*Structural Dynamics and vibration in practice An Engineering Handbook,Douglas Thorby,Elsevier,2008

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Structural Dynamics and vibration in practice An Engineering Handbook,Douglas Thorby,Elsevier,2008,This book is 419 Pages

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Chapter 1 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

Stiffness and flexibility matrices

Damping

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

Chapter 2 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

Chapter 3 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 references

Chapter 4 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 references

Chapter 5 Damping

*Viscous and hysteretic damping mode

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

Chapter 6 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

Chapter 7 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 references

Chapter 8 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 references

Chapter 9 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

Aliasing

Response of systems to periodic vibration

Response of a single-DOF system to a periodic input force references

Chapter 10 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 references

Chapter 11 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 references

Chapter 12 Introduction to Self-Excited Systems

*Friction-induced vibration

Small-amplitude behavior

Large-amplitude behavior

Friction-induced vibration in aircraft landing gear

Flutter

The bending-torsion flutter of a wing

Flutter equations

An aircraft flutter clearance program in practice

Landing gear shimmy references

Chapter 13 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

Accelerometers

Force transducers

Exciters references