More insights into stability analysis of shear-damped laminates: The role of active boundary and lower-order passive distributed dampers under various boundary conditions

¹ Université Polytechnique Hauts-de-France, CÉRAMATHS/DEMAV, Le Mont Houy, 59313 Valenciennes Cedex 9, France
² Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, USA

^* Corresponding author: ozkan.ozer@wku.edu

Received: 20 October 2024
Accepted: 17 April 2025

Abstract

In this study, we investigate the stability of a three-layer laminate composed of two piezoelectric or elastic outer layers surrounding a soft viscoelastic core that resists transverse shear weakly, allowing significant shear deformation. The outer layers exhibit longitudinal vibrations, while the laminate bends uniformly across the layers. These laminates are often considered in the literature because natural passive damping arises from shear deformation within the compliant core, which dissipates energy through its viscoelastic behavior. However, our analysis shows that this damping alone is insufficient to guarantee strong or exponential stability. To address this limitation, we introduce for the first time in the literature a combination of lower-order control designs, including active boundary controls, viscous damping, and structural damping, significantly enhancing the system’s overall stability. We consider three boundary condition scenarios: fully clamped, fully hinged, and clamped on the left with hinged on the right. Through rigorous mathematical techniques and detailed functional analytic estimates involving various multipliers, we demonstrate the necessity of these novel control strategies in achieving both strong and exponential stability. Our results represent a significant advancement in the design and optimization of damping techniques for laminate systems, providing a unique and effective framework that offers practical guidance for developing advanced materials with improved stability characteristics.