Dynamic inverse piezo-effect problem for a long piezoceramic thermoelastic cylinder

Abstract

Objective. The objective of this work is to solve an unrelated dynamic problem of thermoelectroelasticity for a long hollow piezoceramic cylinder under the action of an electric load on its surfaces in the form of a potential difference.Methods. The mathematical formulation of the considered problem of thermoelectroelasticity includes a system of non-selfadjoint differential equations. At the first stage, the authors consider the associated inverse piezoelectric effect problem without taking into account the influence of the temperature field, and at the next stage, study the hyperbolic heat conduction problem (Lord–Shulman theory) for a given (defined) electroelastic field.Result. A new closed solution to the dynamic inverse piezoelectric effect problem for a long piezoceramic thermoelastic cylinder is constructed. The case of the action of a dynamic electric load in the form of a potential difference on its front surfaces is considered. The ambient temperature and the law of convection heat transfer (3-kind boundary condition) are set. The calculated relations obtained using the generalized method of finite integral transformations allow determining the stress-strain state and thermoelectric fields induced in a piezoceramic element under an arbitrary electrical external influence.Conclusion. The constructed solution allows determining the stress-strain state and electric field in a piezoceramic cylinder, as well as analyzing the effect of the induced temperature field on the electroelastic state of the system under consideration using the hyperbolic Lord–Shulman theory of thermal conductivity. Analysis of the numerical results allows concluding that there are insignificant energy losses associated with heating the electroelastic system. The developed calculation algorithm is used in the design of non-resonant and resonant piezoelectric measuring devices.

Keywords

• long piezoceramic cylinder
• thermoelasticity problem
• dynamic action
• finite integral transformations