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.