Electroelasticity and modal analysis of piezofibre disc FibrCD-actuator

A mathematical electromechanical model of a piezofibre coil disk (FibrCD) actuator has been developed, in which a plurality of turns of a piezoelectric cable «core/piezoelectric layer/shielding electrode» are attached to each other with a polymer binder. In the cable, the piezoelectric layer between the core and the outer shield electrode is radially polarized. For an elementary composite cylindrical cell «core/piezoelectric layer/shielding electrode/polymer shell» an exact analytical solution of the coupled boundary value problem of electroelasticity for deformation and electric fields is obtained. Based on this solution, solutions were obtained for effective characteristics: elastic moduli, piezoelectric coefficients of linear expansion and blocking voltages of the fiber structure of the FibrCD actuator; Note here that composite cylindrical cell lengthwise axis makes the axis of symmetry of its efficient transversal-isotropic electroelastic properties. Further, the found effective properties of the fiber structure are used when considering the deformation of the FibrCD disk actuator as a uniform disk with curvilinear cylindrical anisotropy, when the circumferential coordinate is the axis of symmetry of the transversal-isotropic properties of the disk material based on thermal analogy method. The thermal analogy method is applicable to the case in which the electric field strength due to the control voltage applied to the electrode outputs of the piezoelectric cable significantly exceeds the corresponding direct piezoeffect component due to disc deformation. The coefficients of piezoelectric linear expansion and blocking stresses of the fiber structure of the disk were calculated according to the obtained analytical solution in comparison with other analytical and finite element methods in the ANSYS package; conformity and acceptable accuracy of solutions by different methods are confirmed. Additionally, a modal analysis was performed in the ANSYS package: the first six eigenforms and frequencies of oscillations of the disk and ring FibrCD actuators are presented.