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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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Galerkin scheme based determination of first-passage probability of nonlinear system response
TL;DR: In this article, an approximate analytical approach for determining the first-passage probability of the response of a class of lightly damped nonlinear oscillators to broadband random excitations is presented.
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An equivalent linearization technique for nonlinear piezoelectric energy harvesters under Gaussian white noise
Wen-An Jiang,Li-Qun Chen +1 more
TL;DR: The exact solution of equivalent linear system is derived from minimizing the mean-squared of the error and the linear equivalent coefficients are presented by the method of normal truncation.
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On alternative approaches to linearization and Morison's equation for wave forces
TL;DR: In this paper, an alternative approach based on the idea of "corresponding linear forms" which give unbiased estimates for the output quantity required from an analysis is proposed. But the linearization factor varies not only with the nature of the output but also with the relative magnitudes of the drag and inertia terms in the Morison9s equation.
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Time delay induced effects on control of non-linear systems under random excitation
TL;DR: In this article, an approximated approach based on the Taylor expansion of the control forces is introduced to study the time delay effects on non-linear systems under normal white noise, where the original system excited by external white noise is transformed into another one under parametric type excitation.
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Wiener path integrals and multi-dimensional global bases for non-stationary stochastic response determination of structural systems
TL;DR: In contrast to earlier implementations of the WPI technique, the herein developed generalization and enhancement circumvents computationally daunting brute-force discretizations of the time domain in cases where the objective is to determine the complete time-dependent non-stationary response PDF.