Related dynamic axisymmetric thermoelectroelasticity problem for a long hollow piezoceramic cylinder

Abstract

Introduction. The article studies the problem of investigation of coupled nonstationary thermoelectroelastic fields in piezoceramic structures. The main approaches related to the construction of a general solution to the initial non-selfadjoint equations describing the process under consideration are briefly outlined. The work aims at constructing a new closed solution to the axisymmetric thermoelectroelasticity problem for a long piezoceramic cylinder.Materials and Methods. A long hollow cylinder whose electrodated surfaces were connected to a measuring device with large input resistance was considered. On the cylindrical surfaces of the plate, a time-varying temperature was given. The hyperbolic theory of Lord–Shulman thermo-electro-elasticity was used. The closed solution is constructed using a generalized method of finite integral transformations.Results. The developed calculation algorithm makes it possible to determine the stress–strain state of the cylinder, its temperature, and electric fields. In addition, it becomes possible to investigate the coupling of fields in a piezoceramic cylinder, as well as to analyze the effect of relaxation of the heat flow on the fields under consideration.Discussion and Conclusion. The use of assumptions about the equality of the components of the temperature stress tensor and the absence of temperature effect on the electric field allowed us to formulate a self-adjoint initial system of equations and construct a closed solution.

Keywords

• thermoelectroelasticity
• hyperbolic theory
• nonstationary coupled problem
• long piezoceramic cylinder
• finite integral transformations