
Structural Dynamics and Vibration in Practice
An Engineering Handbook
By: Douglas Thorby
Paperback | 8 January 2008
At a Glance
420 Pages
24.13 x 17.15 x 2.54
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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;
-Includes 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.
It 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.
1.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
2.Written by a leading industry expert, with a worked example lead approach for clarity and ease of understanding
3.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
| Preface | p. xiii |
| Acknowledgements | p. xv |
| Basic Concepts | p. 1 |
| Statics, dynamics and structural dynamics | p. 1 |
| Coordinates, displacement, velocity and acceleration | p. 1 |
| Simple harmonic motion | p. 2 |
| Time history representation | p. 3 |
| Complex exponential representation | p. 5 |
| Mass, stiffness and damping | p. 7 |
| Mass and inertia | p. 7 |
| Stiffness | p. 10 |
| Stiffness and flexibility matrices | p. 12 |
| Damping | p. 14 |
| Energy methods in structural dynamics | p. 16 |
| Rayleigh's energy method | p. 17 |
| The principle of virtual work | p. 19 |
| Lagrange's equations | p. 21 |
| Linear and non-linear systems | p. 23 |
| Systems of units | p. 23 |
| Absolute and gravitational systems | p. 24 |
| Conversion between systems | p. 26 |
| The SI system | p. 27 |
| References | p. 28 |
| The Linear Single Degree of Freedom System: Classical Methods | p. 29 |
| Setting up the differential equation of motion | p. 29 |
| Single degree of freedom system with force input | p. 29 |
| Single degree of freedom system with base motion input | p. 33 |
| Free response of single-DOF systems by direct solution of the equation of motion | p. 34 |
| Forced response of the system by direct solution of the equation of motion | p. 38 |
| The Linear Single Degree of Freedom System: Response in the Time Domain | p. 45 |
| Exact analytical methods | p. 46 |
| The Laplace transform method | p. 46 |
| The convolution or Duhamel integral | p. 50 |
| Listings of standard responses | p. 53 |
| 'Semi-analytical' methods | p. 55 |
| Impulse response method | p. 56 |
| Straight-line approximation to input function | p. 56 |
| Superposition of standard responses | p. 56 |
| Step-by-step numerical methods using approximate derivatives | p. 59 |
| Euler method | p. 60 |
| Modified Euler method | p. 62 |
| Central difference method | p. 62 |
| The Runge-Kutta method | p. 65 |
| Discussion of the simpler finite difference methods | p. 69 |
| Dynamic factors | p. 70 |
| Dynamic factor for a square step input | p. 70 |
| Response spectra | p. 72 |
| Response spectrum for a rectangular pulse | p. 72 |
| Response spectrum for a sloping step | p. 74 |
| References | p. 76 |
| The Linear Single Degree of Freedom System: Response in the Frequency Domain | p. 77 |
| Response of a single degree of freedom system with applied force | p. 77 |
| Response expressed as amplitude and phase | p. 77 |
| Complex response functions | p. 81 |
| Frequency response functions | p. 83 |
| Single-DOF system excited by base motion | p. 86 |
| Base excitation, relative response | p. 87 |
| Base excitation: absolute response | p. 91 |
| Force transmissibility | p. 93 |
| Excitation by a rotating unbalance | p. 94 |
| Displacement response | p. 95 |
| Force transmitted to supports | p. 96 |
| References | p. 97 |
| Damping | p. 99 |
| Viscous and hysteretic damping models | p. 99 |
| Damping as an energy loss | p. 103 |
| Energy loss per cycle - viscous model | p. 103 |
| Energy loss per cycle - hysteretic model | p. 104 |
| Graphical representation of energy loss | p. 105 |
| Specific damping capacity | p. 106 |
| Tests on damping materials | p. 108 |
| Quantifying linear damping | p. 108 |
| Quality factor, Q | p. 108 |
| Logarithmic decrement | p. 109 |
| Number of cycles to half amplitude | p. 110 |
| Summary table for linear damping | p. 111 |
| Heat dissipated by damping | p. 112 |
| Non-linear damping | p. 112 |
| Coulomb damping | p. 113 |
| Square law damping | p. 113 |
| Equivalent linear dampers | p. 114 |
| Viscous equivalent for coulomb damping | p. 115 |
| Viscous equivalent for square law damping | p. 116 |
| Limit cycle oscillations with square-law damping | p. 117 |
| Variation of damping and natural frequency in structures with amplitude and time | p. 117 |
| Introduction to Multi-degree-of-freedom Systems | p. 119 |
| Setting up the equations of motion for simple, undamped, multi-DOF systems | p. 119 |
| Equations of motion from Newton's second law and d'Alembert's principle | p. 120 |
| Equations of motion from the stiffness matrix | p. 120 |
| Equations of motion from Lagrange's equations | p. 121 |
| Matrix methods for multi-DOF systems | p. 122 |
| Mass and stiffness matrices: global coordinates | p. 122 |
| Modal coordinates | p. 126 |
| Transformation from global to modal coordinates | p. 127 |
| Undamped normal modes | p. 132 |
| Introducing eigenvalues and eigenvectors | p. 132 |
| Damping in multi-DOF systems | p. 142 |
| The damping matrix | p. 142 |
| Damped and undamped modes | p. 143 |
| Damping inserted from measurements | p. 144 |
| Proportional damping | p. 145 |
| Response of multi-DOF systems by normal mode summation | p. 147 |
| Response of multi-DOF systems by direct integration | p. 155 |
| Fourth-order Runge-Kutta method for multi-DOF systems | p. 156 |
| Eigenvalues and Eigenvectors | p. 159 |
| The eigenvalue problem in standard form | p. 159 |
| The modal matrix | p. 161 |
| Some basic methods for calculating real eigenvalues and eigenvectors | p. 162 |
| Eigenvalues from the roots of the characteristic equation and eigenvectors by Gaussian elimination | p. 162 |
| Matrix iteration | p. 165 |
| Jacobi diagonalization | p. 168 |
| Choleski factorization | p. 177 |
| More advanced methods for extracting real eigenvalues and eigenvectors | p. 178 |
| Complex (damped) eigenvalues and eigenvectors | p. 179 |
| References | p. 180 |
| Vibration of Structures | p. 181 |
| A historical view of structural dynamics methods | p. 181 |
| Continuous systems | p. 182 |
| Vibration of uniform beams in bending | p. 182 |
| The Rayleigh-Ritz method: classical and modern | p. 189 |
| Component mode methods | p. 194 |
| Component mode synthesis | p. 195 |
| The branch mode method | p. 208 |
| The finite element method | p. 213 |
| An overview | p. 213 |
| Equations of motion for individual elements | p. 221 |
| Symmetrical structures | p. 234 |
| References | p. 235 |
| Fourier Transformation and Related Topics | p. 237 |
| The Fourier series and its developments | p. 237 |
| Fourier series | p. 237 |
| Fourier coefficients in magnitude and phase form | p. 243 |
| The Fourier series in complex notation | p. 245 |
| The Fourier integral and Fourier transforms | p. 246 |
| The discrete Fourier transform | p. 247 |
| Derivation of the discrete Fourier transform | p. 248 |
| Proprietary DFT codes | p. 255 |
| The fast Fourier transform | p. 256 |
| Aliasing | p. 256 |
| Response of systems to periodic vibration | p. 260 |
| Response of a single-DOF system to a periodic input force | p. 261 |
| References | p. 265 |
| Random Vibration | p. 267 |
| Stationarity, ergodicity, expected and average values | p. 267 |
| Amplitude probability distribution and density functions | p. 270 |
| The Gaussian or normal distribution | p. 274 |
| The power spectrum | p. 279 |
| Power spectrum of a periodic waveform | p. 279 |
| The power spectrum of a random waveform | p. 281 |
| Response of a system to a single random input | p. 286 |
| The frequency response function | p. 286 |
| Response power spectrum in terms of the input power spectrum | p. 287 |
| Response of a single-DOF system to a broadband random input | p. 288 |
| Response of a multi-DOF system to a single broad-band random input | p. 296 |
| Correlation functions and cross-power spectral density functions | p. 299 |
| Statistical correlation | p. 299 |
| The autocorrelation function | p. 300 |
| The cross-correlation function | p. 302 |
| Relationships between correlation functions and power spectral density functions | p. 303 |
| The response of structures to random inputs | p. 305 |
| The response of a structure to multiple random inputs | p. 305 |
| Measuring the dynamic properties of a structure | p. 307 |
| Computing power spectra and correlation functions using the discrete Fourier transform | p. 310 |
| Computing spectral density functions | p. 312 |
| Computing correlation functions | p. 314 |
| Leakage and data windows | p. 317 |
| Accuracy of spectral estimates from random data | p. 318 |
| Fatigue due to random vibration | p. 320 |
| The Rayleigh distribution | p. 321 |
| The S-N diagram | p. 322 |
| References | p. 324 |
| Vibration Reduction | p. 325 |
| Vibration isolation | p. 326 |
| Isolation from high environmental vibration | p. 326 |
| Reducing the transmission of vibration forces | p. 332 |
| The dynamic absorber | p. 332 |
| The centrifugal pendulum dynamic absorber | p. 336 |
| The damped vibration absorber | p. 338 |
| The springless vibration absorber | p. 342 |
| References | p. 345 |
| Introduction to Self-Excited Systems | p. 347 |
| Friction-induced vibration | p. 347 |
| Small-amplitude behavior | p. 347 |
| Large-amplitude behavior | p. 349 |
| Friction-induced vibration in aircraft landing gear | p. 350 |
| Flutter | p. 353 |
| The bending-torsion flutter of a wing | p. 354 |
| Flutter equations | p. 358 |
| An aircraft flutter clearance program in practice | p. 360 |
| Landing gear shimmy | p. 362 |
| References | p. 366 |
| Vibration testing | p. 367 |
| Modal testing | p. 368 |
| Theoretical basis | p. 368 |
| Modal testing applied to an aircraft | p. 369 |
| Environmental vibration testing | p. 373 |
| Vibration inputs | p. 373 |
| Functional tests and endurance tests | p. 374 |
| Test control strategies | p. 375 |
| Vibration fatigue testing in real time | p. 376 |
| Vibration testing equipment | p. 377 |
| Accelerometers | p. 377 |
| Force transducers | p. 378 |
| Exciters | p. 378 |
| References | p. 385 |
| A Short Table of Laplace Transforms | p. 387 |
| Calculation of Flexibility Influence Coefficients | p. 389 |
| Acoustic Spectra | p. 393 |
| Index | p. 397 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780750680028
ISBN-10: 0750680024
Published: 8th January 2008
Format: Paperback
Language: English
Number of Pages: 420
Audience: Professional and Scholarly
Publisher: Butterworth-Heinemann
Country of Publication: GB
Dimensions (cm): 24.13 x 17.15 x 2.54
Weight (kg): 0.79
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