Transient response of a piezothermoelastic circular disk under axisymmetric heating

Abstract

Summary. Transient temperature, displacement, stress and electric field intensities in a finite circular piezothermoelastic disk undergoing axisymmetric surface beating are examined. Exact solutions to the equations of equilibrium and electrostatics are obtained using a potential function approach based upon two piezothermoelastic potential functions, three piezoelastic potential functions and a piezoelectric potential function. The disk under consideration is assumed to exhibit hexagonal material symmetry of class 6 mm. The initial temperature of the disk is zero; thereafter one face is subjected to linear heat transfer from an adjacent medium (Newton's law of cooling), while the temperature of the other face remains constant. Both faces are taken to be free of traction. The cylindrical boundary of the disk is thermally insulated, electrically charge-free, and constrained against radial deformation. Numerical results are obtained for the stress and the electric potential distributions in a cadmium selenide disk.

Plane stress problem of a piezothermoelastic plate

“…Application of the plane-stress piezothermoelastic formulation presented here is considerably simpler than that of the three-dimensional solution procedure given in [7]. Results indicate that for the plate considered in this study the plane-stress solution is in excellent agreement with the exact three-dimensional solution, even when the thickness of the plate is equal to the plate radius.…”

“…In performing the calculations, the first 50 terms in each infinite series were retained. Plane-stress results for the radial elastic displacement, stresses, electric potential difference and radial electric displacement are compared in Table 1 with the corresponding values calculated using the exact three-dimensional formulation of [7]. Errors associated with the plane-stress approximation are seen to increase with increasing plate thickness-to-radius ratio.…”

“…An exact three-dimensional solution to this problem was derived earlier using a potential function approach [7]. Our purpose here is to assess the validity of the plane-stress approximation for the analysis of piezothermoelastic plates, by providing a comparison of the plane-stress results with those of the exact, more complicated, three-dimensional solution.…”

Application of Hankel Transform for Solving a Fracture Problem of a Cracked Piezoelectric Strip Under Thermal Loading

“…For the numerical calculations, the thermo-electro-elastic properties of the plate are assumed to be ones of cadmium selenide with the following properties (Ashida & Tauchert, 1998). …”

Electrically Excited Nonstationary Vibrations of Thin Circular Piezoelectric Plates

“…The vibrations of piezoceramic bodies polarized across the thickness and subjected to nonstationary loads were studied in [6,7,10,12], naturally neglecting the influence of the in-plane configuration of transducers on the wave processes. For thin transducers, this omission can be remedied by considering the plane stress state and linear distribution of electric potential over the thickness [1,2,4,6,15]. We will use such a problem statement to study the dynamic axisymmetric electromechanical state of thin circular piezoceramic plates polarized across the thickness and subjected to electric excitation.…”