Random vibration

About: Random vibration is a research topic. Over the lifetime, 4494 publications have been published within this topic receiving 69569 citations.

Nonlinear Vibration Models for Extremes and Fatigue

Abstract: Hermite moment models of nonlinear random vibration are formulated. These models use response moments (skewness, kurtosis, etc.) to form non‐Gaussian contributions, made orthogonal through a Hermite series. First‐yield and fatigue failure rates are predicted from these moments, which are often simpler to estimate (from either a time. history or analytical model). Both hardening and softening nonlinear models are developed. These are shown to be more flexible than the conventional Charlier and Edgeworth series, with the ability to reflect wider ranges of nonlinear behavior. Analytical moment‐based estimates of spectral densities, crossing rates, probability distributions of the response and its extremes, and fatigue damage rates are formed. These are found to compare well with exact results for various nonlinear models, including nonlinear oscillator responses and quasi‐static responses to Morison wave loads.

An introduction to random vibrations and spectral analysis

Abstract: An introduction to random vibrations and spectral analysis , An introduction to random vibrations and spectral analysis , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

Vibration: Fundamentals and Practice

Abstract: VIBRATION ENGINEERING Introduction Study of Vibration Application Areas History of Vibration Organization of the Book Problems TIME RESPONSE Introduction Undamped Oscillator Heavy Springs Oscillations in Fluid Systems Damped Simple Oscillator Forced Response Problems FREQUENCY RESPONSE Introduction Response to Harmonic Excitations Transform Techniques Mechanical Impedance Approach Transmissibility Functions Receptance Method Problems VIBRATION SIGNAL ANALYSIS Introduction Frequency Spectrum Signal Types Fourier Analysis Random Vibration Analysis Other Topics of Signal Analysis Order Analysis Machine Monitoring and Fault Diagnosis Problems MODAL ANALYSIS Introduction Degrees of Freedom and Independent Coordinates System Representation Modal Vibrations Orthogonality of Natural Modes Static Modes and Rigid Body Modes Other Modal Formulations Forced Vibration Damped Systems State-Space Approach Problems DISTRIBUTED-PARAMETER SYSTEMS Introduction Transverse Vibration of Cables Longitudinal Vibrations of Rods Torsional Vibration of Shafts Flexural Vibration of Beams Damped Continuous Systems Vibration of Membranes and Plates Problems VIBRATION DAMPING Introduction Types of Damping Representation of Damping in Vibration Analysis Measurement of Damping Interface Damping Problems VIBRATION INSTRUMENTATION Introduction Vibration Exciters Control System Performance Specification Motion Sensors and Transducers Torque, Force, and Other Sensors Problems SIGNAL CONDITIONING AND MODIFICATION Introduction Amplifiers Analog Filters Modulators and Demodulators Analog-Digital Conversion Bridge Circuits Linearizing Devices Miscellaneous Signal Modification Circuitry Signal Analyzers and Display Devices Problems VIBRATION TESTING AND HUMAN RESPONSE Introduction Representation of a Vibration Environment Pre-Test Procedures Testing Procedures Some Practical Information Vibration Excitations on Humans Human Response to Vibration Regulation of Human Vibration Problems EXPERIMENTAL MODAL ANALYSIS Introduction Frequency Domain Formulation Experimental Model Development Curve Fitting of Transfer Functions Laboratory Experiments Commercial EMA Systems Problems VIBRATION DESIGN AND CONTROL Introduction Specification of Vibration Limits Vibration Isolation Balancing of Rotating Machinery Balancing of Reciprocating Machines Whirling of Shafts Design through Modal Testing Passive Control of Vibration Active Control of Vibration Control of Beam Vibrations Problems APPENDIX A: DYNAMIC MODELS AND ANALOGIES Model Development Analogies Mechanical Elements Electrical Elements Thermal Elements Fluid Elements State-Space Models Response Analysis and Simulation APPENDIX B: NEWTONIAN AND LAGRANGIAN MECHANICS Vector Kinematics Newtonian (Vector) Mechanics Lagrangian Mechanics APPENDIX C: REVIEW OF LINEAR ALGEBRA Vectors and Matrices Vector-Matrix Algebra Matrix Inverse Vector Spaces Determinants System of Linear Equations Quadratic Forms Matrix Eigenvalue Problem Matrix Transformations Matrix Exponential APPENDIX D: LAPLACE TRANSFORM Introduction Laplace Transform Response Analysis Transfer Function APPENDIX E: DIGITAL FOURIER ANALYSIS AND FFT Unification of the Three Fourier Transform Types Fast Fourier Transform (FFT) Discrete Correlation and Convolution Digital Fourier Analysis Procedures APPENDIX F: SOFTWARE TOOLS SIMULINK MATLAB Control Systems Toolbox LabVIEW APPENDIX G: RELIABILITY CONSIDERATIONS FOR MULTI-COMPONENT UNITS Failure Analysis Bayes' Theorem INDEX

Simulation of Ergodic Multivariate Stochastic Processes

Abstract: A simulation algorithm is proposed to generate sample functions of a stationary, multivariate stochastic process according to its prescribed cross-spectral density matrix. If the components of the vector process correspond to different locations in space, then the process is nonhomogeneous in space. The ensemble cross-correlation matrix of the generated sample functions is identical to the corresponding target. The simulation algorithm generates ergodic sample functions in the sense that the temporal cross-correlation matrix of each and every generated sample function is identical to the corresponding target, when the length of the generated sample function is equal to one period (the generated sample functions are periodic). The proposed algorithm is based on an extension of the spectral representation method and is very efficient computationally since it takes advantage of the fast Fourier transform technique. The generated sample functions are Gaussian in the limit as the number of terms in the frequency discretization of the cross-spectral density matrix approaches infinity. An example involving simulation of turbulent wind velocity fluctuations is presented in order to demonstrate the capabilities and efficiency of the proposed algorithm.

Simulation of Multi-Dimensional Gaussian Stochastic Fields by Spectral Representation

Abstract: The subject of this paper is the simulation of multi-dimensional, homogeneous, Gaussian stochastic fields using the spectral representation method. Following this methodology, sample functions of the stochastic field can be generated using a cosine series formula. These sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic field when the number of terms in the cosine series is large. The ensemble-averaged power spectral density or autocorrelation function approaches the corresponding target function as the sample size increases. In addition, the generated sample functions possess ergodic characteristics in the sense that the spatially-averaged mean value, autocorrelation function and power spectral density function are identical with the corresponding targets, when the averaging takes place over the multi-dimensional domain associated with the fundamental period of the cosine series. Another property of the simulated stochastic field is that it is asymptotically Gaussian as the number of terms in the cosine series approaches infinity. The most important feature of the method is that the cosine series formula can be numerically computed very efficiently using the Fast Fourier Transform technique. The main area of application of this method is the Monte Carlo solution of stochastic problems in structural engineering, engineering mechanics and physics. Specifically, the method has been applied to problems involving random loading (random vibration theory) and random material and geometric properties (response variability due to system stochasticity).