Free Vibration of a Rectangular Parallelepiped Using the Theory of a Cosserat Point

Abstract

Free vibration of a rectangular parallelepiped composed of a homogeneous linear elastic isotropic material is studied. The parallelepiped is modeled as an isotropic Cosserat point and simple formulas are developed to predict the lowest frequencies of vibration. Within the context of the theory, extensional and shear vibrations are uncoupled. The lowest extensional frequency predicted by the Cosserat theory is compared with available exact solutions and with predictions of thin rod theory. Finally, by introducing a simple modification of the director inertia coefficient it is shown that the Cosserat predictions of the extensional frequencies are correct.