MECHANICS OF DEFORMABLE SOLIDS

Original article

https://doi.org/10.24866/2227-6858/2025-1/3-17

Shlyakhin D.A., Yurin V.A.

Dmitry A. Shlyakhin, Doctor of Engineering Sciences, Professor, Head of Department of Structural Mechanics, Engineering Geology, Grounds and Foundations, Samara State Technical University (Samara, Russian Federation), d-612-mit2009@yandex.ru; https://orcid.org/0000-0003-0926-7388

Vladimir A. Yurin, Post-Graduate Student, Assistant of Department of Structural Mechanics, Engineering Geology, Grounds and Foundations, Samara State Technical University (Samara, Russian Federation), get8ack@mail.ru; https://orcid.org/0009-0008-7412-9540

Non-axisymmetric coupled problem of thermoelectroelasticity for a long multi-layered cylinder

Abstract. To enhance the efficiency and accuracy of temperature piezoceramic sensors, it is essential to develop algorithms for solving various problems of the thermoelectroelasticity theory. Characterizing the relatively weak coupling effect between fields of different physical natures leads to construction of closed analytical solutions. In this article authors consider the problem of thermoelectroelasticity for a long multi-layered cylinder, one layer of which is made permanently from piezoceramics, while the others vary in material, thickness and arrangement within the structure. On the inner surface of the cylinder, a boundary condition of the first kind is applied in the form of a non-stationary non-axisymmetric thermal impact. On the outer surface, a law of convective heat exchange (third kind boundary condition) and a constant ambient temperature are specified. The surfaces of the piezoceramic layer are coated with electrodes and connected to a measuring device with high input resistance, moreover the inner surface of the piezoceramics is grounded. The limitation on the rates of thermal impact and structure thickness changes allowed to use the equations of equilibrium, electrostatics and heat conduction into the mathematical formula. The initial boundary value problem is solved in a coupled formulation. A closed solution to the non-self-adjoint system of differential equations was constructed by using Fourier transforms along the circumferential coordinate and generalized biorthogonal finite integral transforms along the radial coordinate. The resulting dependencies allowed for the description of thermal, electrical and elastic fields in the multi-layered cylinder, as well as the analysis of the influence of the physical and mechanical characteristics of the materials and layer thicknesses on the magnitude of the induced electrical signal under non-axisymmetric non-stationary thermal impact.

Keywords:non-axisymmetric problem of thermoelectroelasticity, long multi-layered cylinder, piezoceramics, Fourier transforms, biorthogonal finite integral transforms

See the reference in English at the end of the article

For citation: Shlyakhin D.A., Yurin V.A. Non-axisymmetric coupled problem of thermoelectroelasticity for a long multi-layered cylinder. FEFU: School of Engineering Bulletin, 2025, no. 1(62), pp. 3–17. (In Russ.).