Dynamics and chaotic analyses of a variable edge composite sandwich plate with an anti-chiral NPR honeycomb core

The vibration problems of composite sandwich plates (CSPs) are frequently observe in engineering applications. Based on this observation, this paper investigates the dynamic response and chaotic phenomena of CSPs to elucidate the dynamic effects of the complex edge and multiple parameters on CSPs. In this paper, a quadrilateral CSP with a variable edge is proposed, based on the Winkler-Pasternak elastic foundation. One edge of the CSP is defined as a variable edge according to classical curve function forms. The CSP consists of an anti-tetrachiral honeycomb core with negative Poisson's ratio (NPR) and two face sheets. Based on the classical shell theory and von Karman nonlinear assumption, the motion differential equation of proposed system under external periodic excitation vertical to the CSP and the boundary condition of four-sided simply supported is established, and the dynamic characteristics of the system are calculated theoretically by using the Galerkin's method. The effects of geometric parameters on the nonlinear dynamic response of the system are discussed. To validate the reliability and accuracy of theoretical results, corresponding numerical calculation via finite element method is conducted for comparison. The results show numerical calculation showed good agreement with theoretical results. The elastic foundation significantly enhances the load-carrying capacity. Compared to the case without an elastic foundation, the vibration amplitude drops to 20%, while the natural frequencies increase by 119% to 126%. With excitation load increasing, anti-tetrachiral NPR core exhibits better vibration absorption capacity than traditional honeycomb core, and mechanical properties of core are improved by increasing cell number or thickness. Through analysis of the Lyapunov exponent, it is found that the CSP becomes unstable when the excitation frequency approaches the natural frequency or the excitation load exceeds the critical load. Among edge-defined power, arc and absolute exponential function, the CSP with arc function shows the best load-bearing capacity.