Electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal circular plates with simply supported or clamped boundary conditions

Abstract

A three-dimensional (3D) electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal (QC) circular plates with simply supported or clamped boundary conditions is presented through a state vector approach. Both perfect and imperfect bonds between the layers are considered by adjusting the parameter sets in the model. Governing equations for the plates subjected to electric or elastic load on the bottom surfaces are derived using the state equations and the propagator matrix method. We explicitly obtain the analytical solution by writing the physical variables as Bessel series expansions and polynomial functions with respect to the radial coordinate. The solution is validated by comparing the numerical results with the 3D finite element analysis. The basic physical quantities of the plates in the phonon, phason, and electric fields are computed in the numerical examples. Result shows that the QC layers as coatings decrease the deflection in the phonon and phason fields of plates. The phonon–phason coupling elastic modulus and piezoelectric constant produce positive and negative effects on the magnitudes of stresses. Besides, compliance coefficients of the weak interface in the phonon field contribute more to the variations than those in the phason field.