Summary
The application and the advantages of the method of certain generalized quasi-moment functions are demonstrated by way of a simple mechanical example. The stress of the considered viscoelastic beam, subjected to a stochastically variable temperature, is described by a nonlinear (casea) or a linear (caseb) equation of first order with stochastic coefficients resulting by passing Gaussian white noise through a linear shaping filter. As a result, the final differential equation system is nonlinear also in caseb. The mean value, the variance (for the casea andb), the covariance function and the spectral density (for caseb only) of the stress are estimated by means of linear quasi-moment equations with good convergence. In contrast to this, the results which were obtained by the normal distribution method, here being used as the basic approximation, are affected with great deviations.
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Sperling, L. Approximate analysis of nonlinear stochastic differential equations using certain generalized quasi-moment functions. Acta Mechanica 59, 183–200 (1986). https://doi.org/10.1007/BF01181663
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DOI: https://doi.org/10.1007/BF01181663