基于时域最小残值法求解含间隙非线性气动弹性系统的半解析解  

Semi-analytical solution of nonlinear aeroelastic systems with freeplay based on the time-domain minimum residual method

作　　者：秦英泉 刘祚秋 刘济科 刘广 QIN Yingquan;LIU Zuoqiu;LIU Jike;LIU Guang(School of Aeronautics and Astronautics,Sun Yat-sen University,Shenzhen 518107,China;Shenzhen Key Laboratory of Intelligent Microsatellite Constellation,Shenzhen 518107,China)

机构地区：[1]中山大学航空航天学院,广东深圳518107 [2]深圳市智能微小卫星星座技术与应用重点实验室,广东深圳518107

出　　处：《中山大学学报（自然科学版）（中英文）》2023年第6期98-106,共9页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(12172387);广东省基础与应用基础研究基金(2021A1515110750,2023A1515010028);深圳市科技计划(ZDSYS20210623091808026)。

摘　　要：采用时域最小残值法求解了含间隙非线性气动弹性系统的半解析周期解。首先,将气动弹性系统的周期解展开为傅里叶级数,并截断前N项作为系统的近似解析解;通过对近似解求导,获得系统的速度和加速度函数;并将位移、速度和加速度函数回代到原始的气动弹性系统,将半解析解求解问题转化为一个非线性最小二乘优化问题。最后,通过增强响应灵敏度方法来迭代求解该最小值问题。在迭代过程中,Tikhonov正则化和“置信域限制”被用来增强算法的收敛性。数值算例表明,时域最小残值法可以快速获得高精度的半解析解。The semi-analytical periodic solution of a nonlinear aeroelastic system with freeplay was solved by the time-domain minimum residual method.First,the periodic solution of the aeroelastic system is expanded into the Fourier series,and the first N term is truncated as the approximate analytical solution.Then,the velocity and acceleration of the system are obtained by taking the derivative of the approximate solution in the time.And the displacement,velocity and acceleration functions are substituted back into the original aeroelastic system.Then,the problem of solving the semi-analytical solution is transformed into a nonlinear least-square optimization problem.Finally,such minimum value optimization problem is iteratively solved by the enhanced response sensitivity approach.In the above iteration,the Tikhonov regularization and“trust-region constraint”are used to enhance the algorithm’s convergence.Numerical examples show that the time-domain minimum residual method can quickly obtain high-precision semi-analytical solutions.

关 键 词：间隙非线性 时域最小残值法 周期解 TIKHONOV正则化 

分 类 号：V21[航空宇航科学与技术—航空宇航推进理论与工程]