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Introduction to Structural Dynamics

ISBN-10: 0521865743

ISBN-13: 9780521865746

Edition: 2006

Authors: Bruce K. Donaldson, Michael J. Rycroft, Wei Shyy

List price: $180.00
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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. 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.
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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

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