Response of Cantilever Model with Inertia Nonlinearity under Transverse Basal Gaussian Colored Noise Excitation

Abstract

Considering the curvature nonlinearity and longitudinal inertia nonlinearity caused by geometrical deformations, a slender inextensible cantilever beam model under transverse pedestal motion in the form of Gaussian colored noise excitation was studied. Present stochastic averaging methods cannot solve the equations of random excited oscillators that included both inertia nonlinearity and curvature nonlinearity. In order to solve this kind of equations, a modified stochastic averaging method was proposed. This method can simplify the equation to an Itô differential equation about amplitude and energy. Based on the Itô differential equation, the stationary probability density function (PDF) of the amplitude and energy and the joint PDF of the displacement and velocity were studied. The effectiveness of the proposed method was verified by numerical simulation.