Static deformation of a multilayered one-dimensional hexagonal quasicrystal plate with piezoelectric effect

Quasicrystals （QCs） are sensitive to the piezoelectric （PE） effect. This paper studies static deformation of a multilayered one-dimensional （1D） hexagonal QC plate with the PE effect. The exact closed-form solutions of the extended displacement and traction for a homogeneous piezoelectric quasicrystal （PQC）plate are derived from an eigensystem. The general solutions for multilayered PQC plates are then obtained using the propagator matrix method when mechanical and electrical loads are applied on the top surface of the plate. Numerical examples for several sandwich plates made up of PQC, PE, and QC materials are provided to show the effect of stacking sequence on phonon, phason, and electric fields under mechanical and electrical loads, which is useful in designing new composites for engineering structures.

Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

A mathematical model for nonlocal vibration and buckling of embedded two-dimensional(2 D) decagonal quasicrystal(QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2 D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional(3 D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories.Numerical examples are provided to display the effects of the quasiperiodic direction,length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence,and medium elasticity on the vibration frequency and critical buckling load of the 2 D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate.This feature is useful since the frequency and critical buckling load of the 2 D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

Bending Deformation of Multilayered One-Dimensional Quasicrystal Nanoplates Based on the Modified Couple Stress Theory

The modified couple stress theory has been applied in many nanomaterials except for nano-quasicrystals.In this paper,the modified couple stress theory is firstly adopted to analyze the static bending deformation of multilayered one-dimensional(ID)hexagonal quasicrystal(QC)nanoplates under surface loadings.The general solutions for the extended displacement and traction vectors in a simply supported and homogeneous QC nanoplate are derived by solving an eigenvalue problem reduced from the governing equations.Utilizing the propagator matrix method,the analytical solutions of multilayered ID QC nanoplates are then obtained by assuming that the layer interfaces are continuous.Numerical examples for some kinds of nanoplates made up of QC and crystal(BaTiOa)are provided to illustrate the effects of the material length parameter,the number of layers and the stacking sequence of nanoplates on the phonon and phason fields,which is helpful for the application of QCs to surface coating and solar energy selective absorber.