Nonlinear Dynamical Modeling and Control Strategies for Vibration Mitigation in Smart Structural Systems

Abstract

The development of smart structural systems, combining sensors, actuators and intelligent controllers, has become the solution breakthroughs in the vibration attenuation of civil, aerospace, and mechanical structures. Such systems provide real time monitoring, adaptive response and increased structural resilience. But traditional linear control models cannot be used to correctly describe the natural nonlinearities of real-life structures, i.e. geometric stiffening, material hysteresis and actuator saturation. In order to overcome these shortcomings, this paper develops a detailed model of nonlinear dynamical modeling and control of intelligent structural systems. The governing equations are obtained through Hamilton’s principle, finite element discretization with electromechanical coupling of piezoelectric actuators and the nonlinear damping effects. Three higher-level control approaches are devised, namely: (i) nonlinear state feed-back that compensates the nonlinearities of a system, (ii) sliding mode control that stabilizes the system robustly in the presence of uncertainties, and (iii) Lyapunov-based adaptive control that can achieve global asymptotic stability with minimal control efforts. A smart cantilever beam with harmonic and impulsive excitations and simulation studies are carried out. The findings prove that nonlinear controllers are much superior to the conventional linear methods with up to 65 percent of the response peak, 40 percent of the energy consumption, and a high degree of tolerance to adverse changes in parameters of ±10 percent. Of the experimented methods, Lyapunov-based adaptive control has the best trade-off between vibration, and energy consumption whereas the sliding mode control has the best robustness to modeling uncertainties. According to the findings, nonlinear modeling and higher control are of utmost significance in the development of resilient, energy-efficient and intelligent infrastructures. The work enhances the next generation smart structural systems development and offers a scalable base to implement in the US level infrastructure, aerospace engineering and smart city applications.