Analytic Bifurcation Investigation of Cylindrical Shallow Shells under ‎Lateral Stochastic Excitation

In this paper، the nonlinear behavior، instability and bifurcation phenomena in the response of a cylindrical shallow shell under lateral white noise excitation are studied. The structure interacts with a general non aging viscous medium that can be modeled by relaxation or creep kernels. Using the powerful FPK equation and some practical and logical simplifications، an exact solution for such complex system including nonlinearity، viscoelasticity and randomness is obtained. Since all statistical properties of response such as mean، variance، statistical moments، central moments، etc. can be obtained from the probability density function، the behavior of this function including the number and sign of its roots and their effects on the stability، bifurcation phenomenon and the type of bifurcation is investigated and studied. In this process، using some non dimensional quantities، the governing equation and the probability density function are rearranged such that the results of simulations can be used for a broad band of cylindrical shallow shells. Finally، using some examples، the variations of the non dimensional quantities on the whole behavior، stability and bifurcation type of response are studied.