Free Vibrations of a Micro/Nano Spherical Shell Based on Modified Couple Stress Theory

In small scale systems such as micro-electro-mechanics (MEMs) or nano-electro-mechanics (NEMs) systems, distance between atoms or molecules are comparable with the dimensions of the system. So, classical continuum theories are not applicable in analyzing such systems. Micro sphere and Fullerene (C60) are good examples of spherical low scale structures that are used in such devices. Therefore, many theories in different field such as MD (Molecular Dynamic), strain gradient theory, non-local elasticity, couple stress theory etc. have been developed. In the paper, free vibrations of a micro/nano scale spherical shell are studied based on first order shear deformation theory and modified couple stress theory (MCST). MCST is one of the well-known theories among non-classical elasticity theories which can capture the size effect in the small scale investigation. In the literature governing equations of modified couple stress for spherical shells has been developed by using Hamilton’s principle. Equations have been solved by using a semianalytical method called GDQ (Generalized Differential Quadrature). Natural frequencies are exactly calculated and are validated by comparing them with MD simulation of C60. Also, the effects of changing different geometrical and scale parameters on natural frequencies are studied in this investigation. It is shown that scale parameter is the most effective parameter on the natural frequencies of the micro / nano sphere.