Coupled nonstationary axisymmetric problem of the thermal electrical elasticity for a circular multilayer plate

The paper considers a circular multilayer plate made of the elastic and electroelastic (piezoceramic) materials at its cylindrical surface hinged fastening. Mathematical formulation of the coupled nonstationary axisymmetric initial-boundary value problem of the thermal electrical elasticity includes the not self-adjoint systems of partial differential equations, as well as the thermal conductivity boundary conditions of the first, third, and fourth kind. Using the equilibrium equations imposes a restriction on the rate of external load alteration in the form of temperature on the plate upper front surface. The paper considers a three-layer electroelastic system to ensure definiteness of the constructed algorithm. Using the method of finite integral transformations makes it possible to construct a closed solution. The one-component Hankel transform is applied along the radial variable in carrying out the procedure of the variables incomplete separation; and a new class of vector transforms based on the multicomponent relationship of the eigenvector functions biorthogonality of the two homogeneous boundary value problems is applied along the axial coordinate. Such transforms allow constructing an adjoint operator, without which it is impossible to solve the not self-adjoint linear boundary value problems. A three-layer structure consisting of the metal substrate that increases the transducer strength properties, piezoceramic plate and heat-insulating layer is selected as the numerical example. The paper analyzes relationship between this structure layers height and the electric pulse determined by connecting the piezoelectric plate electroded equipotential surfaces to a measurement device with the high input resistance. The obtained results make it possible to justify a rational program of experiments in the design and development of the thermal piezoceramic transducers and to reduce the volume of the full-scale research.
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