# SHEN Zhiyuan-Regarding to use the effective Kirshhoff plate property to model a microbeam

I am studying the vibrational behaviour of a microbeam made of a polymer (Fig. 1). I came across your paper "Equivalent models of corrugated panels" and find the effective material modelling reported in that paper very helpful for solving my modelling problem. I got some problems that I want to seek for your advices.

1.                         (b)

Fig. 1, (a) a microbeam model. (b) the double-layered perforation structure of the microbeam

The microbeam has a double-layered perforation structure (Fig. 1, (b)). The perforation rate is different on the two layers, which are connected via arrays of pillars. Both perforation and pillars are closer packed in y-direction (the beam length direction) than the x-direction (the beam width direction) to render an anisotropic in plane material property. The thickness/side length ratio in the paddle part is 1/25 (width= 100 micrometre; thickness = 4 micrometer) so the paddle part can be treated as a Kirchhoff plate. The width of the beam, however, gradually tapers to 10 micrometer at its clamped end. Can I treat the whole microbeam as a Kirshhoff plate and use the effective Kirshhoff plate model to predict the vibrational frequencies and mode shape of this microbeam? Will the tapering make the structure invalid to be treated as a Kirchhoff plate? Is there other effective plate model better suited for this microbeam?

The fabricated micro-beam in fact got curvature due to processing residue stress. Can the effective Kirshhoff plate flexibility tensor be assigned to a curved shell in a COMSOL model? Will the shell model with the correct curvature together with the effective Kirshhoff plate flexibility tensor be enough to predict the vibrational behavior of the microbeam?