بهینه سازی یکپارچه ساختاری و توپولوژی کنترل برای صفحه هوشمند پیزوالکتریک بر اساس الگوریتم ژنتیک

The integrated optimization of structural topology, number and positions of the actuators and control parameters of piezoelectric smart plates is investigated in this paper. Based on the optimal control effect in the independent mode control and singular value decomposition of the distributed matrix of total performance index for all physical control forces for piezoelectric smart plate, a new criterion, where several large values in singular values are selected, is put forward to determine the optimal number of the assigned actuators in the coupled modal space control. Furthermore, the optimal positions of actuators are ascertained by singular value decomposition of the modal distributing matrix. The integrated optimization model, including the optimized objective function, design variables and constraint functions, is built. The design variables include the logic design variables of structural topology, the number and positions of actuators as well as the control design parameters. Some optimal strategies based on genetic algorithm (GA), such as structural connection checking and structural checkerboard checking and repairing technique, are used to guide the optimization process efficiently. The results of two numerical examples show that the proposed approach can produce the optimal solution with clear structural topology and high control performance.

In recent years, because more and more stringent performance requirements are imposed in advanced engineering application, considerable attention has been paid to structural vibration control. There are two classical routes to suppress/reduce structural vibration. One is to implement vibration control, such as passive control, semi-active control and active control. The other is to implement structural dynamic optimization, including size optimization, shape optimization and topology optimization. Especially, the dynamic topology optimization becomes the research emphasis up to now. Xu et al. [1] put forward topology group concept for truss topology optimization with frequency constraint, where nodal mass is taken into consideration. Jog [2] proposed the global measure and local measures for minimizing the vibrations of structures subjected to periodic loading. Rong et al. [3] presented the topology optimization of continuous structures under stochastic excitations based on ESO. Guan et al. [4] optimized cable-supported bridges with frequency constraint incorporating ‘nibbling’ technique. Du et al. [5] dealt with the topology optimization problems formulated directly with the design objective of minimizing the sound power validated from the structural surfaces into a surrounding acoustic medium. Traditionally, structural dynamic optimization and vibration control are separately carried out so that the optimal control effect cannot obtained, i.e., structural parameters are optimized first and then an optimal controller is designed. How to deal with the strong coupling between structural dynamics and active control is a well-recognized challenge for the design of piezoelectric smart structures. At present, the problem has received much attention in the field of piezoelectric structural design. Some papers deal with the integrated optimization of structure and control in order to acquire hybrid optimization effect. Xu et al. [6] and [7] studied the integrated optimization of structure and control for piezoelectric intelligent trusses, in which actuators/sensors positions are also taken as the design variables. Zhu et al. [8] investigated simultaneous optimization with respect to the structural topology, actuator locations and control parameters of an actively controlled plate structure, where the topology design variables are relaxed to take all values between 0 and 1 and structural and control design variables are not treated within same framework. But most of these researches mainly focus on simple designs such as the integrated optimization of structural size and control, where the structural topology is predetermined. The integrated optimization problem of structural topology and control has not been extensively treated despite it is very important, including the number and positions of actuators. This paper is organized as follows: in Section 2, based on the optimal control effect for the control design in the independent modal space, a new method based on singular value decomposition is presented determine the optimal number and positions of actuators. The integrated topology optimization model, including the design variables, the objective function and the constraint functions, is built in Section 3. Section 4 introduces the corresponding optimization algorithm combing genetic algorithm with the checking technique of structural topology effectivity. Finally in Section 5, two numerical examples are used to highlight and demonstrate the validity of the proposed method.

In order to suppress structural vibration more efficiently, the integrated structural and control design of piezoelectric smart plate for vibration control is studied in this paper. First, based on the control effect in independent modal space, how to ascertain the optimal number and positions of PZT actuators in coupled modal space is presented. Second, a new optimization strategy based on RTTLDV coupled with topology effectiveness checking, including structural connectivity checking and structural checkerboard checking and repairing is put forward to deal with the integrated optimization of structural topology and control for piezoelectric smart plates. Finally, numerical simulations are carried out on a cantilever piezoelectric smart plate and a piezoelectric smart plate with four simple supported corners, where structural topology, the number and positions of actuators and the control parameters are taken as the design variables. The results of numerical examples show that the proposed approach can produce clear structural topology and high control performance. In numerical example one, it is obvious that the optimal topology layout and the positions of actuators vary with different cases. Actuators are often placed in the position where the deformations of the elements are much larger for all controlled modes. For numerical example two, the same structural topologies can be obtained for two cases though the optimal model is different and the placement of actuators is also different.