Actuator Effect of a Piezoelectric Anisotropic Plate Model

Abstract

This paper addresses the actuator effect of a piezoelectric anisotropic plate model, depending on the location of the applied electric potentials, and for different clamped boundary conditions. It corresponds to integer optimization problems, whose objective functions involve the displacement of the plate. We adopt the two-dimensional piezoelectric anisotropic nonhomogeneous plate model derived in Figueiredo and Leal [1]. This model is first discretised by the finite element method. Then, we describe the associated integer optimization problems, which aim to find the maximum displacement of the plate, as a function of the location of the applied electric potentials. In this sense, we also introduce a related multi-objective optimization problem, that is solved through genetic algorithms. Several numerical examples are reported. For all the tests, the stiffness matrices and force vectors have been evaluated with the subroutines planre and platre, of the CALFEM toolbox of MATLAB [2], and, the genetic algorithms have been implemented in C ++ .

Modeling and numerical study of actuator and sensor effects for a laminated piezoelectric plate

“…We remark that the numerical study for the actuator problem presented in this paper constitutes a continuation of results in the previous work [4]. Differently from the model considered in the present paper, in [4] the plates under consideration are mechanically monoclinic and the modified piezoelectric coefficients are independent of the thickness variable. Thus, the tangential and transversal mechanical displacements are uncoupled and the problem simplifies considerably.…”

“…These optimization problems are solved by the elitist genetic algorithms described in [3]. We remark that the numerical study for the actuator problem presented in this paper constitutes a continuation of results in the previous work [4]. Differently from the model considered in the present paper, in [4] the plates under consideration are mechanically monoclinic and the modified piezoelectric coefficients are independent of the thickness variable.…”

“…Moreover, let L e and S e be the matrices that correspond to the derivatives of the shape functions of the bilinear and the non-conforming finite elements, respectively (cf. (38) and (39) in [4]).…”

“…We also utilize the 2 • 8-matrix M and the 12 • 1-vector N e that correspond, respectively, to the four shape functions of the bilinear finite element and the twelve shape functions corresponding to the non-conforming finite element defined inx (cf. (26) and (27) in [4]). Moreover, let L e and S e be the matrices that correspond to the derivatives of the shape functions of the bilinear and the non-conforming finite elements, respectively (cf.…”

Integrated and Consistent Active Control Formulation and Piezotransducer Position Optimization of Plate Structures considering Spillover Effects

“…Many researchers for optimizing their work have used the GA [34][35][36][37]. The terminology used for GA is brought in Table 1.…”