On the free vibrations of size-dependent closed micro/nano-spherical shell based on the modified couple stress theory

• Free vibrations of a micro/nano-sphere is analyzed based on modified couple stress theory.
• Accuracy and validity of the results are approved by comparing them with the experimental results.
• New scale parameters are proposed for spherical nano-gold, nano-silver and fullerene.
• Effects of different geometries and scale parameter on frequencies are investigated.
• It is approved that increasing scale parameters has more effect on higher mode numbers.

Since classical theory is incapable to justify size-dependency of small scale systems such as micro-electro-mechanics (MEMs) or nano-electro-mechanics (NEMs) systems, modified couple stress theory (MCST) has been developed in order to capture the size effect in the small size investigation. A novel study on the free vibrations of the micro/nano-scale spherical shell based on First-order Shear Deformation Theory (FSDT) and MCST is done. Fullerene (C60C60) is an appropriate example of spherical micro-scale structures. The governing equations of the modified couple stress spherical shell are derived by using Hamilton's principle. Obtained equations are solved using Generalized Differential Quadrature (GDQ) method. The influences of changing geometrical parameter and scale parameter on the natural frequency are investigated. It is shown that the scale parameter is extremely effective on the natural frequency of the micro/nano-sphere. This issue is bolder in the thick spherical shell. Finally, proper scale parameters are proposed for different nano-scale spheres by comparing numerical results with experimental results.