Free vibration of a micro-scale composite laminated Reddy plate using a finite element method based on the new modified couple stress theory

Abstract

In this study, a non-confirming element which is a combination of the BCIZ and refined triangular non-conforming element is developed for the free vibration analysis of micro-scale angle-ply laminated Reddy plate based on the new modified couple stress theory. Strain and curvature components of the micro-scale composite laminated Reddy plates based on the new modified couple stress theory use the first- and the second-order derivatives of the transverse displacement. Therefore, the functions are required to satisfy both C0 and C1 to be continuous. There are two types of shape functions for the transverse displacement in the present element. One satisfies the C0 continuity condition exactly while the other satisfies the C1 weak continuity condition. Numerical examples are given in which the results for a simply supported cross-ply micro-scale composite laminated plate obtained by the present element coincide well with the solutions of the analytical Fourier series solutions. We also investigated the effects of ply orientation, boundary conditions and length-to-thickness ratio on the natural frequencies of a micro-scale composite laminated plate using the finite element method (FEM).

Keywords

• Non-conforming element
• New modified couple stress theory
• Composite laminated Reddy plate
• Scale effects
• Free vibration