Size-dependent nonlinear harmonically soft excited oscillations of nonlocal strain gradient FGM composite truncated conical microshells with magnetostrictive facesheets

Abstract

This paper investigates the size-dependent nonlinear primary resonant dynamics of truncated conical microshells (TSMs) made of magnetostrictive facesheets with a functionally graded material (FGM) under external magnetic field and mechanical harmonic soft excitation. To accomplish this purpose, a framework is established using a microstructure-dependent third-order shear deformation shell (TSDS) model based on nonlocal strain gradient continuum elasticity. By employing discretized differential operators achieved from generalized differential quadrature (GDQ) technique, a numerical solution is adopted to acquire nonlocal strain gradient amplitude- and frequency-responses for the primary resonant dynamics of FGM-TCMs. The jump phenomenon related to the loss of first stability branch and jumping down to lower stable branches could occur in the nonlinear primary resonances of FGM composite TCMs. It is illustrated that frequency-response bends to right by the hardening-type of nonlinearity. This pattern is enhanced by nonlocal size effect, which is weakened under strain gradient size dependency. Also, it can be observed that at higher material gradient index values, the hardening-type of nonlinearity enhances and nonlocal strain gradient frequency-response bends to right more considerably.