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Random vibration and statistical linearization
J.B. Roberts,Pol D. Spanos +1 more
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TLDR
In this paper, a comprehensive account of statistical linearization with related techniques allowing the solution of a very wide variety of practical non-linear random vibration problems is given, and the principal value of these methods is that they are readily generalized to deal with complex mechanical and structural systems and complex types of excitation such as earthquakes.Abstract:
Interest in the study of random vibration problems using the concepts of stochastic process theory has grown rapidly due to the need to design structures and machinery which can operate reliably when subjected to random loads, for example winds and earthquakes. This is the first comprehensive account of statistical linearization - powerful and versatile methods with related techniques allowing the solution of a very wide variety of practical non-linear random vibration problems. The principal value of these methods is that unlike other analytical methods, they are readily generalized to deal with complex mechanical and structural systems and complex types of excitation such as earthquakes.read more
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Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters
TL;DR: In this article, the authors proposed a method to calculate the time-dependent reliability of linear vibratory systems with random parameters excited by non-stationary Gaussian processes, which combines principles of random vibrations, the total probability theorem and recent advances in timedependent reliability using an integral equation involving the up-crossing and joint upcrossing rates.
Reliability quantification of plates subjected to random vibration and temperature loads
TL;DR: In this article, a random vibration analysis model for packaged plates is proposed for base excited random vibration coupled with temperature loads, and a reliability quantification model is proposed, too, based on this model, and the closed form solution for IWN is derived and the numerical procedure for BLWN is presented.
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Random response of preisach hysteretic systems
TL;DR: In this paper, an approximate method for analyzing the response of Preisach hysteretic systems with non-local memory under stationary Gaussian excitation is proposed and the covariance matrix equation of system response is derived.
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Error analysis of statistical linearization with Gaussian closure for large degree- of-freedom systems
TL;DR: In this article, an analysis of the error induced by applying the method of equivalent statistical linearization (ESL) to randomly excited multi-degree-of-freedom (m.d.) geometrically nonlinear shear-frame structures as the number of degrees of freedom increases is presented.
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A homotopic approach to domain determination and solution refinement for the stationary Fokker–Planck equation
TL;DR: The recursive use of a modified norm induced on the solution domain by the most recent estimate of the stationary probability density function, is shown to significantly improve the accuracy of the approximation over the standard L 2 -norm based Galerkin error projection.