基于标准粒子群优化算法的压电片位置与尺寸优化

摘要

悬臂梁式压电振动能量回收装置上压电片的粘贴位置和尺寸是影响回收电能的重要因素.提出了采用标准粒子群算法对压电片粘贴位置和尺寸进行同时优化的方法.首先推导了悬臂梁能量回收装置的能量方程;然后以能量方程为目标函数、运用标准粒子群优化算法获得了前三阶模态下压电片粘贴位置和尺寸优化结果;最后运用Abaqus软件计算得到前三阶模态下压电振动能量回收装置的固有频率和点电压,并由能量方程计算得到开路能量,根据点电压和开路能量分析得到了压电片最优位置和尺寸.运用标准粒子群算法获得的压电片位置和尺寸优化结果与仿真分析结果基本吻合:一阶模态下,压电片最优贴片位置在梁根部,最优尺寸约为梁长一半;二阶模态下,最优贴片位置在梁中部,最优尺寸约为梁长一半;三阶模态下,最优贴片位置在梁的三分之二处,最优尺寸约为梁长的三分之一.%The location and size of the piezoelectric patch on the cantilever for vibration energy harvester are the im-portant factors that influence the recovery of the electric energy. A kind of novel method using the standard particle swarm optimization ( PSO) algorithm was put forward for optimizing the location and size of the piezoelectric patch. Firstly, the energy equation of the cantilevered vibration energy harvester was analyzed and deduced. Secondly, the optimization program of standard PSO algorithm which takes the energy equation as the objective function was com-piled using MATLAB software, so that the optimal location and size of the piezoelectric patch for the first three or-ders of modes were obtained by running the optimization program. Lastly, the natural frequency and local point volt-age of the cantilevered piezoelectric vibration energy harvester for the first three orders of modes were computed by using the Abaqus software, and the open-circuit energy can be calculated using the energy equation, and then the optimal location and size of the piezoelectric patch can be obtained by analyzing the local point voltage and open-circuit energy. The results of the optimal location and size of the piezoelectric patch from implementing the standard PSO algorithm are consistent with the analysis results from Abaqus software. The detailed results are as follows that the optimal location is at the root of the cantilever and the size is about half length of the cantilever under the first mode, and the optimal location is at the middle and the size is about half the length of the beam under the second mode, and they are the two-thirds and about one-third beam length under the third mode.