rotations

Conservation Laws

Generalized Coordinates

Virtual Quantities and the Variational Operator

The Lagrange Equations

Kinetic Energy

Summary

Exercises

Further Explanation of the Variational Operator

Kinetic Energy and Energy Dissipation

A Rigid Body Dynamics Example Problem

Mechanical Vibrations: Practice Using the Lagrange Equations

Introduction

Techniques of Analysis for Pendulum Systems

Example Problems

Interpreting Solutions to Pendulum Equations

Linearizing Differential Equations for Small Deflections

Summary

**Conservation of Energy versus the Lagrange Equations**

**Nasty Equations of Motion**

**Stability of Vibratory Systems**

Exercises

The Large-Deflection, Simple Pendulum Solution

Divergence and Flutter in Multidegree of Freedom, Force Free Systems

Review of the Basics of the Finite Element Method for Simple Elements

Introduction

Generalized Coordinates for Deformable Bodies

Element and Global Stiffness Matrices

More Beam Element Stiffness Matrices

Summary

Exercises

A Simple Two-Dimensional Finite Element

The Curved Beam Finite Element

FEM Equations of Motion for Elastic Systems

Introduction

Structural Dynamic Modeling

Isolating Dynamic from Static Loads

Finite Element Equations of Motion for Structures

Finite Element Example Problems

Summary

**Offset Elastic Elements**

Exercises

Mass Refinement Natural Frequency Results

The Rayleigh Quotient

The Matrix Form of the Lagrange Equations

The Consistent Mass Matrix

A Beam Cross Section with Equal Bending and Twisting Stiffness Coefficients

Damped Structural Systems

Introduction

Descriptions of Damping Forces

The Response of a Viscously Damped Oscillator to a Harmonic Loading

Equivalent Viscous Damping

Measuring Damping

Example Problems

Harmonic Excitation of Multidegree of Freedom Systems

Summary

Exercises

A Real Function Solution to a Harmonic Input

Natural Frequencies and Mode Shapes

Introduction

Natural Frequencies by the Determinant Method

Mode Shapes by Use of the Determinant Method

**Repeated Natural Frequencies**

Orthogonality and the Expansion Theorem

The Matrix Iteration Method

**Higher Modes by Matrix Iteration**

Other Eigenvalue Problem Procedures

Summary

**Modal Tuning**

Exercises

Linearly Independent Quantities

The Cholesky Decomposition

Constant Momentum Transformations

Illustration of Jacobi's Method

The Gram-Schmidt Process for Creating Orthogonal Vectors

The Modal Transformation

Introduction

Initial Conditions

The Modal Transformation

Harmonic Loading Revisited

Impulsive and Sudden Loadings

The Modal Solution for a General Type of Loading

Example Problems

Random Vibration Analyses

Selecting Mode Shapes and Solution Convergence

Summary

**Aeroelasticity**

**Response Spectrums**

Exercises

Verification of the Duhamel Integral Solution

A Rayleigh Analysis Example

An Example of the Accuracy of Basic Strip Theory

Nonlinear Vibrations

Continuous Dynamic Models

Introduction

Derivation of the Beam Bending Equation

Modal Frequencies and Mode Shapes for Continuous Models

Conclusion

Exercises

The Long Beam and Thin Plate Differential Equations

Derivation of the Beam Equation of Motion Using Hamilton's Principle

Sturm-Liouvilie Problems

The Bessel Equation and Its Solutions

Nonhomogeneous Boundary Conditions

Numerical Integration of the Equations of Motion

Introduction

The Finite Difference Method

Assumed Acceleration Techniques

Predictor-Corrector Methods

The Runge-Kutta Method

Summary

**Matrix Function Solutions**

Exercises

Answers to Exercises

Solutions

Solutions

Solutions

Solutions

Solutions

Solutions

Solutions

Solutions

Solutions

Fourier Transform Pairs

Introduction to Fourier Transforms

Index

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