Dynamic shape control of sub-regions of linear elastic beams by self-stress actuation

Abstract

This chapter presents a paper that discusses dynamic shape control of subregions of linear elastic beams by self-stress actuation. Control can be realized by sources of self-stress acting in the linear elastic background beam. In many practical applications, it is sufficient to control only a subregion of the beam. Self-stress can only be applied within the subregion. This chapter investigates distribution of self-stress. which—when superimposed on the disturbance—results in a zero displacement and cross-sectional rotation of the subregion of the beam given the transient external disturbance of the beam. Only deflection and cross-sectional rotation relative to a motion that satisfies nonhomogenous kinematic boundary conditions are zero. The relative motion of the subregion then can be represented by a convolution integral. Hence, it vanishes if the kernel of the convolution integral vanishes. This latter condition is met if the self-stress resultants correspond to the statically admissible bending moment and transverse shear force.