Transversal vibration of a parametrically excited beam: influence of rotatory inertia and transverse shear on stochastic stability of deformable forms and processes

Abstract

The partial differential equation of transversal stochastic vibration of a parametrically excited beam was derived. The beam is graded by an ideal elastic material, and it is subject to axial stochastic external excitation. The influence of rotatory inertia of beam cross section and transverse shear of beam cross section under the transverse force, and the corresponding members in the partial differential equation are taken into account. Bernoulli particular integral method and Lagrange method of variation constant are used for the transformation problem. The asymptotic averaged method is used for obtaining the first approximation of Itô stochastic differential equations. The sets of Lyapunov exponents are obtained.