Study On Vibration Nano-Quasicrystal Layered Plate Based On Modified Couple Stress Theory

Quasicrystal is a new type of solid intermediate between crystal and amorphous.It has multiple rotational symmetry.The quasi-periodic atoms are often arranged in an orderly and directional arrangement,but do not repeat periodically.Compared with ordinary materials,quasicrystals have many unique physical properties,such as higher strength and hardness,corrosion resistance,low thermal conductivity,low electrical conductivity,low coefficient of friction and high resistivity.In engineering practice,quasicrystals are usually used as material reinforcement phases,composite materials and coating technologies in the form of powder.Experiments have shown that quasicrystals as a particle-reinforced phase sprayed on polymers,metal matrix composites and alloys can greatly improve the mechanical properties of these materials.Therefore,it is of great theoretical significance to study the dynamic mechanics of the layered plate structure composed of quasicrystalline materials and classical elastic materials at the nanoscale.Firstly,based on the modified couple-stress theory,free vibration and forced vibration of the three-dimensional structure of simply-supported and multilayered one-dimensional(1D)quasicrystal(QC)nanoplates are studied.The traction-free boundary conditions on both the top and bottom surfaces of nanoplates are used in the free vibration analysis,and a harmonic excitation is assumed to be applied on the top surface in the forced vibration analysis.By solving the eigenvalue problem of the final motion control equation,the general solutions of the phonon field,phase field of the extended displacement and stress of the nanoplate are derived.Utilizing the propagator matrix method,the general solutions of the natural frequency and mode shape of free vibration,and displacements of forced vibration for phonon and phason fields are obtained.Numerical examples are given to analyze the effects of thickness,material length scale parameter,stacking sequence of nanoplates on the vibration responses of homogeneous and sandwich nanoplates.The results indicate that different from the nonlocal theory,the modified couple-stress theory has a stiffness reinforcement effect.Secondly,based on the free vibration and forced vibration of the three-dimensional structure of 1D QC nanoplates,the piezoelectric effect of the quasicrystal is considered.The variation trend of natural frequency,mode of free vibration and forced vibration displacements of phonon field,phase field and electric field free vibration is analyzed after adding electric field.Numerical examples show that the natural frequency and mode of free vibration are greatly affected when the 1D hexagonal piezoelectric quasicrystal is at different positions on the nanoplate.With the change of forced frequency in forced vibration,the displacement of phonon and phase fields under the harmonic excitation of applied phonon field and the harmonic excitation of electric load have completely different trends.Finally,considering the variation of the quasi-periodic direction,the free vibration and forced vibration of the three-dimensional structure of the simply-supported multilayered two-dimensional(2D)QC nanoplates are investigated.According to the change of quasiperiodic direction,the governing equations of motion in three different cases are derived.According to the corresponding boundary conditions,the general solutions of free and forced vibrations are obtained.Numerical examples show that the change of quasi-periodic direction has a great influence on the mode shapes of phase fields of the two sandwich nanoplates.The stacking sequence and material length parameters have a great influence on change of the natural frequency of free vibration.