摘要
通过减基法研究了有阻尼线弹性结构的谐响应。首先,把特定的载荷频率范围离散成有限点,并通过对数采样法进行预采样。然后,引入贪婪算法对样本进行自适应训练,得到一组向量,用施密特正交化方法进行正交归一化,构造一个最优减基空间,通过伽辽金映射把原运动方程中的矩阵映射到其中,得到一个减缩系统。最后,将原问题的减缩解映射回原空间,在保证了效率和精度的前提下得到了原系统的近似解。算例表明,减基法有效提高了有阻尼结构谐响应分析的效率。
The harmonic response of linear elastic structures with damping was analyzed using a reduced-basis method （RBM）. Firstly the frequency domain was discretized into limited points. And a logarithmic sampling method was used to select samples. The greedy algorithm was suggested to train the samples adaptively and a series vectors were obtained. A Gram-Schmidt algorithm was used to orthogonalize the vectors, then a optimum reduced-basis space was constructed. After the Galerkin projection of matrices into the reduced basis space, a reduced system was obtained and can be solved efficiently. The reduced solution was obtained. By projecting the reduced solution back into the original space, the approximate solution of the original system subjected to a harmonic load was obtained efficiently and accurately. The numerical examples herein demonstrate that reduced-basis method can perform harmonic response analysis of linear structures with damping well.
出处
《中国机械工程》
EI
CAS
CSCD
北大核心
2010年第11期1283-1288,共6页
China Mechanical Engineering
基金
国家杰出青年基金资助项目(10725208)
"十一五"国防基础科研基金资助项目(A1420080166)
教育部长江学者与创新团队发展计划资助项目(531105050037)
湖南大学汽车车身先进设计制造国家重点实验室自主研究课题资助项目(60870003)
关键词
减基法
贪婪算法
对数采样法
谐响应
阻尼
reduced- basis method
greedy algorithm
logarithmic sampling method
harmonic response
damping
