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Thorby D. Structural Dynamics and Vibration in Practice: An Engineering Handbook

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Thorby D. Structural Dynamics and Vibration in Practice: An Engineering Handbook
Elsevier Ltd., 2008. 419 p. — ISBN:978-0-7506-8002-8.
This straightforward text, primer and reference introduces the theoretical, testing and control aspects of structural dynamics and vibration, as practised in industry today.
Written by an expert engineer of over 40 years experience, the book comprehensively opens up the dynamic behavior of structures and provides engineers and students with a comprehensive practice based understanding of the key aspects of this key engineering topic.
Key features
Worked example based makes it a thoroughly practical resource
Aimed at those studying to enter, and already working in industry;
Presents an applied practice and testing based approach while remaining grounded in the theory of the topic
Makes the topic as easy to read as possible, omitting no steps in the development of the subject;
ncludes the use of computer based modelling techniques and finite elements
Covers theory, modelling testing and control in practice
Written with the needs of engineers of a wide range of backgrounds in mind, this book will be a key resource for those studying structural dynamics and vibration at undergraduate level for the first time in aeronautical, mechanical, civil and automotive engineering. It will be ideal for laboratory classes and as a primer for readers returning to the subject, or coming to it fresh at graduate level.
t is a guide for students to keep and for practicing engineers to refer to: its worked example approach ensures that engineers will turn to Thorby for advice in many engineering situations.
Presents students and practitioners in all branches of engineering with a unique structural dynamics resource and primer, covering practical approaches to vibration engineering while remaining grounded in the theory of the topic
Written by a leading industry expert, with a worked example lead approach for clarity and ease of understanding
Makes the topic as easy to read as possible, omitting no steps in the development of the subject; covers computer based techniques and finite elements
Basic Concepts
Statics, dynamics and structural dynamics
Coordinates, displacement, velocity and acceleration
Simple harmonic motion
Time history representation
Complex exponential representation
Mass, stiffness and damping
Mass and inertia
Stiffness and flexibility matrices
Energy methods in structural dynamics
Rayleigh’s energy method
The principle of virtual work
Lagrange’s equations
Linear and non-linear systems
Systems of units
Absolute and gravitational systems
Conversion between systems
The SI system
The Linear Single Degree of Freedom System: Classical Methods
Setting up the differential equation of motion
Single degree of freedom system with force input
Single degree of freedom system with base motion input
Free response of single-DOF systems by direct solution of the equation of motion
Forced response of the system by direct solution of the equation of motion
The Linear Single Degree of Freedom System: Response in the Time Domain
Exact analytical methods
The Laplace transform method
The convolution or Duhamel integral
Listings of standard responses
‘Semi-analytical’ methods
Impulse response method
Straight-line approximation to input function
Superposition of standard responses
Step-by-step numerical methods using approximate derivatives
Euler method
Modified Euler method
Central difference method
The Runge–Kutta method
Discussion of the simpler finite difference methods
Dynamic factors
Dynamic factor for a square step input
Response spectra
Response spectrum for a rectangular pulse
Response spectrum for a sloping step
The Linear Single Degree of Freedom System: Response in the Frequency Domain
Response of a single degree of freedom system with applied force
Response expressed as amplitude and phase
Complex response functions
Frequency response functions
Single-DOF system excited by base motion
Base excitation, relative response
Base excitation: absolute response
Force transmissibility
Excitation by a rotating unbalance
Displacement response
Force transmitted to supports
Viscous and hysteretic damping models
Damping as an energy loss
Energy loss per cycle – viscous model
Energy loss per cycle – hysteretic model
Graphical representation of energy loss
Specific damping capacity
Tests on damping materials
Quantifying linear damping
Quality factor, Q
Logarithmic decrement
Number of cycles to half amplitude
Summary table for linear damping
Heat dissipated by damping
Non-linear damping
Coulomb damping
Square law damping
Equivalent linear dampers
Viscous equivalent for coulomb damping
Viscous equivalent for square law damping
Limit cycle oscillations with square-law damping
Variation of damping and natural frequency in structures with amplitude and time
Introduction to Multi-degree-of-freedom Systems
Setting up the equations of motion for simple, undamped, multi-DOF systems
Equations of motion from Newton’s second law and d’Alembert’s principle
Equations of motion from the stiffness matrix
Equations of motion from Lagrange’s equations
Matrix methods for multi-DOF systems
Mass and stiffness matrices: global coordinates
Modal coordinates
Transformation from global to modal coordinates
Undamped normal modes
Introducing eigenvalues and eigenvectors
Damping in multi-DOF systems
The damping matrix
Damped and undamped modes
Damping inserted from measurements
Proportional damping
Response of multi-DOF systems by normal mode summation
Response of multi-DOF systems by direct integration
Fourth-order Runge–Kutta method for multi-DOF systems
Eigenvalues and Eigenvectors
The eigenvalue problem in standard form
The modal matrix
Some basic methods for calculating real eigenvalues and eigenvectors
Eigenvalues from the roots of the characteristic equation and eigenvectors by Gaussian elimination
Matrix iteration
Jacobi diagonalization
Choleski factorization
More advanced methods for extracting real eigenvalues and eigenvectors
Complex (damped) eigenvalues and eigenvectors
Vibration of Structures
A historical view of structural dynamics methods
Continuous systems
Vibration of uniform beams in bending
The Rayleigh–Ritz method: classical and modern
Component mode methods
Component mode synthesis
The branch mode method
The finite element method
An overview
Equations of motion for individual elements
Symmetrical structures
Fourier Transformation and Related Topics
The Fourier series and its developments
Fourier series
Fourier coefficients in magnitude and phase form
The Fourier series in complex notation
The Fourier integral and Fourier transforms
The discrete Fourier transform
Derivation of the discrete Fourier transform
Proprietary DFT codes
The fast Fourier transform
Response of systems to periodic vibration
Response of a single-DOF system to a periodic input force
Random Vibration
Stationarity, ergodicity, expected and average values
Amplitude probability distribution and density functions
The Gaussian or normal distribution
The power spectrum
Power spectrum of a periodic waveform
The power spectrum of a random waveform
Response of a system to a single random input
The frequency response function
Response power spectrum in terms of the input power spectrum
Response of a single-DOF system to a broadband random input
Response of a multi-DOF system to a single broad-band random input
Correlation functions and cross-power spectral density functions
Statistical correlation
The autocorrelation function
The cross-correlation function
Relationships between correlation functions and power spectral density functions
The response of structures to random inputs
The response of a structure to multiple random inputs
Measuring the dynamic properties of a structure
Computing power spectra and correlation functions using the discrete Fourier transform
Computing spectral density functions
Computing correlation functions
Leakage and data windows
Accuracy of spectral estimates from random data
Fatigue due to random vibration
The Rayleigh distribution
The S–N diagram
Vibration Reduction
Vibration isolation
Isolation from high environmental vibration
Reducing the transmission of vibration forces
The dynamic absorber
The centrifugal pendulum dynamic absorber
The damped vibration absorber
The springless vibration absorber
Introduction to Self-Excited Systems
Friction-induced vibration
Small-amplitude behavior
Large-amplitude behavior
Friction-induced vibration in aircraft landing gear
The bending-torsion flutter of a wing
Flutter equations
An aircraft flutter clearance program in practice
Landing gear shimmy
Vibration testing
Modal testing
Theoretical basis
Modal testing applied to an aircraft
Environmental vibration testing
Vibration inputs
Functional tests and endurance tests
Test control strategies
Vibration fatigue testing in real time
Vibration testing equipment
Force transducers
Appendix A A Short Table of Laplace Transforms
Appendix B Calculation of Flexibility Influence Coefficients
Appendix C Acoustic Spectra
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