Exact three-dimensional analysis for static torsion of piezoelectric rods

Abstract

a b s t r a c tBased on the theory of elasticity, exact analytical and numerical solutions of piezoelectric rods under static torsion are studied. In this paper, direct solution method is used. The main scope is to check the extension of validity of assumptions in previous papers that had been made based on linear distribution of electric potential through the cross section and their influences on deflection and the angle of rotation. Stress and electric induction functions are employed to obtain the exact solution of the static and electrostatic equilibrium equations under torsional loading. It is shown that previous assumptions are valid only in some types of piezoelectric materials, while in other types these assumptions lead to considerable deviations from accurate modeling. The present analytical solutions are compared with three-dimensional finite element analysis results and absolute agreements are found. At the end of this article, torsional rigidity, shape-effects on induced piezoelectric deformation and the range of valid region for linear distribution of electric potential assumption have been studied.

Torsion analysis of cracked circular bars actuated by a piezoelectric coating

“…The torsion problem of intact piezoelectric bars or beams has been treated by a few researchers [1][2][3][4][5][6]. However, the torsion problem of cracked piezoelectric bars or cracked isotropic bars with a piezoelectric coating has not been considered.…”

“…Using the theory of elasticity, exact analytical and numerical solutions for the static torsion problem of a piezoelectric rod were found by Maleki et al [4]. The region of validity for assumption of a linear distribution of electric potential through the cross-section and shape effects on induced piezoelectric deformation were studied.…”

Theory of semiconductor solid and hollow nano‐ and microwires with hexagonal cross‐section under torsion

“…The effect of torsion on magnetoimpedance of amorphous microwires has been modeled in (). The properties of piezoelectric rods under torsion have been discussed in (). The torsional effect on piezoelectric quartz discs has been discussed in ().…”

Analysis of longitudinal and torsional resonance vibrations of a piezoelectrically excited bar by introducing piezoelectric loss coefficients

“…Slender piezoelectric ceramics stacked with passive layers are the most commonly practiced piezo-actuator structure in actuator, ultrasonic motor, energy harvesting, vibration damping, and sensor applications (Bendary et al, 2010;Bonello and Rafique, 2011;Ferreira et al, 2004;Gaudenzi, 2009;Li, 2011;Maleki et al, 2011;Roy and Yu, 2009;Uchino and Giniewicz, 2003;Watson et al, 2009). Their simple, low-cost, and slender design, which is reinforced by passive elements, is the main reason of their popularity.…”