Analysis of functionally graded and laminated piezoelectric cantilever actuators subjected to constant voltage

Abstract

Functionally graded and laminated piezoelectric cantilever actuators are investigated. Each material parameter of the functionally graded actuator can be an arbitrary continuous function of the thickness coordinate of the beam, while the property of each layer in the laminated actuator is uniform. Piezoelectricity solutions for the two actuators subjected to a constant electric potential difference are presented. Firstly, the partial differential equations for the plane problem of functionally graded piezoelectric materials, which govern the stress function and electric displacement function, are derived. Secondly, the stress function is assumed to be an undetermined function of the thickness coordinate, and the electric displacement function is assumed as a linear function of the longitudinal coordinate. In such a case, the stress and electric displacement function can be acquired through successive integrations. The analytical expressions of axial force, bending moment, shear force, displacements, electric displacements and electric potential are then deduced. The analytical solutions are finally obtained, with the integral constants completely determined from the boundary conditions. Comparisons of the present analytical solutions with beam theory, finite element method and experiments indicate that the analytical solutions are effective and exact, while certain deviations of the beam theory can be found.

Dynamic Analytical Solution of a Piezoelectric Stack Utilized in an Actuator and a Generator

“…To give accurate theoretical guidance for designing the piezoelectric stack, an improved theoretical model is of great significance. Piezo-elasticity theory has been successfully used to study piezoelectric composite structures, including piezoelectric curved actuators [51,52], multi-layer piezoelectric cantilever [4,6] and cement-based piezoelectric composites [15,53], functionally graded piezoelectric beams [54,55], and laminated piezoelectric hollow spheres [56]. In addition, assuming the electric field to be spatially varying rather than spatially constant is more accurate for describing the electric field [57,58], which is still not well-applied in the analysis of piezoelectric stacks.…”

Electromechanical analysis of piezoelectric beam-type transducers with interlayer slip

“…k s → ∞ and k s → 0 correspond to perfect bonding and smooth contact at the interface, respectively. differentiating (17) with respect to x results in…”

“…Using the Timoshenko beam theory, the electro-mechanical response of a thick laminated piezoelectric actuator was investigated in [14]; and the static bending, free vibration, and dynamic response of monomorph, bimorph, and multimorph actuators made of functionally graded piezoelectric materials were analyzed [15]. In [16] and [17], the piezo-elasticity solutions for functionally graded piezoelectric beams under the plane stress condition are deduced. Based on the theory of piezo-elasticity, shi and his colleagues studied the mechanical and electrical behaviors of several piezoelectric actuators, including multi-layer piezoelectric beams, piezoelectric curved actuators, functionally graded piezoelectric beams [18]- [22].…”

Thermo-Electro-Mechanical Analysis of a Curved Functionally Graded Piezoelectric Actuator with Sandwich Structure

“…Using classical laminate theory, the electroelastic behavior of a piezoelectric composite actuator with functionally graded microstructure were analyzed in [11,12]. Huang et al [13,14] derived the analytical solutions for FGP beams under both mechanical and electrical loads from the two-dimensional equations of piezoelectricity, in which the elastic, piezoelectric and dielectric coefficients of the piezoelectric beams were assumed to vary along the beam thickness direction only. By using stress function approach, Shi and his co-workers [15,16,17,18] obtained a set of exact solutions for the FGP cantilevers with varying piezoelectric parameter g 31 or the elastic parameter s 33 under different loading conditions.…”