Wave propagation and vibration responses in porous smart nanocomposite sandwich beam resting on Kerr foundation considering structural damping

摘要

This paper deals with wave propagation and vibration of a porous beam embedded via nanocomposite piezoelectric layers. Various patterns of reinforcement of the face sheets by non-uniform graphene nanoplatelets (GPLs) are considered through modified Halpin-Tsai micromechanics model to approximate the Young modulus and Poisson's ratio of graphene/piezoelectric polymer layers. The sandwich's face sheets, due to their characteristics, are regarded as sensor and actuator with which the wave velocity and frequency of structure can be controlled and for this reason, a proportional-differential (PD) controller is handled. So as to model the structure much more realistic, the material characteristic of whole system are hypothesized as viscoelastic state according to Kelvin-Voigt model and Kerr viscoelastic foundation is developed which include two springs, two dampers and one shear elements as well. For mathematical modelling of system, refined zigzag theory (RZT) is exercised and using energy method, the motion equations are obtained. Analytical procedure is utilized for solving the governing equations as well as calculating the wave velocity and frequency of the sandwich structure. A precise parametric study is carried out focusing GPLs volume percent and distribution pattern, geometrical parameter of every layer, piezoelectric properties of GPLs, porosity dispersion of the core, exerted voltage and structural damping and their effects on the wave propagation and vibration of system. Results show that increase in the porous coefficient lead to decline in the wave velocity and frequency. In addition, considering the piezoelectric properties of GPLs enhances the wave velocity and frequency of the sandwich structure.