Nonlinear impulsive and vibration analysis of nonlocal FG-CNT reinforced sandwich plate by considering agglomerations

Abstract

This paper is focused on impulsive and subsequent vibration response of a nano-scale composite sandwich plate considering both nonlocal effect and nanoparticle agglomerations. In particular, the core is homogeneous polymethyl methacrylate (PMMA) and the face sheet is PMMA matrix with functionally graded carbon nanotubes (short for FG-CNT). The material properties are given by Eshelby-Mori-Tanaka's approach taking into account of CNT agglomerations. The equations of motion for the FG-CNT reinforced nanoplate are derived based on nonlocal strain gradient theory, Reddy's higher order shear deformation theory and von-Karman nonlinear deformation theory. The impulsive and vibration problems for simply supported FG-CNT plates are solved using Galerkin method and Newton iteration method where the solutions have been verified with the literature. By considering impulsion of step load, exponential load and sinusoidal load and, it is found that weaker size effect, fewer CNT agglomerations, higher CNT content, smaller functional gradient, thinner core, bigger aspect ratio and larger length thickness ratio can enhance the stiffness of the nanoplate and thus will induce smaller center displacement during the load process and higher free vibration frequency after unloading, regardless of load type. However, the subsequent vibration amplitude is significantly influenced by the impulsive load type. Among the material parameters, minimizing size effect and agglomerations could greatly improve the structural stiffness whereas the improvement by varying functional gradient is very limited. It is the first time that a FG-CNT reinforced sandwich plate, especially considering nonlocal effect and nanoparticle agglomerations, is treated in the context of impulsive and subsequent vibration problems. The solutions presented in this paper could provide a benchmark for the design and manufacture of such a composite nanoplate.