基于多维模态方法的流体二维非线性强迫晃动分析

发布时间：2018-06-17 05:24

  本文选题：多维模态 + 二维非线性晃动　； 参考：《振动与冲击》2017年16期

【摘要】：基于多模态方法分析了二维容器内液体的强迫非线性晃动问题,采用绝对速度势函数描述动坐标下的流体非线性运动,根据Bateman-Luke变分原理,将非线性自由边值问题转化为等效的泛函极值问题,将自由液面波高函数和绝对速度势函数展开为广义Fourier级数,得到相互耦合的有限维非线性模态系统(一组非线性常微分方程),采用Runge-Kutta(龙格-库塔)法求解非线性常微分方程组,从而得到液体的强迫非线性晃动响应,分别模拟并讨论了矩形容器内液体在强地震作用下的晃动响应、在水平谐波作用下的普通共振稳态响应、在竖向谐波作用下的参数共振稳态响应,预测了液体在普通共振与参数共振共同作用下的液面响应。将多模态结果与其它数值方法的结果进行了对比,计算结果表明,多模态方法在长时间非线性稳态响应分析上具有其独特的优势。
[Abstract]:Based on the multimodal method, the forced nonlinear sloshing of the liquid in a two-dimensional container is analyzed. The absolute velocity potential function is used to describe the nonlinear motion of the fluid in the moving coordinates. According to the Bateman-Luke variational principle, the nonlinear motion of the fluid is described. The nonlinear free boundary value problem is transformed into an equivalent functional extreme value problem, and the wave height function and the absolute velocity potential function of the free liquid surface are expanded into generalized Fourier series. The coupled finite dimensional nonlinear modal system (a set of nonlinear ordinary differential equations) is obtained. The Runge-Kutta (Runge-Kutta) method is used to solve the nonlinear ordinary differential equations, and the forced nonlinear sloshing response of the liquid is obtained. The sloshing response of liquid in rectangular container under strong earthquake, the common resonance steady state response under horizontal harmonic action and the parametric resonance steady state response under vertical harmonic action are simulated and discussed respectively. The surface response of liquid under the interaction of common resonance and parametric resonance is predicted. The multimodal results are compared with those of other numerical methods. The results show that the multimodal method has its unique advantages in the long time nonlinear steady-state response analysis.
【作者单位】： 同济大学水利工程系;
【基金】：国家自然科学基金资助项目(51279133)
【分类号】：O353.1;TU318;TV314
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本文编号：2029899