本文選題：多維模態(tài) + 二維非線性晃動��； 參考：《振動與沖擊》2017年16期

【摘要】：基于多模態(tài)方法分析了二維容器內(nèi)液體的強迫非線性晃動問題,采用絕對速度勢函數(shù)描述動坐標下的流體非線性運動,根據(jù)Bateman-Luke變分原理,將非線性自由邊值問題轉(zhuǎn)化為等效的泛函極值問題,將自由液面波高函數(shù)和絕對速度勢函數(shù)展開為廣義Fourier級數(shù),得到相互耦合的有限維非線性模態(tài)系統(tǒng)(一組非線性常微分方程),采用Runge-Kutta(龍格-庫塔)法求解非線性常微分方程組,從而得到液體的強迫非線性晃動響應,分別模擬并討論了矩形容器內(nèi)液體在強地震作用下的晃動響應、在水平諧波作用下的普通共振穩(wěn)態(tài)響應、在豎向諧波作用下的參數(shù)共振穩(wěn)態(tài)響應,預測了液體在普通共振與參數(shù)共振共同作用下的液面響應。將多模態(tài)結(jié)果與其它數(shù)值方法的結(jié)果進行了對比,計算結(jié)果表明,多模態(tài)方法在長時間非線性穩(wěn)態(tài)響應分析上具有其獨特的優(yōu)勢。
[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.
【作者單位】： 同濟大學水利工程系;
【基金】：國家自然科學基金資助項目(51279133)
【分類號】：O353.1;TU318;TV314
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本文編號：2029899