Active vibration suppression of smart laminated beams using layerwise theory and an optimal control strategy

Abstract

Vibration suppression of laminated composite beams using the smart structures concept is presented in the present work. The smart system consists of a laminated composite beam as the host structure and piezoceramic and PVDF patches as the actuation and sensing elements. To treat the material and geometric inhomogeneities through the thickness of the laminated smart structure, a finite element model based on the layerwise displacement theory which incorporates the electro-mechanical coupling effects has been developed. The state space model of the active laminated beam is then used to design the control system. A linear quadratic regulator (LQR) controller is designed to achieve vibration suppression of the laminated smart beam. The effects of the laminate configuration and locations of sensors/actuators on controlled response are investigated. An experimental set-up has been developed to determine the natural frequency and damping factor of the smart laminated beam. The experimental measurements are then used to design a control mechanism with LQR to suppress the vibration response of the system. Open-loop and closed-loop responses of the system have been obtained experimentally and compared with the corresponding simulation results to demonstrate the accuracy and efficiency of the present approach in the vibration control of laminated smart structures.

Finite element analysis of actively controlled smart plate with patched actuators and sensors

“…A survey on various control algorithms employed for active vibration control study for smart structures is presented by Alkhatib and Golnaragi [1]. In most of the reported works, classical constant gain velocity feedback (CGVF) control algorithm [8,13,14,21,23] is employed for active vibration control of smart beams and plates. The CGVF control algorithm always yields stable control system if the piezoelectric actuators and sensors are perfectly collocated.…”

Effects of structural configuration on vibration control of smart laminated beams under random excitations?

“…Layer-wise displacement theory can provide an accurate and efficient model for the vibration analysis of laminated structures [6]. The present author and colleagues [7] provided a comparison between the ESL theories and the layer-wise theory on the vibration control of smart-laminated beams. In designing an optimal control mechanism, Linear Quadratic Regulator (LQR) is an efficient approach to determine the optimal feedback gain.…”

“…The finite element model for a smart laminated beam based on the layer-wise approximation for displacements and electric potential can be obtained as [7]. …”

Active vibration control of an arbitrary thick piezolaminated beam with imperfectly integrated sensor and actuator layers

“…The effect of sensor location (while keeping the actuator location fixed) on the performance of the controller was evaluated and discussed. Zabihollah et al (2007) used an experimental set-up along with a finite element model based on the coupled layerwise theories (LWTs) with layerwise linear variation of in-plane displacements to investigate optimal (LQR) vibration control of laminated piezoelectric composite beams. The LWTs was found to yield accurate results, while the computational cost amplifies with increasing the number of layers.…”