Stochastic dynamic systems with complex‐valued eigensolutions

Sharif Rahman

24 citations0/0 files storedInternational Journal for Numerical Methods in Engineering

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Abstract

Abstract A dimensional decomposition method is presented for calculating the probabilistic characteristics of complex‐valued eigenvalues and eigenvectors of linear, stochastic, dynamic systems. The method involves a function decomposition allowing lower‐dimensional approximations of eigensolutions, Lagrange interpolation of lower‐dimensional component functions, and Monte Carlo simulation. Compared with the commonly used perturbation method, neither the assumption of small input variability nor the calculation of the derivatives of eigensolutions is required by the method developed. Results of numerical examples from linear stochastic dynamics indicate that the decomposition method provides excellent estimates of the moments and/or probability densities of eigenvalues and eigenvectors for various cases including large statistical variations of input. Copyright © 2007 John Wiley & Sons, Ltd.

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References

1999General foundations of high‐dimensional model representations 2001High Dimensional Model Representations 2003Theorems and examples on high dimensional model representation 2004A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics 2002Practical Approaches To Construct RS-HDMR Component Functions 1972Random Eigenvalue Problems in Structural Analysis 2005Decomposition methods for structural reliability analysis 1972Monte Carlo Solution of Nonlinear Vibrations

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2017Homotopy approach for random eigenvalue problem 2013Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure 2009Probability Distributions of Natural Frequencies of Uncertain Dynamic Systems

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