Nonlocal strain gradient-based geometrically nonlinear vibration analysis of double curved shallow nanoshell containing functionally graded layers

Abstract

It is a fact that while examining the mechanical behavior of nano/microscopic materials, size effects become apparent. This study aims at presenting a new approach to geometrically nonlinear vibration analysis of double curved shallow nanoshell on Kerr foundation containing functionally graded layers under the impacts of harmonic loading in the framework of nonlocal strain gradient theory and the classical shell theory. The three-parameter Kerr model is founded on the independence of the upper and lower elastic layers related to the shear layer. The motion equations of the double curved shallow nanoshell are deduced by introducing the Von Kármán strain-displacement relations. Governing equations are solved by displacement function method and Galerkin method to achieve the deflection differential equation, the fourth-order Runge-Kutta methods are implemented to solve the deflection differential equation of the dynamic system. In this study, the obtained outcomes are compared with other publications indicating that the theoretical results agree with the previously published ones. Afterward, the article investigates the effects of the material length scale parameter, the nonlocal parameter, the geometric parameters and the material properties on the geometrically nonlinear vibration analysis of the double curved shallow nanoshell containing functionally graded layers. This research paper can provide extensive references and valuable guidelines for the impact and application of double curved shallow nanoshell structures containing functionally graded layers.