Comparison between numerical result and variationalsolution shows that the method used in this work is effective for studying flow-induced vibration of pipeline on offshore platform.
比较等截面管道的变分解和数值解，说明此方法用于研究海洋平台输液管道的流体激振是有效的。
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Thus, the theory of state space is combined with variationalsolution, and the variational results for free vibration frequency of the laminates with arbitrary thickness are calculated.
The fine scales solution in the variational multiscale finite element method, which can be acquired by analytical or numerical technique, has an important impact on the final numerical solution.