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Regarding to use the effective Kirshhoff plate property to model a microbeam

SHEN Zhiyuan's picture

I am studying the vibrational behaviour of a microbeam made of a polymer (Fig. 1). The beam consists of a paddle part and a tapered part and is fixed at the tapered end.

 

 

 

Fig. 1, a microbeam model.

 

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?

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