A three-dimensional Peano series solution for the vibration of functionally graded piezoelectric laminates in cylindrical bending

Abstract

Abstract. The available three-dimensional (3D) solutions reported for the analysis of Functionally Graded Piezoelectric (FGP) laminates are based on this simplifying assumption that the FGP layer consists of a number of homogeneous sub-layers. The accuracy of these formulations not only is dependent on the number of sub-layers, but also leads to inaccurate results in the prediction of higher natural frequencies of the FGP laminates. In the present paper, a 3D Peano series solution is developed for the cylindrical bending vibration of the FGP laminates. This novel formulation exactly satis es the equations of motion, the charge equation, and the boundary and interface conditions of the continuously nonhomogeneous piezoelectric layers. The obtained solution is exact because no a priori assumption for the displacement components and the electric potential along the thickness direction of FGP layers is introduced. The in uences of the di erent functionally gradient material properties and di erent electric boundary conditions on the natural frequencies and mode shapes of the FGP laminate have also been studied through examples. The present solution and its obtained numerical results can be employed to assess the accuracy of di erent FGP laminated beam/plate theories. It can also be used for FGP vibration behavior comprehension purposes.

State-Space Approaches to Complex Structures in Aerospace

“…The results, which agreed well with those of existing analytical solutions and finite element models, verified the effectiveness of the method. In contrast to the existing works on FGMs with a certain exponential law for the variations of physical fields along the thickness direction, Lezgy-Nazargah [47] performed an exact analysis of cylindrical bending of FGM piezoelectric laminates with arbitrary gradient compositions based on the SSA. The exact solutions, which exhibited excellent agreement with the published results, could be used to assess the accuracy of approximate plate theories and numerical methods.…”

Parametric electro‐mechanical dispersive behaviors of guided waves in the functionally graded piezoelectric annular plate

“…In particular, the introduction of piezoelectric materials makes functionally gradient piezoelectric materials (FGPM), which have huge potential in communication devices, flexible electronics, thermoelectric devices, energy collectors, and so forth. Functionally graded piezoelectric materials take advantages of piezoelectricity and gradients, including the electric and mechanical effects [2,3], which have been used widely in engineering applications including sensors, actuators, and intelligent electro-mechanical systems [4,5]. Although they have excellent performance, their structures are often special-shaped structures with complex cross sections due to the influence of complex working environment, so it is particularly important to detect such structures.…”

A Coupling Electromechanical Inhomogeneous Cell-Based Smoothed Finite Element Method for Dynamic Analysis of Functionally Graded Piezoelectric Beams

“…e results have been found in good agreement with the reference solutions for various electrical and mechanical constrained conditions. Meanwhile, the 3D exact state-space solution [18] and Peano series solution [19] were developed for the cylindrical bending vibration of the FGPM laminates, respectively. Layerwise FEM was adopted to investigate the displacement and stress responses of an FGPM bimorph actuator [20].…”