Topology optimization of piezoelectric curved shell structures with active control for reducing random vibration
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RESEARCH PAPER
Topology optimization of piezoelectric curved shell structures with active control for reducing random vibration Jingjuan Zhai 1 & Linyuan Shang 1 & Guozhong Zhao 2 Received: 14 April 2019 / Revised: 29 July 2019 / Accepted: 4 October 2019 # Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract This paper investigates topology optimization of the surface electrode coverage on piezoelectric sensor/actuator layers attached to a curved shell structure subjected to stationary random force excitation, with the aim to minimize the random vibration response under active control. In the optimization model, the power spectral density (PSD) of displacement response at the specified point is considered as the objective function. The pseudo-densities describing the surface electrode distribution are assigned as the design variables, and an artificial active damping model with penalization is employed to suppress intermediate density values. The voltage across each actuator is determined by velocity feedback control law. Pseudo excitation method (PEM) is introduced to analyze random vibration response of a piezoelectric curved shell structure with active control. In this context, the adjoint variable method for the sensitivity analysis of displacement PSD with respect to topological design variables is derived. Numerical examples fully demonstrate the validity of the proposed approach. Keywords Topology optimization . Piezoelectric curved shell . Vibration . Active control . Stationary random excitation
1 Introduction Main structures of aircraft, submarines, and high-speed train etc. are structures in which thin curved shells are used. They are lightweight and have little inherent damping, so that small disturbance can easily induce unwanted structural vibrations, which may lead to catastrophic failure, danger, uncomfortable environment, and so on. Thus, the structure vibration must be effectively suppressed to meet stringent requirements for vibration-sensitive missions. One promising method to address the issues is to use the technology of smart structures. Amongst many smart materials, piezoelectric materials has been widely recognized as one of the most potential candidates due to many of its favorable characteristics such as low Responsible Editor: YoonYoung Kim * Linyuan Shang [email protected] 1
College of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China
2
State Key Laboratory of Structural Analysis for Industrial Equipments, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China
weight, high bandwidth quick response, low cost, and easy implementation (Chee et al. 1998; Peng et al. 2005). Piezoelectric materials can be configured in different ways to improve the performance of piezoelectric devices. Better geometric designs may lead to a better utilization of the piezoelectric materials. Up to now, a number of methods have been developed for the optimal design of piezoelectric device (see, e.g., Ryou et al. 1998; Silva 200
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