Dynamic stability recognition of cylindrical shallow shells in Kelvin–Voigt viscoelastic medium under transverse white noise excitation

Abstract

Dynamic stability analysis of cylindrical shallow shells, as one of the fundamental elements of many engineering structures, is very important in the design of such systems. In many practical applications, the external loads are essentially random in time and space; thus, using the stochastic analysis is recommended. In this article, the dynamic stability of a nonlinear cylindrical shallow shell in a viscous medium under transverse stochastic excitation is investigated analytically. The probability density function of the response is computed using the Fokker–Planck–Kolmogorov equation. Using a series of non-dimensional variables, the governing equation and the probability density function are rewritten so that the results become applicable for a broadband of cylindrical shallow shells. A root locus study on the probability density function is done to obtain the border curves of instability in terms of non-dimensional quasi-slenderness ratio and the mean value of the transverse load. A complete study on the quality and types of instability and bifurcation with respect to defined non-dimensional parameters is made. Finally, the analytic probability density functions are validated using the Monte Carlo simulation.