The work develops a generalized approach to the study of thickness (radial) vibrations arising in the piezoceramic plates, cylinders, spheres under electrical loads. The state of the problem and the main approaches, used in the problems of studying the oscillations of electroelastic bodies, are described. The use of multilayer elements with electroded interface surfaces and variable direction of polarization of the layers increases the conversion efficiency of electrical energy into mechanical energy, so multilayer piezoceramic plates, cylinders, spheres with changing polarization directions with electroded interfaces are considered. Because of piezoelectric elements are often embedded in the housing and supplemented with matching layers to protect against mechanical damage, it is necessary to study their effect on the oscillations of the element. The proposed approach makes it possible to study the vibrations of plane, cylindrical and spherical bodies with layers made of various electroelastic and elastic materials. Numerical implementation is carried out using finite differences. Nonstationary oscillations of PZT-4 ceramic elements at zero initial conditions are investigated. Oscillations of multilayer plates, cylinders and spheres with and without an external elastic or viscoelastic reinforcing layer under impulse and harmonic unsteady loads are investigated and compared. There are found own frequencies for 5-layer bodies of different geometry with and without an external layer. The first natural frequency for cylinder and sphere corresponds to the radial mode of oscillations, while the second natural frequency for cylinders and spheres and the first for flat bodies are almost equal and correspond to thickness mode. The transient processes in the elements under impulse loads and the influence of the outer elastic layer (housing or matching layer) are studied, taking into account the Rayleigh attenuation. It is established that for a flat layer the outer layer increases the amplitude and the period of free vibrations after removing the load, and for cylinders and spheres it decreases. The presence of an elastic layer enhances the third and dampens the fourth natural frequency of the transducer, thereby expanding the frequency range of its operation.

'єва. Розрахунок багатошарового електромеханічного перетворювача циліндричної форми при різних ти-пах поляризації в нестаціонарних режимах роботи. Розвинуто чисельний спосіб дослідження коливань циліндричних багатоша-рових електромеханічних перетворювачів з електродованими поверхнями спряження при електричних збуреннях. Проводиться дослідження параметрів електромеханічного стану перетворювача в динаміці в залежності від кількості електродованих шарів та напрямку поляризації. Встановлено залежність періодичності радіальних коливань від геометричних розмірів та пропорційність між амплітудними значеннями переміщень та напружень циліндрів з зустрічно поляризованими шарами та кількістю шарів. Дослі-джено коливання зовнішньої поверхні та їх періодичність при збільшенні внутрішнього отвору циліндра.Ключові слова: п'єзокерамічний перетворювач, нестаціонарні коливання, електричне збурення, багатошаровий п'єзоелемент, напрямок поляризації L. Grigoryeva. Calculation of cylindrical multilayer electromechanical transducer at different polarization types in nonstationary modes. Numerical research method for oscillations of cylindrical multilayer electromechanical transducers with electrode conjugation surfaces at electrical disturbances is developed. Electromechanical state parameters of transducer depending on the number of electrode layers and polarization direction are investigated dynamically. Dependence of the radial oscillations frequency on geometric dimensions and proportionality between amplitude values of displacements and stresses in cylinders with oncoming polarization layers and the number of layers are established. Correlation between outer surface oscillations and cylinder inner opening size is studied.Keywords: piezoceramic transducer, non-stationary oscillations, electrical disturbances, multilayer piezoelectric element, polarization direction Introduction. Piezoceramic electromechanical multilayer cylindrical transducers are often used in acoustoelectric devices for receiving and emitting an acoustic signal including non-stationary one. In this regard it is necessary to study the transmission of electroelastic disturbances in multilayer piezoceramic bodies of cylindrical shape under various manufacturing parameters and operating conditions.In this work oscillations of a multilayer piezoceramic hollow cylinder with electrode surfaces of separation of layers are explored. Oscillations are caused by sudden potential difference, alternatingsign for the adjacent layers. An important issue in designing such bodies is the choice of polarization direction of layers, which affects the emissive ability of the element. Therefore the study of electromechanical state of the piezoelectric element in different polarization types and the choice of optimal variant is accepted as the purpose of the work.Analysis of recent research and publications. Research of oscillations of piezoceramic elements of constructions with non-stationary electrical and mechanical loads is an important aspect for the mechanics of conjugated fields...

The article considers the numerical study of multicriteria optimization of the minimum surface shell of a rectangular contour taking into account the thermal load. The authors cover the theoretical formulation of multicriteria parametric optimization. A method of constructing this minimal surface on a rectangular contour is described. The specifics of the issuance of thermal power load in the optimization calculation, which is in all initial indicators and coefficients. The types of work of target functions are shown, namely: under what conditions they conflict, under what conditions they consolidate, under what conditions they are independent of each other. The numerical study uses the author's software, which allows in automatic mode a multicriteria optimization calculation with target functions - weight and Mises stress, design variables - thickness from 1 to 200 mm, presented as a Mises voltage of 240 MPa. The result showed that the target functions of the conflict change, but the weight decreases by 20%, and the Mises voltage decreases by 37% of the elements. From the graph of the change of objective functions according to the optimal height, what is the point for the objective functions - weight and stress according to Mises is absence. The overall purpose of the study shows the possibility of using authoring software to use two types of optimization: optimization of shapes in the form of these minimum surface parameters on rectangular and multicriteria optimization together on the object under study, which is interesting and applied research in structural mechanics.

Devices that convert vibration energy into electricity and are capable of its accumulation (energy harvesting) are very promising both in mechanical engineering (damping oscillations with the conversion of excess energy into electricity) and in electronics and the environment (systems for energy storage and replenishment). That systems convert extra motion of engineering devises into electrical energy used for their autonomous operation or for power supply of other devices [1]. Another application is portable electronics, where energy storage devices can power or charge mobile phones or other devices. When energy sources are limited, energy harvesting plays an important role in the environment. Energy harvesting as a separate direction began to develop in the 1990s. Human, bicycle, water flow, low-frequency oscillations in mechanisms, etc. can be used as sources of mechanical energy for the piezoelectric transducer. Usually, due to steady oscillations, piezoelectric elements produce alternating electric current, showing the greatest efficiency at resonant frequencies. Most piezoelectric power sources produce power of the order of milliwatts, which is small enough for system use but sufficient for portable devices. Piezoelectric systems can convert the movement of the human body, such as the movement of legs and arms, shocks and blood pressure to obtain energy from implanted or portable sensors. Piezoelectric elements are built into running and walking roads, shoes, pavement, etc. One of the priority areas of research is the development of autonomous wireless sensors that receive energy from the measured signal, or use other ways to obtain mechanical energy. Their use becomes relevant in atypical tasks - measuring oscillations in hard-to-reach places of rotating mechanisms, seismic sensors and so on. Smart roads can play an important role in electricity generation. The incorporation of piezoelectric material into the road can convert the pressure exerted by moving cars into voltage and current.

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