Frequency analysis of a graphene platelet–reinforced imperfect cylindrical panel covered with piezoelectric sensor and actuator

Abstract

The main point of the current study is that the frequency analysis of a graphene platelets–reinforced composite (GPLRC) imperfect panel covered with piezoelectric sensor and actuator (PISA) based on the 3D elasticity theory is investigated. Rule of mixture is employed to obtain varying mass density and Poisson’s ratio, while module of elasticity is computed by modified Halpin-Tsai model. The governing equations are obtained using the 3D elasticity theory. By using Fourier series expansion along the longitudinal and latitudinal directions for the stress and displacement fields, a closed form solution is derived. The novelty of the current study is the consideration of the GPLRC panel and PISA, as well as imperfection are implemented on the proposed model using theory of 3D elasticity. Due to perfect bonding between piezoelectric layers and core the compatibility conditions are derived. Finally, influences of PISA thickness, graphene platelet (GPL) distribution pattern, porosity, span angle of panel, number of layers and GPL weight function on the dynamic stability of the GPLRC smart imperfect panel are presented. Another important consequence is that the sandwich panels with lower span angle have better natural frequency. In other words, to obtain desirable frequency response using structures which their shape is similar to GPLRC plate is more recommended than those resemble to GPLRC cylindrical shell.