Wave Dispersion Analysis In Graphene-Piezoelectric Sandwich Nanoplates

Piezoelectric materials are extensively applied as sensors,actuators,transducers,medical imaging,and ultrasonic motors.With the continuous development of micro-nano technology,applications of piezoelectric nanostructures in nano-sensing,nano-actuating,nano-switching and nano-power supply have attracted great attention.The role of scale effects in micro-and nanostructures has become a key issue.Nonclassical continuum theory is the best approach in studying scale effects along with experimental tests and molecular dynamics simulations.However,researchers have found that scale effect could manifest both softening and hardening.Therefore,non-local strain gradient theory was creatively proposed to solve this problem.With the progress of nanocomposites,graphene has been applied as a strong reinforcement for improving the stiffness of structures.Piezoelectric sandwich nanoplates could perform both sensing and actuation tasks in various applications.However,study on the wave propagation behaviors of graphene-reinforced sandwich nanoplates integrated with piezoelectric layers is still very rare.The main aim of this paper was to develop a wave model for piezoelectric sandwich nanoplates with scale effect and the influences of scale effect,surface effect,viscoelastic foundation,thermal electric field and other factors on the medium-wave dispersion properties of graphene-piezoelectric sandwich nanoplates were discussed based on non-local strain gradient theory.The specific research contents are as follows:(1)Wave propagation properties of graphene-reinforced piezoelectric sandwich nanoplates have been discussed.The sandwich nanoplate was consisted of a graphene-reinforced nanocomposite layer and two piezoelectric surface layers under an electric field.Graphene was uniformly distributed in composite layer and the upper and lower piezoelectric surface layers performed actuation and induction functions,respectively.The material properties of nanocomposite layers were evaluated according to modified Halpin-Tsai model and mixing principle.The governing equations of nanoplates were derived based on Hamilton’s principle.According to the theory of non-local strain gradients,non-local motion equations of what were obtained.The characteristic equation was derived from harmonic solution.The coupling influence of scale effect and wavenumber on frequency was discussed in detail and the action range of scale effect was described.Furthermore,the mechanism of weight fraction and geometric size of graphene on nanoplate stiffness was also analysed.(2)The wave propagation behaviors of graphene-reinforced piezoelectric sandwich nanoplates under axial force and hygrothermal conditions were studied.Governing equations were derived based on hygrothermal constitutive equation and first-order shear theory of composite nanoplates.According to higher-order non-local strain gradient theory,non-local motion equations were derived.Strong and weak relationships among non-local parameters and length-scale parameters on sandwich nanoplate stiffness were clarified.In addition,frequency properties of sandwich nanoplates were studied based on hygrothermal and force-electric fields.The effects of plate thickness ratio and elastic foundation on the dispersion properties of nanoplates were also determined.(3)The problem of wave dispersion in functionally graded graphene-reinforced piezoelectric sandwich nanoplates deposited on viscoelastic foundation was elucidated.Visco-Pasternak model was applied to investigate the role of viscoelastic foundation.Four different types of graphene were distributed in composite layer.Governing equations were derived based on third-order shear deformation theory and Hamilton’s principle.The effects of various factors such as scale effect,damp heat effect,graphene distribution,and viscoelastic foundation on wave propagation characteristics were systematically investigated.The law of coupling effect of scale effect and wave number on wave phase velocity was also discussed.The effects of different graphene distribution patterns on nanoplate stiffness were analyzed and the most reasonable graphene distributions were determined.The combined effects of elastic coefficient,shear coefficient,damping,and wave number on the phase velocity of sandwich nanoplates were discussed in detail and the critical damping of nanoplates was determined.(4)Wave propagation properties in functionally graded graphene-reinforced piezoelectric sandwich nanoplates with surface effects were analyzed.The surface effects of both upper and lower piezoelectric layers were also considered.Surface piezoelectric,surface elasticity and surface residual stress were taken into account in the derived constitutive equations.Sandwich nanoplates were deposited on orthotropic viscoelastic foundations with four parameters.Displacement field was determined based on the theory of sinusoidal shear deformation.Motion equations were derived according to Hamilton’s principle and non-local strain gradient theories.The influences of surface effects,scale effects,graphene distribution,and orthotropic viscoelastic foundation on wave propagation behaviors were comprehensively studied.The role of surface effects on the dispersion behaviors of sandwich nanoplates was also explored.The effect of orthotropic foundation on the wave frequency of nanoplate was clearly articulated and the ranges of elastic coefficient and damping on dispersion curves were given.The combined effects of the two shear coefficients and orthotropic angle on nanoplate stiffness were also determined.Finally,the effect ranges of dimensionless scale parameters on the dimensionless dispersion curves of sandwich nanoplates were presented.