Nonlinear semi-analytical nonlocal strain-gradient dynamic response investigation of phase-transition-induced transversely graded hierarchical viscoelastic nano/microplates

Abstract

A functionally graded Boltzmann hierarchical viscoelastic model with both stress- and strain-gradient nonlocalities is developed and implemented to extract results that are more precise than results of Eringen's nonlocal elasticity model. The available size-dependent vibration analyses of the nano/microplates have focused on the frequency analysis and even not the time-dependent transient vibration analyses. In the present research, the forced and transient responses of the microplates are studied comprehensively, for the first time, using a three-element standard solid viscoelastic model. The studied transversely symmetric graded viscoelastic microplate and the relevant function of the material properties variations contain notable hints as well. Furthermore, the resulting new sixth-order nonlocal strain gradient integrodifferential equations are solved by a special technique that includes an analytical spatial Navier series-type solution and a trapezoidal and Runge–Kutta integration schemes, in time domain. Finally, the influences of the stress- and strain-gradient nonlocality parameters and the viscoelasticity parameters on the dynamic behaviors of the viscoelastic FGM microplates are investigated in details. Results show that the effects of the strain gradient nonlocality on the viscodynamic results may be much remarkable than those of the length scale nonlocality, in microscales.

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

“…The present research is devoted to nonlinear dynamic lateral deflection and impact analysis of the particle-reinforced FG hyperelastic plates based on the accurate plate theory recently proposed by Shariyat [22,23], taking into account the thickness variations during the loading, even in the element scale. Only a limited number of articles have analyzed the vibration of the structures in the time-domain [24][25][26][27][28][29][30]. The governing equations are developed based on the principle of minimum total potential energy.…”