Orthotropic piezoelectric patches for control of symmetric laminates via an integral equation

Formulation of the problem for the feedback displacement control of a vibrating laminated plate with orthotropic piezoelectric sensors and actuators is given in terms of an integral equation. The objective is to develop a formulation which facilitates the numerical solution to obtain the eigenfrequencies and eigenfunctions of the piezo-controlled plate. The control is carried out via piezoelectric sensors and actuators which are of orthorhombic crystal class mm2 with poling in the z direction. The initial formulation of the problem is given in terms of a differential equation which is the conventional formulation most often used in the literature. The conversion to an integral equation formulation is achieved by introducing an explicit Green’s function. Explicit expressions for the kernel of the integral equation are given and the method of solution using the new formulation is outlined. The solution technique involves approximating the integral equation with an infinite system of linear equations and using a finite number of these equations to obtain the numerical results.