An approach dealing with inertia nonlinearity of a cantilever model subject to lateral basal Gaussian white noise excitation

•We concentrated on the vibrating cantilever model with curvature nonlinearity the inertia nonlinearity under white noise excitation. and on the stochastic effects caused by the inertia nonlinearity which has never been emphasized in formal literatures.•The stochastic averaging method for strong nonlinearity was applied. The longitudinal inertia nonlinear term was expanded in Taylor series. The truncation error happening during the Taylor series expanding was the main reason of the error. A prediction-correction method was proposed to improve the performance of the theoretical predicting. An uniform inextensible slender cantilever model with longitudinal inertia nonlinearity under lateral basal Gaussian white noise excitation was studied. The effect of inertia nonlinearity was especially taken into account, which is the main novelty of this study. A modified stochastic averaging method for strong nonlinearity was applied to transform the system into an Ito differential equation about the transient equivalent amplitude. After that, a prediction-correction method was presented to improve the predicting accuracy. The stationary probability density function (PDF) of transient equivalent amplitude, as well as the joint PDF of the displacement and velocity was studied. The reliability function and the probability density of first passage failure time were also investigated by the theoretical analysis and the Monte Carlo simulation. The Monte Carlo results vindicated these approaches.