减基法, 贪婪算法, 对数采样法, 谐响应, 阻尼

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. 