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<sub>s</sub>) 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<sub>d</sub> , 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<sub>s</sub> and P<sub>d</sub> 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.