Journal of Theoretical
and Applied Mechanics
0, 0, pp. , Warsaw 0

Free vibration of hyper-elastic microbeam, using an ‘augmented Biderman model’

Ardeshir Karami Mohammadi, Saeed Danaee Barforooshi
A new augmented Biderman model inspired by the modified couple stress theory has been introduced to investigate the effect of small size in addition to the effect of nonlinearity of materials. Using this model, free vibration of a hyper-elastic micro beam is investigated. In the Biderman model for hyper-elastic materials, strain energy does not include the effect of small size. A term inspired by the modified coupling stress theory, related to the small size effect, is added to the Biderman strain energy function. Then, in order to calculate the added term, the correlation between the material constants in the Biderman model and the linear elastic constants is obtained. The equation of motion is obtained using the Extended Hamilton principle and then is solved using the Galerkin and perturbation methods. Effect of thickness to length ratio on normalized frequency was studied for different modes. It was shown that when thickness gets larger in comparison with length scale parameter, the normalized frequency tends to classical Biderman results.

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