Piezo-electric control of nonlinear modal interaction in stiffened structures

摘要

With the objective of unraveling the issues involved in the piezo-electric control of the structures afflicted by nonlinearities, two examples are studied, viz. the problem of an axially compressed imperfect column resting on a softening elastic foundation and an imperfect stiffened plate with coincident local and overall critical loads.It is shown that the buckling capacity (the maximum static load, P_s) of these structures can be increased by piezo-electric patches actuated by feedback voltage proportional to the extreme fiber strains. In particular, in the case of stiffened plate piezo-electric patches conveniently located at the top and bottom tips of the stiffener can adequately perform this task. Next the control of these structures set into motion by a sudden application of a lateral load is investigated. The ensuing vibrations are controlled by voltages proportional to the strain rates sensed at the same locations. The control is feasible as long as the axial compression < P_d , the dynamic instability load. The optimality of the 'velocity control' is studied by appropriately varying the feedback gain.In the case of stiffened plate, stabilizing the stiffener has the effect of mitigating the local buckling displacements and amplitudes of the plate thus counteracting the adverse effects of interaction. However, it is shown that local buckling oscillations can be scotched by adding a thin longitudinal piezo-electric patch on the surfaces of the plate panel. While the control within the benchmark values of P_s and P_d in the static and dynamic cases is facile, any increase beyond these values are fraught with steeply increasing demand of electric field strength and consumption of energy.