Vibration Control and Dynamical Model of a Thermal-Electrical-Mechanical Coupled Smart Cantilevered Beam

Abstract

Abstract. Piezoelectric actuators used in vibration control and high precision control have been known widely in recent years. Especially in aeronautics and MEMS systems, their use is spread from vibration suppression to position control. In this paper, a finite element model (FEM) of a piezoelectric actuator and cantilever in thermal environment is presented to suppress vibration effectively. In other words, the finite element model is namely thermal-electrical-mechanical coupled FEM. Based on a 8-node plane finite element, the modal analysis, the harmonic analysis and the transient analysis have been obtained in the current work. Therefore a transfer function model will be attained through the harmonic analysis by identification method in order to control vibration by control law. In addition, the controller will be designed with the adaptive pole placement control (APPC). Finally, through simulation, the thermal influence is considerable for natural frequencies, harmonic response and free vibration. Moreover, the APPC is a significant plan to vibration control in the paper. IntroductionApplications of smart materials, such as piezoelectric materials, magnetostrictive materials, magneto-rheological fluids, electrorheological fluids and shape memory alloys, have been developed increasingly in recent years. Piezoelectric materials can be the most popular smart materials in actuators applications by reason of low power consumption, low weight, and ease in bonding with the structures. In [1], Meng, G., L. Ye, et al. present a scheme involving dynamic modeling of a smart structure, designing laws and closed-loop simulation in a finite element environment. Actually, the piezoelectric materials and the structures will expand with heat and contract with cold, the piezoelectric materials will produce voltage when the temperature value is difference in both ends and the piezoelectric materials will generate heat when applied high voltage. In [2], this paper presents the dynamic analysis of the influence of the coupling between thermal, electrical and mechanical fields for different modes; in [3], in this paper a finite element model is developed for the active control of thermally induced vibration of laminated composite shells with piezoelectric sensors and actuators.There are many methods to model the system's dynamical model. First, the theory method is common in many researches. The finite element model is mainstream means for mechanical systems in modern world. It can be derived using Hamilton's principle and Lagrange variation theory. in [4], the system equations can be derived using Hamilton's principle and the assumed mode method; There is other modeling way: identification modeling, in [5], this study presents results of multimodal vibration suppression of a smart flexible cantilever beam with piezoceramic actuator and sensor by suing a pole placement controller; in [6], V. SETHI and G. SONG put forward subspace identification after acquiring a model frame. Moreover the control laws for vibration suppression va...