The research presented here delves into the nonlinear dynamics and structural stability of taper arc-auxetic plates that come with the application of piezoelectric patches, consequently, looking at their applications in sports equipment. The construction consists of an arc-like auxetic core with a negative Poisson’s ratio, along with piezoelectric face sheets to give the structure better mechanical performance. The plates have a variable thickness distribution, which is important in absorbing energy and deforming the material, hence under dynamic loading conditions. Transverse shear deformation plays an essential role in the proper analysis of tapered plates, and for that, higher-order shear deformation theory (HSDT) is used in a way to reveal the effects of this deformation. The main equations are obtained via Hamilton's principle, which is a strong tool for the dynamic behavior of the system. A numerical solution is achieved using the differential quadrature method (DQM) based on high-order derivatives of the Gauss–Chebyshev–Lobatto function, and an iterative procedure offering high accuracy in the computation for complex geometries and boundary conditions. The findings reveal the auxetic design's effect on the dynamic response, thereby marking its ability to dissipate energy and resistance to impact as major properties for sports equipment. The stability analysis also highlights the impact of piezoelectric actuation on the effectiveness of the system, thereby indicating the potential of using it for active vibration control. This research allows new development in the advanced sports gear materials area, where, among the dynamic stability and energy management, the performance optimization is the main concern.
Lin et al. (Thu,) studied this question.