Vibration suppression of composite sandwich beams

Abstract

Although some investigations such as buckling and free vibration of composite sandwich beams have been done analytically, very few analytical work about the forced vibration of composite sandwich beams can be found in the literature. In our study, we get the closed-form solution for the free vibration problems and derive an orthogonality relation consisting the effects of rotary inertia and shear deformation. Unlike the usual orthogonality relation for shallow beams in which the modal shapes are the shapes of deflections corresponding to the natural frequencies, the relation for the composite sandwich beams cannot stand without including the rotation angles. Through the establishment of the orthogonality relation, the forced vibration problems can then be solved by modal analysis. The analytical solution of the forced vibration is useful for the study of vibration suppression. In this study we investigate smart composite sandwich beams with surface bonded piezoelectric sensors and actuators. By combining the present vibration analysis with the classical optimal control method, an observed-state feedback control system for the composite sandwich beams is designed. To show the importance of considering the effects of rotary inertia and shear deformation on the natural frequencies and mode shapes of composite sandwich beams, several illustrative examples are done. Numerical examples of vibration suppression of cantilevered composite sandwich beams are also implemented, which show that their first few vibration modes are successfully controlled.