Propagation Characteristics Of Elastic Waves In Functionally Graded Couple-stressed Plates

The new generation of micro/nano-scale materials used in nano-electromechanical,nano-electronics,physics and biology fields has the characteristics of intelligence,miniaturization,multi-field coupling and anisotropy.Micro/nano-scale structures made of functionally graded material(FGM)have shown great potential in a variety of applications and work environments.In practical engineering applications,micro/nano-scale materials often withstand dynamic working loads represented by elastic waves.By studying the wave characteristics of elastic waves in micro/nano-scale structures,it can provide a theoretical basis for the measurement of micro/nano-scale material parameters,non-destructive testing and performance control.The size-dependent feature of micro/nano-scale materials makes classical continuous theory unable to accurately predict the mechanical characteristics of such structures,and the inhomogeneity of FGM also makes the analysis of the wave characteristics of FGM micro/nano-scale structures difficult.Based on the modified couple stress theory,the extended Legendre polynomial series expansion method is used to study the wave characteristics of FGM micro/nano-scale structures.The advantage of this method is that it is not necessary to construct the displacement solution of each layer of wavelets in the multilayered micro/nano-scale structure,and the FGM micro/nano-scale structure can be calculated without layering.By using this method,the wave characteristics of elastic waves in multi-layer homogeneous orthotropic micro/nano plates and FGM micro/nano plates are studied in this paper.The correctness and convergence of the method are discussed.The effects of length scale parameters,boundary conditions,and material gradient distribution on the reflection and transmission behavior of P and SH waves are analyzed.The effects of the couple stress and material gradient form on the stiffness,resonance frequency,wave velocity,and stress of FGM are discussed.The results show that the effect of the couple stress and the gradient form change the effective elastic stiffness of the FGM plate,which in turn changes the resonant frequency and shifts the same resonant frequency to the high frequency region.Some resonances can be avoided by properly controlling the gradient field.With the development of nano-electromechanical and micro-electro-mechanical systems,micro/nano-scale structures made of functionally graded piezoelectric materials(FGPM)have a wide range of potential applications and design prospects.This paper studies the wave characteristics of elastic waves in FGPM micro/nano plates.The reflection and transmission coefficients of P wave and SH wave are calculated,and two kinds of electrical boundary conditions are discussed.The effects of piezoelectricity,electrical boundary conditions,and couple stress on the reflection and transmission behavior of P and SH waves are discussed.The electrical potentials,electrical displacements,critical angles and stresses are given.The results show that when a local minimum of reflectivity is reached at a certain fh or angle of incidence,the electrical displacement,potential and stress will also reach a local minimum or maximum.This relationship can be used to achieve mutual monitoring between physical quantities.Finally,the dispersion characteristics of Lamb and SH waves in FGM micro/nano plates are studied in this paper.The effects of couple stress on the velocity and dispersion of guided waves are discussed.The differences in the dispersion characteristics of guided waves in FGM micro/nano plates and homogeneous micro/nano plates are compared.The effects of length scale parameters in different directions are analyzed.The results show that the effect of the couple stress increases the degree of the Lamb wave and SH wave dispersion in the FGM plate,and increase its wave velocity.The dispersion of Lamb waves in FGM micro/nano plates is more serious than that of homogeneous micro / nano plates.