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| Preface | |
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| Acknowledgements | |
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| Basic Concepts | |
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| Statics, dynamics and structural dynamics | |
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| Coordinates, displacement, velocity and acceleration | |
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| Simple harmonic motion | |
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| Time history representation | |
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| Complex exponential representation | |
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| Mass, stiffness and damping | |
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| Mass and inertia | |
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| Stiffness | |
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| Stiffness and flexibility matrices | |
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| Damping | |
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| Energy methods in structural dynamics | |
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| Rayleigh's energy method | |
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| The principle of virtual work | |
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| Lagrange's equations | |
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| Linear and non-linear systems | |
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| Systems of units | |
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| Absolute and gravitational systems | |
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| Conversion between systems | |
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| The SI system | |
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| References | |
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| The Linear Single Degree of Freedom System: Classical Methods | |
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| Setting up the differential equation of motion | |
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| Single degree of freedom system with force input | |
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| Single degree of freedom system with base motion input | |
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| Free response of single-DOF systems by direct solution of the equation of motion | |
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| Forced response of the system by direct solution of the equation of motion | |
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| The Linear Single Degree of Freedom System: Response in the Time Domain | |
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| Exact analytical methods | |
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| The Laplace transform method | |
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| The convolution or Duhamel integral | |
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| Listings of standard responses | |
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| 'Semi-analytical' methods | |
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| Impulse response method | |
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| Straight-line approximation to input function | |
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| Superposition of standard responses | |
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| Step-by-step numerical methods using approximate derivatives | |
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| Euler method | |
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| Modified Euler method | |
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| Central difference method | |
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| The Runge-Kutta method | |
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| Discussion of the simpler finite difference methods | |
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| Dynamic factors | |
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| Dynamic factor for a square step input | |
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| Response spectra | |
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| Response spectrum for a rectangular pulse | |
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| Response spectrum for a sloping step | |
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| References | |
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| The Linear Single Degree of Freedom System: Response in the Frequency Domain | |
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| Response of a single degree of freedom system with applied force | |
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| Response expressed as amplitude and phase | |
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| Complex response functions | |
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| Frequency response functions | |
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| Single-DOF system excited by base motion | |
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| Base excitation, relative response | |
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| Base excitation: absolute response | |
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| Force transmissibility | |
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| Excitation by a rotating unbalance | |
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| Displacement response | |
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| Force transmitted to supports | |
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| References | |
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| Damping | |
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| Viscous and hysteretic damping models | |
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| Damping as an energy loss | |
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| Energy loss per cycle - viscous model | |
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| Energy loss per cycle - hysteretic model | |
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| Graphical representation of energy loss | |
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| Specific damping capacity | |
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| Tests on damping materials | |
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| Quantifying linear damping | |
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| Quality factor, Q | |
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| Logarithmic decrement | |
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| Number of cycles to half amplitude | |
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| Summary table for linear damping | |
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| Heat dissipated by damping | |
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| Non-linear damping | |
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| Coulomb damping | |
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| Square law damping | |
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| Equivalent linear dampers | |
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| Viscous equivalent for coulomb damping | |
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| Viscous equivalent for square law damping | |
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| Limit cycle oscillations with square-law damping | |
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| Variation of damping and natural frequency in structures with amplitude and time | |
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| Introduction to Multi-degree-of-freedom Systems | |
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| Setting up the equations of motion for simple, undamped, multi-DOF systems | |
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| Equations of motion from Newton's second law and d'Alembert's principle | |
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| Equations of motion from the stiffness matrix | |
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| Equations of motion from Lagrange's equations | |
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| Matrix methods for multi-DOF systems | |
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| Mass and stiffness matrices: global coordinates | |
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| Modal coordinates | |
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| Transformation from global to modal coordinates | |
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| Undamped normal modes | |
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| Introducing eigenvalues and eigenvectors | |
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| Damping in multi-DOF systems | |
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| The damping matrix | |
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| Damped and undamped modes | |
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| Damping inserted from measurements | |
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| Proportional damping | |
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| Response of multi-DOF systems by normal mode summation | |
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| Response of multi-DOF systems by direct integration | |
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| Fourth-order Runge-Kutta method for multi-DOF systems | |
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| Eigenvalues and Eigenvectors | |
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| The eigenvalue problem in standard form | |
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| The modal matrix | |
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| Some basic methods for calculating real eigenvalues and eigenvectors | |
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| Eigenvalues from the roots of the characteristic equation and eigenvectors by Gaussian elimination | |
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| Matrix iteration | |
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| Jacobi diagonalization | |
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| Choleski factorization | |
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| More advanced methods for extracting real eigenvalues and eigenvectors | |
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| Complex (damped) eigenvalues and eigenvectors | |
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| References | |
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| Vibration of Structures | |
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| A historical view of structural dynamics methods | |
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| Continuous systems | |
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| Vibration of uniform beams in bending | |
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| The Rayleigh-Ritz method: classical and modern | |
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| Component mode methods | |
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| Component mode synthesis | |
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| The branch mode method | |
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| The finite element method | |
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| An overview | |
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| Equations of motion for individual elements | |
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| Symmetrical structures | |
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| References | |
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| Fourier Transformation and Related Topics | |
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| The Fourier series and its developments | |
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| Fourier series | |
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| Fourier coefficients in magnitude and phase form | |
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| The Fourier series in complex notation | |
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| The Fourier integral and Fourier transforms | |
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| The discrete Fourier transform | |
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| Derivation of the discrete Fourier transform | |
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| Proprietary DFT codes | |
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| The fast Fourier transform | |
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| Aliasing | |
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| Response of systems to periodic vibration | |
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| Response of a single-DOF system to a periodic input force | |
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| References | |
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| Random Vibration | |
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| Stationarity, ergodicity, expected and average values | |
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| Amplitude probability distribution and density functions | |
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| The Gaussian or normal distribution | |
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| The power spectrum | |
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| Power spectrum of a periodic waveform | |
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| The power spectrum of a random waveform | |
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| Response of a system to a single random input | |
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| The frequency response function | |
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| Response power spectrum in terms of the input power spectrum | |
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| Response of a single-DOF system to a broadband random input | |
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| Response of a multi-DOF system to a single broad-band random input | |
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| Correlation functions and cross-power spectral density functions | |
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| Statistical correlation | |
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| The autocorrelation function | |
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| The cross-correlation function | |
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| Relationships between correlation functions and power spectral density functions | |
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| The response of structures to random inputs | |
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| The response of a structure to multiple random inputs | |
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| Measuring the dynamic properties of a structure | |
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| Computing power spectra and correlation functions using the discrete Fourier transform | |
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| Computing spectral density functions | |
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| Computing correlation functions | |
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| Leakage and data windows | |
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| Accuracy of spectral estimates from random data | |
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| Fatigue due to random vibration | |
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| The Rayleigh distribution | |
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| The S-N diagram | |
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| References | |
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| Vibration Reduction | |
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| Vibration isolation | |
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| Isolation from high environmental vibration | |
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| Reducing the transmission of vibration forces | |
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| The dynamic absorber | |
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| The centrifugal pendulum dynamic absorber | |
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| The damped vibration absorber | |
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| The springless vibration absorber | |
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| References | |
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| Introduction to Self-Excited Systems | |
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| Friction-induced vibration | |
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| Small-amplitude behavior | |
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| Large-amplitude behavior | |
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| Friction-induced vibration in aircraft landing gear | |
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| Flutter | |
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| The bending-torsion flutter of a wing | |
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| Flutter equations | |
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| An aircraft flutter clearance program in practice | |
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| Landing gear shimmy | |
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| References | |
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| Vibration testing | |
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| Modal testing | |
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| Theoretical basis | |
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| Modal testing applied to an aircraft | |
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| Environmental vibration testing | |
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| Vibration inputs | |
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| Functional tests and endurance tests | |
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| Test control strategies | |
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| Vibration fatigue testing in real time | |
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| Vibration testing equipment | |
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| Accelerometers | |
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| Force transducers | |
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| Exciters | |
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| References | |
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| A Short Table of Laplace Transforms | |
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| Calculation of Flexibility Influence Coefficients | |
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| Acoustic Spectra | |
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| Index | |