Scale Effects Analysis Of Laminates Vibration Based On New Modified Couple Stress Theory By Finite Element Method

A free vibration model of composite laminated Mindlin plate(span-depth ratio at 10-20) is established based on the new modified couple stress theory for anisotropic material. In this theory, the curvature tensor is asymmetric, while the couple stress bending moment is symmetry. Hamilton's principle is employed to derive the governing equations of motion and boundary conditions. This new model can be reduced to the model of composite laminated thin plate based on the modified couple stress theory, and the model of composite laminated Mindlin plate based on classical theory. An example of natural frequencies analysis with a cross-ply simple supported square-plate is used to show the scale effects of the natural frequencies. Numerical results show that the present model can capture the scale effects of free vibration of micro-scale composite laminated Mindlin plate.And then, a refined triangular plate element based on new modified couple stress theory is firstly developed for free vibration analysis of composite laminated Mindlin plate. The present element can satisfy C1 weak continuity condition and C0 continuity condition. Numerical results show that the present element can capture the scale effects of free vibration of micro-scale laminated composite plate with various complex boundary conditions. Moreover, the numerical results of the present element for simply supported square plates, can coincide with corresponding analytical results.