Small Scale Effects on the Large Amplitude Nonlinear Vibrations of Multilayer Functionally Graded Composite Nanobeams Reinforced with Graphene-Nanoplatelets

摘要: The main purpose of the present investigation is to analyze more comprehensively size-dependent nonlinear free vibration response multilayer functionally graded graphene platelet-reinforced composite (GPLRC) nanobeams. As a consequence, both hardening stiffness and softening size effect are taken into consideration by implementation nonlocal strain gradient elasticity theory within framework third-order shear deformation beam theory. platelet (GPL) nanofillers dispersed uniformly or in accordance with three different patterns based on layerwise change their weight fraction through individual layers. Halpin-Tsai micromechanical scheme utilized estimate effective material properties GPLRC With aid Hamilton's principle, non-classical governing differential equations motion derived. After that, an improved perturbation technique conjunction Galerkin method employed achieve explicit analytical solution for frequency It indicated that at zero amplitude, pattern GPL dispersion has no influence significance dependencies. However, taking large amplitude account, nonlocality effects O-GPLRC X-GPLRC nanobeams minimum maximum, respectively.