Hamiltonian Mechanics Formulation of Smart Membrane Structure

In this paper, electromechanical equations of motion of smart membrane shell structure (SMSL) are presented. The SMSL is made of polyvinylidene fluoride (PVDF) that has piezoelectricity effect. The PVDF laminate has considered as shallow cylindrical membrane with circular shape of cross section and unity Lame parameters. The actuation mechanism is applied in piezoelectricity relations of SMSL. For this aim, polarization vector is parallel to the applied electric field intensity vector both parallel to the diagonal directions. Extended Hamilton’s principle of analytical mechanics is mechanized and the system dynamics is exploited. Then, by assuming a series form function for displacement and inserting it in dynamic equation without presence of external load, the first three transverse frequencies and corresponding mode shapes of SMSL are calculated

Keywords:

Smart Structures , PVDF , Membrane Shell , Hamilton’s Mechanics