Control of bending oscillation of cantilevers via adaptive materials technology

Abstract

This paper is concerned with the problem of controlling the bending oscillations of cantilevers subjected to time-dependent external excitations. The structural model consists of a thin-walled beam of arbitrary cross section and includes a number of nonclassical effects, such as transverse shear, secondary warping, and heterogeneity. The control is achieved via the converse effect of piezoelectric materials bonded to or embedded into the host structure. A dynamic control law relating the piezoelectrically induced bending moment to the angular velocity at the tip of the structure is implemented, and the closed-loop eigenvalues and dynamic response to harmonic excitations are highlighted. A computational methodology based on the extended Galerkin's technique for determining the closed-loop frequency-response characteristics is used, and numerical results revealing the strong implications of the adaptive technology are displayed. (Author)