Thermoelectroelastic response of a piezoelectric cylinder with D_∞ symmetry under axisymmetric mechanical and thermal loading

Abstract

Carbon-neutral and biodegradable materials such as wood and poly-L-lactic acid play an important role in reducing environmental loads. Therefore, this study theoretically analyzed the thermoelectroelastic problem for a solid cylinder with D ∞ symmetry subjected to a distributed torsional shear stress as a mechanical input and to a nonuniform temperature distribution as a thermal disturbance, in order to gain an elementary understanding of the thermal effects on the electroelastic field in cylindrical bodies with D ∞ symmetry. The displacement components are expressed in terms of the elastic displacement potential function, the piezoelastic displacement potential function, and the thermoelastic displacement potential functions, and the electric field components are expressed in terms of the electric potential function. Subsequent to presenting the fundamental equations for thermoelectroelasticity, the governing equations for the above potential functions are derived based on the above fundamental equations. These governing equations are solved by a Fourier transform technique, and the theoretical solutions of the thermoelectroelastic field quantities are obtained. Furthermore, by performing numerical calculations, the distributions of the field quantities are illustrated graphically, and the structures of the thermoelectroelastic field are discussed qualitatively and quantitatively. Moreover, by quantitatively evaluating the ratio of the thermally disturbed electric displacement to the undisturbed electric displacement reflecting the mechanical input, the necessity of the thermoelectroelastic analyses, as treated in this paper, is clearly demonstrated.

Electroelastic analysis for a sheared <i>D</i>_∞ piezoelectric cylinder disturbed by transient temperature distribution

“…The value of 0 4 T  is selected as a practical example. This value corresponds to   , which was illustrated to be realistic in previous research (Ishihara et al, 2017b). The value of   mech r D in Eq.…”

“…1. These concerns motivated the present authors to further consider thermal effects by solving thermoelectroelastic problems in D  cylinders (Ishihara et al, 2017b(Ishihara et al, , 2018. The thermoelectroelastic field was determined for infinite cylinders receiving mechanical input and thermal disturbance simultaneously, and the thermally disturbed noise was found to possibly reach comparable levels with reference to the mechanically induced signal (Ishihara et al, 2017b(Ishihara et al, , 2018.…”

“…Therefore, in considering the influence of thermal environment in practical applications, it is inevitable to include transient nature. However, the aforementioned investigations (Ishihara et al, 2017b(Ishihara et al, , 2018 were concerned only with a steady temperature field.…”

Axisymmetric elasticity solution for an undrained saturated poro-piezoelastic thick disk

“…They consider elastic moduli and dielectric permeabilities of the coating, which vary independently with depth according to arbitrary functions. M. Ishihara et al analyzed the thermoelectro elastic solid cylinder with D ∞ symmetry under axisymmetric mechanical and thermal loading [14]. They consider distributed torsional shear stress as a mechanical load and nonuniform temperature distribution as a thermal disturbance.…”