Dynamic instability analysis of magneto-electro-elastic beams with uncertain parameters under static and parametric electric and magnetic fields

Abstract

Parameters uncertainty effects on the dynamic instability behavior of magneto-electro-elastic beams subjected to parametric electric and magnetic excitations are investigated. Several random parameters that may follow various distribution laws are considered. Based on the Timoshenko beam model, a dynamic stochastic problem is formulated. The differential quadrature method is used for the space domain and a modal time domain is formulated. Frequency and time domains are considered and various stochastic methodological approaches are elaborated for numerical solutions. The vibration and divergence instability with respect to static electric and magnetic fields are analyzed. For the random analysis the general polynomial chaos, conditional and Monte Carlo methods are used and a large number of random coefficients as well as random external parametric excitations are considered. The effects of considered random parameters on the dynamic and parametric responses with respect to electric and magnetic fields are investigated.