Axisymmetric bending analysis of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate

Abstract

Within a framework of the state space method, an axisymmetric solution for functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate is presented in this paper. Applying the finite Hankel transform onto the state space vector, an ordinary differential equation with constant coefficients is obtained for the circular plate provided that the free boundary terms are zero and an exponential function distribution of material properties is assumed. The ordinary differential equation is then used to obtain the stress, displacement and electric components in the physical domain of the elastic simply supported circular plate through the use of the propagator matrix method and the inverse Hankel transform. The numerical studies are carried out to show the validity of the present solution and reveal the influence of material inhomogeneity on the axisymmetric bending of the circular plate with different layers and loadings, which provides guidance for the design and manufacture of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate.

Static Electro-Mechanical Response of Axisymmetric One-Dimensional Piezoelectric Quasicrystal Circular Actuator

“…As for the axisymmetric problem of 1D piezoelectric QC circular actuators, all the phonon-phason-electric field coupling responses are independent of θ. The governing equations for the axisymmetric problem of 1D hexagonal piezoelectric QC circular plate actuators in the absence of body forces and free charges can be expressed in the non-dimensionalized form as [20,25]: As for the axisymmetric problem of 1D piezoelectric QC circular actuators, all the phonon-phason-electric field coupling responses are independent of θ. The governing equations for the axisymmetric problem of 1D hexagonal piezoelectric QC circular plate actuators in the absence of body forces and free charges can be expressed in the nondimensionalized form as [20,25]:…”

“…In terms of the state space method, Ding et al [19] made an investigation on the free axisymmetric vibration of transversely isotropic piezoelectric circular plates. By extending the state space method, Li et al [20] studied the influence of the properties of functionally graded materials on piezoelectric quasicrystal circular plates. By using the direct displacement method, Wang et al [21] studied the axisymmetric bending of transversely isotropic and functionally graded circular plates under arbitrarily transverse loads.…”

Interaction of collinear interface cracks between dissimilar one‐dimensional hexagonal piezoelectric quasicrystals

“…Li et al [25] performed the fracture analysis of a transversely isotropic, piezoelectric quasicrystal cylinder under axial shear, and found that the quasicrystal fracture is governed by the phonon or phason field, depending on the phonon-phason loading ratio. Within a framework of the state space method, Li et al [26] presented an axisymmetric solution for a functionally graded, 1D, hexagonal piezoelectric QC circular plate.…”