Determination of spectral densities of dynamic characteristics of a nonlinear model of structure

Autor: A. V. Berezovskii, O. N. Tushev
Rok vydání: 2013
Předmět:
Zdroj: Journal of Machinery Manufacture and Reliability. 42:14-21
ISSN: 1934-9394
1052-6188
DOI: 10.3103/s1052618813010147
Popis: A stochastic problem of the dynamics of a nonlinear model of structure is considered. The problem is solved with the use of an expansion of the solution in the truncated orthogonal basis of eigenvectors of the linear model. It is assumed that nonlinearities of the system do not result in a fundamental change in its dynamical behavior, but contribute a significant quantitative correction relative to the linear model. The nonlinear characteristics are statistically linearized. The coefficients of statistical linearization are formally interpreted as some variations in the corresponding elements of the stiffness matrix of the linear model. Spectral densities, displacement variances of the linearized system, as well as its eigenvalues and eigenvectors, are represented as a power series expansion in the above variations considering linear or square approximations. To find the coefficients in the expansion, the sensitivity theory is used. This allows one to form a set of algebraic transcendental equations in displacement variances, which is solved by the method of successive approximations. Then all the target spectral densities are found. The results are illustrated by examples.
Databáze: OpenAIRE
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