Active control of the strained state of an asymmetric trimorphic beam under nonstationary modes of operation

We consider the problem of active control of the strained state of an asymmetric trimorphic beam with floating end faces. The nonstationary mechanical load applied to the trimorph is an unknown function of time. The electric signal, varying in time according to a law that is determined by the proposed criterion, is supplied to the electrodes of one of the piezolayers working under the mode of inverse piezoelectric effect. Here, the state of the beam is sustained close to unstrained. The formation of the controlling electric signal and the identification of the external mechanical action are carried out on the basis of the known potential difference, which arises between the electrodes of the second piezolayer, working under the mode of direct piezoelectric effect. The problem is solved using the Laplace integral transformation in time. As a result of the analytic transition to the space of originals, we determine the required quantities from the system of Volterra integral equations, which is solved with the help of regularizing algorithms. The results of calculations and their analysis are also presented.