Nonlinear dynamics and structural stability of arc-auxetic-tapered plates with piezoelectric patches for sports equipment applications

Abstract

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 results denote the dynamic response change of auxetic design to its energy dissipation and impact resistance properties, thus marking those two as the main characteristics for sport equipment. Besides, the stability analysis has also shown that piezoelectric actuation has an effect on the system’s performance, thus indicating the possibility of applying it for active vibration control. This study opens a new chapter in the field of innovative sports materials, where, besides dynamic stability and energy management, performance optimization is the key factor.