Nonlinear stochastic vibration of GPRMF cylindrical shell with harmonic and white noise excitations

Abstract

This study focuses on analyzing the behavior of a graphene platelet reinforced metal foams (GPRMF) cylindrical shell under both harmonic and random excitation using advanced stochastic methods. A nonlinear stochastic differential equation describes the shell's random vibration, and the probability density function (PDF) of the vibration response is calculated using the random integral approach. The methodology demonstrates high accuracy in capturing the system's dynamic properties. The impact of external excitation frequency on the marginal and joint PDFs is thoroughly examined. The study shows that external excitation frequency significantly impacts the marginal and joint probability density functions of the vibration response. By utilizing the amplitude response curve under pure harmonic excitation, the stochastic vibration behavior under combined harmonic and white noise excitations can be effectively predicted. The study further explores the effects of random excitation strength and other parameters on the vibration response, providing insights into the displacement response and its statistical characteristics. The results validate the methods employed and highlight their capability in accurately predicting the complex dynamic behavior of GPRMF cylindrical shells.