Vibration characteristics of multilayer functionally graded microplates with variable thickness reinforced by graphene platelets resting on the viscoelastic medium under thermal effects

Due to their improved mechanical properties and adaptability, microplates with tailored variable thickness profiles are becoming essential parts of advanced micro- and nanoelectromechanical systems (MEMS and NEMS). This study conducts a thorough analytical analysis of the vibration properties of thermally loaded, multilayer functionally graded graphene platelet-reinforced composite (FG-GPLRC) microplates of linearly or parabolically varying thickness resting on viscoelastic medium under different boundary conditions. The Halpin-Tsai micromechanical model and the law of mixtures are employed to calculate the effective material characteristics for various reinforcement distributions in the microplate. These distributions encompass uniformly symmetric and asymmetric arrangements. The study utilized the first-order shear deformation theory (FSDT) in conjunction with the modified strain gradient theory (MSGT) and Hamilton's principle to generate the dynamic governing equations for the structure, accounting for size-dependent effects. The resulting equations are afterwards solved using the utilization of the Galerkin technique. This enables the evaluation of the proposed solution's correctness and precision. The impact of various factors on vibration behavior is investigated through numerical analysis. These factors encompass length scale parameters, temperature fluctuations, temperature distribution profiles, boundary conditions, the distribution pattern of the GPL, taper constants in both unidirectional and bidirectional scenarios, the weight fraction of the GPL.