Vibration analysis of scale-dependent thin shallow microshells with arbitrary planform and boundary conditions

Abstract

The current article presents a thorough investigation into the natural frequencies and mode shapes of thin doubly curved shallow microshells by taking into account the influence of material length scale parameter. The mathematical model of system is obtained by applying the Hamilton's principle along with the modified couple stress theory and the Kirchhoff-Love's shell theory. In order to extract the free vibration characteristics of system, the finite element method is employed. Several comparative studies are then conducted to verify the quadrilateral thin shallow shell element. The numerical results are presented for the thin cylindrical, spherical, and hyperbolic paraboloidal shallow microshells with different planforms including rectangle, triangle, circle, and ellipse. Thin microplate as a special case of thin shallow microshell is also analyzed. A profound examination on the numerical results is also performed to divulge the impacts of scale-dependency accompanied by the geometrical parameters and boundary conditions on the free vibration response of system.