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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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On the determination of the power spectrum of randomly excited oscillators via stochastic averaging: An alternative perspective
TL;DR: In this article, a perspective on the veracity of the conditional power spectral density (PSD) derivation is provided by utilizing spectral representations both for the excitation and for the response processes of the nonlinear system; this is done in conjunction with a stochastic averaging treatment of the problem.
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Polynomial chaos expansions for optimal control of nonlinear random oscillators
TL;DR: In this article, the polynomial chaos decomposition of stochastic variables and processes is implemented in conjunction with optimal control of nonlinear dynamical systems, and the results reveal that the performance of the controlled oscillators is greatly improved, as gaged by probabilistic quantities of interest.
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Stochastic Response of Offshore Platforms by Statistical Cubicization
TL;DR: In this paper, a method of statistical cubicization is proposed to predict stochastic response of offshore platform to a Morison-type nonlinear random wave loading, where the nonlinearity is replaced by an equivalent polynomial expansion up to cubic order.
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The engineering merit of the “Effective Period” of bilinear isolation systems
Nicos Makris,Georgios Kampas +1 more
TL;DR: In this paper, a parametric analysis of the forced vibration response of a wide collection of bilinear isolation systems subjected to pulse and seismic excitations is presented, where the authors employ Fourier and Wavelet analysis together with a powerful time domain identification method for linear systems known as the Prediction Error Method.
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Finite element solution of Fokker–Planck equation of nonlinear oscillators subjected to colored non-Gaussian noise
TL;DR: In this article, a 3D finite element (FE) formulation is developed to solve the corresponding 3-D Fokker Planck (FP) equations, where the joint probability density functions of the state variables are typically non-Gaussian and are used for computing the crossing statistics of the response, an essential metric for time variant reliability analysis.