Exact closed-form solution for non-local vibration and biaxial buckling of bonded multi-nanoplate system

Abstract

In recent years, nonlocal elasticity theory is widely used for the analytical and computational modeling of nanostructures. This theory, developed by Eringen, has shown to be practical for the vibration and buckling analysis of nanoscale structures and reliable for predesign procedures of nano-devices. This paper considers buckling and dynamic analysis of multi-nanoplate systems. This type of system can be relevant to composite structures embedded with graphene sheets. Exact solutions for the natural frequencies and buckling loads of multi-nanoplate systems have been proposed by considering that the multi-nanoplate system is embedded within an elastic medium. Nonlocal elasticity theory is utilized for the mathematical establishment of the system. The solutions of the homogenous system of differential equations are obtained using the Navier's method and trigonometric method. An asymptotic analysis is proposed to show the influence of increasing number of nanoplates in the system. Analytical expressions are validated with existing results in the literature for some special cases. Numerical results based on the analytical expressions is shown to quantify the effects of the change in nonlocal parameter, stiffness coefficients of the elastic mediums and the number of layers on the natural frequencies and buckling load.