Introduction. The development of ultrasonic technology requires the creation of piezoelectric transducers with improved operational and metrological characteristics. One of the most promising directions is the use of composite materials. As shown in the literature, porous piezoceramics possess a unique property: their piezoelectric modulus d33 is practically independent of porosity, whereas the elastic moduli noticeably decrease as porosity increases. This opens up possibilities for the design of high-performance devices, particularly composites with a polymer matrix and porous piezoelectric ceramic rods with axial polarization. However, despite the sufficient study of their static properties, theoretical analysis of the dynamic behavior of such structures, including their simplified two-dimensional models, under bending vibrations and longitudinal polarization, is virtually absent in the scientific literature. In this regard, the objective of the work is to develop a simplified mathematical model for the analysis of bending vibrations of a layered plate of the specified composite and to identify the effect of porosity on its dynamic characteristics.

Materials and Methods. The structure is made of a piezoelectric composite consisting of several layers. Each layer is 1–3 piezoelectric composite, formed by a polymer matrix and porous longitudinally polarized piezoceramic rods. The mathematical formulation of the boundary value problems is performed within the framework of the linear theory of electroelasticity. Based on Kirchhoff-Love hypotheses and assumptions regarding the electric potential distribution, an applied method for calculating steady-state bending vibrations of a layered plate is proposed. The adequacy of the approach is verified through its comparison with the results of finite element modeling implemented in the ACELAN package.

Results. The key outcome of the study was the development and successful testing of an applied theory that reduced the three-dimensional boundary-value problem of electroelasticity for layered piezoelectric elements to a simpler two-dimensional formulation. This significantly reduced calculation time compared to traditional finite element methods while maintaining the required accuracy. To verify the proposed model, numerical testing was performed by comparing it with calculations in the ACELAN software package. The comparative analysis showed almost complete agreement between the results in the low-frequency range, including the precise determination of the first bending mode frequency. The obtained correspondence confirmed the high adequacy and reliability of the developed method, demonstrating its applicability as an efficient tool for the analysis and optimal design of piezoelectric devices.

Discussion. One of the key challenges in the design of layered piezoelectric transducers is the high resource intensity of three-dimensional modeling without transitioning to efficient characteristics, which significantly limits optimization possibilities. The proposed approach, based on reducing the three-dimensional problem to a two-dimensional one, represents a significant step forward in addressing this issue. Its main advantage is the reduction in computational costs and the possibility of using simpler software tools compared to “heavy” CAE packages in numerical analysis. This opens the way to multiple runs, including those employing evolutionary algorithms, in the process of searching for the optimal geometry and structure of the piezoelectric element. Validation of the model based on comparison with calculations in the ACELAN finite element package has shown a high degree of correspondence in the low-frequency region, which confirms its adequacy for practical application. At the same time, the identified limitations related to the frequency range and differences in the elastic properties of the layers outline the boundaries of applicability and set directions for subsequent research.

Conclusion. As a result of the conducted research, an efficient calculation method has been developed and tested. It reduces the three-dimensional boundary value problem of electroelasticity for layered piezoelectric elements to a two-dimensional formulation. The main outcome is a significant acceleration of numerical modeling while maintaining accuracy. It is shown that the proposed theory provides high correctness of results in the low-frequency range, up to the first flexural mode, which has been confirmed by comparison with reference data from finite element analysis in ACELAN. This demonstrates the practical significance of the method as an efficient tool for the iterative search for the optimal design of converters. Prospects are opening up for its application in engineering practice when designing new types of piezoceramic devices, as well as for the further development of applied theory — in the direction of expanding the frequency range and adapting to more complex multilayer structures.