A new insight on vibrations and buckling of a cantilevered beam under a constant piezoelectric actuation

If external axial forces are not acting on a cantilevered beam, the resultant axial force at any cross section along the beam is equal to zero. Thus according to classical beam theories the lateral vibrations of a cantilevered beam are not influenced by applying a constant electric voltage to collocated surface bonded piezoelectric layers or patches. The purpose of this note is to show that in-plane cross sectional deformations due to small lateral vibrations, that are assumed to have negligible influence in the case of classical beam theories, may change the situation drastically. When coupled with the internal stresses due to the constant electric voltage, these small cross sectional deformations result in a significant influence on the free lateral vibrations. A simple example exhibits the phenomenon. Good agreement between experimental and theoretical results is presented, concerning the frequencies of the first mode of free vibrations and the buckling voltage.