Study On Static Deformation And Free Vibration Of A Multilayered Piezoelectric Quasicrystal Plate

Quasicrystals are a new solid structure that differs from both crystals and non-crystals.Due to its many excellent properties such as corrosion resistance,low thermal conductivity,low coefficient of friction,low porosity,high hardness and high wear resistance,quasicrystals are increasingly being applied to surface modification and composite materials.Therefore,studying the layered structure of quasicrystal composites is of great significance in engineering practice.Firstly,the static deformation of one-dimensional hexagonal piezoelectric quasicrystal multilayered plate subjected to surface mechanical loads of phonon field and electrical loads is studied.By assuming the general solution of the extended displacement(elastic displacements of phonon and phason,and electric potential),the governing equations for a one-dimensional hexagonal piezoelectric quasicrystal homogenous and simply-supported plate are derived by combining with the basic equations.The boundary value problem is transformed into solving the eigen-system problem.The generalized solutions of the extended displacement and extended stress(stresses of phonon and phason fields,and electric displacement)of one-dimensional hexagonal piezoelectric quasicrystal homogenous plate are obtained.By using the propagator matrix method,exact solutions of a one-dimensional hexagonal piezoelectric quasi-crystal multilayered plates subjected to surface mechanical loads of phonon field and electrical loads,respectively,are obtained.Numerical examples are provided to consider the variation of phonon field,phason field and electric field of sandwich plates composed of piezoelectric quasicrystal,piezoelectric and quasicrystal materials with the thickness and stacking sequence of plates under the static deformation.Secondly,free vibration of two-dimensional decagonal quasicrystal homogenous plates is studied.By assuming the general solution of the extended displacement,the governing equations for the free vibration problem of two-dimensional decagonal quasicrystal homogenous and simply supported plates are derived by and combining the basic equations.The boundary value problem is transformed into solving the eigen-system problem.The general solution of the extended displacement of a homogenous plate with two-dimensional decagonal quasicrystals is obtained.According to the boundary conditions,exact solutions of the natural frequency and mode of the two-dimensional decagonal quasicrystal uniform plate are obtained.Numerical example are provided to consider the effect of the change of quasi-period direction on the natural frequency and mode shape in a two-dimensional decagonal symmetrical quasi-crystal homogenous plate.Finally,free vibration of two-dimensional decagonal quasicrystal multilayered is further considered.By assuming the general solution of the extended displacements,the governing equations are derived from the basic equations.The boundary value problem is transformed into solving eigen-system problem and the general solution is then obtained.By using the propagator matrix method,exact solutions of the natural frequencies and shape of the two-dimensional decagonal quasicrystal multilayered plates are obtained.Numerical examples are illustrated to show the variation of the natural frequency and mode shape of the sandwich plates composed of two-dimensional decagonal quasicrystals and piezoelectric materials with the stacking sequence.