# Optimizing Energy Conversion in a Piezo Disk Using a Controlled Supply of Electrical Load
## 1 Introduction
In this paper, the possibility of increasing the efficiency of energy conversion at certain resonance frequencies is studied along with the possibility of turning off some frequencies from the working spectrum of the element with the help of a controlled energy input. Mathematically, we have the problem of determining the largest value of a non-negative function and its zero on a segment. A brief overview of model situations: a piezoceramic body with an internal elliptical crack, a piezoceramic body with an external elliptical crack, and a piezoceramic body with a spherical cavity are investigated in [4]. The dependencies of stresses and electrical displacements on the shape of the cavity are obtained for the cases of electrical and solely mechanical loads. Paper [5] considered the simulation of a Rosen-type ring piezoelectric transformer. The developed model is based on the Hamiltonian approach, which allows obtention of the main parameters and estimation of the efficiency for the first radial vibrational modes. The methodology and presentation of the final results are described in detail. The input bandwidth and the distribution of the electric potential on the surface of the secondary part are compared with numerical and experimental data. The electromechanical model of the disk piezoelectric transformer (PT) is studied in works [6; 7]. To analyze models of this type, the vibration characteristics of the piezoelectric disc with free boundary conditions are preliminarily analyzed. According to the results of the vibration analysis of the piezoelectric disk, the operating frequency and vibration mode of the PT are selected. Then, the electromechanical equations of motion for the PT can be obtained based on [PERSON]'s principle. [PERSON]'s principle can be used to model the coupled electromechanical system for a transformer. Papers [8; 9] experimentally deal with the radial in-plane vibration characteristics of disk-shaped piezoelectric transducers. The radial in-plane motion, which is induced due to Poisson's ratio in the piezoelectric disk polarized in the thickness direction, is measured using an in-plane laser vibrometer, and the natural frequencies are measured using an impedance analyzer. The experimental results are compared with theoretical predictions obtained by simplified theoretical and finite-element analyses. It appears that the fundamental mode of a piezoelectric disk transducer is a radial mode, and its radial displacement distribution from the center to the perimeter is not monotonic but shows a maximum slightly apart from the perimeter. Actuators based on piezoelectric materials have gained high popularity in the development of microrobotic systems due to their high throughput, high resolution, and high force density. However, one of the main disadvantages is the low relative stroke. One of the methods of optimizing the topology, which is used to maximize the drive stroke, is studied in [10]. Along with the optimization of the material density, the optimization of the polarity of the electrodes is considered. This approach allows combination of both material expansion and compression to increase the output volume of the actuator. Optimization of the topology of a node consisting of a piezoelectric layer attached to a plate with a support is considered in [11]. The object of optimization is the piezoelectric layer. The SIMP (Solid Isotropic Material with Penalization) method with forced oscillations by harmonic electrical excitation is considered and applied. The maximum dynamic displacement is reached. It is proven that the considered objective function can be used under certain boundary conditions to optimize sound radiation. The vibration models obtained as a result of the optimization are analyzed in comparison with modes from the analysis of eigenvalues. Multi-frequency optimization is achieved using adaptive weighted sums. As a second optimization criterion, a flat frequency response is included in the optimization process.