船舶双层底结构振动的流固耦合分析
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摘要
船用主机产生的激励直接作用的区域为机舱,双层底结构作为主机的基础,一方面影响船用主机的振动,另一方面也是影响主机与整个船体耦合振动的关键部位。以大连海事大学校船“育鲲”轮为例,为了增加船体的总纵强度和底部的局部强度,双层底结构中设置有纵横隔板和肋板,同时包含主机滑油循环柜,舱底水舱,燃油溢油舱等舱室。舱室中充有各种液体,且其中的液体高度经常发生变化,液体高度的改变可能会对主机和双层底结构的耦合振动产生一定的影响。舱室中的肋板将液面划分为多个区域,出现多个自由液面共存的情况,肋板一部分浸入到液体中,存在着结构与双侧液体同时发生耦合作用的问题,这些都是进行主机与双层底整体耦合振动分析中需要考虑的问题。
本文的研究工作针对上述问题展开,采用矩阵分块方法求解了部分充液箱体振动方程,给出了结构两侧同时存在液体的情况下,耦合矩阵的形成过程和方法。建立了箱体内多个自由液面并存的晃动模型。分析了充液箱体在外部激励下的响应问题,最后将理论分析的结果应用到实船的主机和双层底结构的耦合振动分析,具体的工作如下。
1.构建了压力-位移形式的流体和结构耦合振动的数学模型,采用有限元法对简支梁与流体耦合振动问题进行求解,整体振型以梁振动为主导,耦合频率远远小于流体单独振动的频率,也低于简支梁单独振动频率。采用缩减法对同一问题进行分析,给出了左侧和右侧特征值解法的具体表达形式,采用较少数量的特征向量进行运算时,会导致系统高阶次频率值略有升高,在耦合界面的信息的准确传递上,右侧特征值解法拥有更明显的优势。
2.给出了势函数-位移形式的流固耦合振动方程以及对称形式的方程,针对二维部分充液箱体的振动问题,采用矩阵分块的方法对该问题的特征方程进行了求解。当箱内液面高度较低时,仅导致整体频率下降,对振型影响不大；当液面升高到一定程度时,整体的某些阶次振型出现变化。对十字型隔板液箱的自由振动进行了实验与仿真对比分析,二者的结果吻合良好,整体的固有频率与充液高度成反比,充液高度较低时,箱体底板在较高阶次出现明显的模态位移。充液高度较高时,液体的脉冲作用得到了加强,在较低阶次也能引起底板产生模态位移。
3.建立了刚性箱体内液体晃动模型,采用有限元法和解析法对该模型进行求解,二者结果吻合良好,液体低频晃动频率随着液体高度升高而增加,基频增加的幅度最大,自由液面波形交替呈现对称和非对称形式,低频晃动伴随着液体质心在水平方向的变化。采用伽辽金法求解了简支梁与单侧液体的耦合振动问题,与有限元法求解的结果吻合良好,但耦合振动的频率略低于液体自由晃动的频率,与简支梁单独振动的频率值相差较大,低频振动中以液体晃动为主导,梁的弹性模量对较低阶次耦合振动频率影响较大,液面的升高导致系统的频率上升。推导了梁与双侧液体耦合振动方程,应用有限元法进行了求解,计算结果与已有的试验数据吻合良好。分析了三维液箱内液体低频晃动问题,隔板的存在使箱内液体晃动频率下降,隔板使液体出现多个自由液面,得到了相似表面波和相同特征频率的结果。
4.以大连海事大学校船“育鲲”轮为参考建立模型,求解了船用主机与充液双层底之间的耦合振动,通过改变充液的高度来研究二者之间的自由振动特性,其中的液体分为带有自由液面晃动效应和不带有自由液面晃动效应两种。考虑液体的高频振动情况下,充液高度的改变对系统的较低阶次的频率没有影响,充液比的上升使双层底主导的振型在较低阶次出现,双层底的模态位移有所减少。考虑液体低频晃动的情况时,主机和双层底结构均没有出现明显的模态位移,求得的前16阶次频率值相同,表明结果为液体晃动的频率。考虑主机的激励的情况,对主机与双层底的流固耦合系统进行了强迫振动分析。主机出现X型振动,充液高度的变化对主机上的节点振动响应影响较小,而对双层底结构上节点节点振动响应影响明显,自由液面对整体在强迫作用下的响应影响不大。考虑液面晃动的情况下,靠近滑油舱壁两侧的液体节点的位移方向相反,最大相对位移出现在两缸侧推力最大的时刻。本文具有一定的科学和工程意义。
The zone where the marine main engine's forces exciting at directly is the engine room. As the foundation of the main engine, the double bottom tank does not only affect the vibration of main engine, but also is the key part which influence the coupled vibration between main engine and the hull. Take the DMU ship'Yu-kun'for example; to gain the overall longitudinal strength and the part strength of the bottom, the double bottom tank is equipped with wash and transverse plates, ribbed slabs, main engine oil tank, bilge tank, fuel oil overflow, etc. There are many kinds of liquid in cabins, and the height of the liquid is usually changed, which may affect the coupled vibration. The ribbed slabs cut the liquid surface into many zones, and many free surfaces exist in the mean time. Parts of the ribbed slabs immerse in the liquid, so there is coupled vibration of structure with two sides liquid. All these problems should beconsidered in the analysis of the coupled vibration of main engine and double bottom tank.
Based on the problems mentioned above, this paper solves the partially filled liquid tank's vibration equations by matrix block method. The coupled matrix is given under the condition of the structure coupled with two-side liquid. The sloshing model of liquid tank with many free surfaces is constructed. The liquid tank's response under excitation is analysed. Finally, the results of the analysis are applied in the coupled vibration of 'Yu-kun'ship's main engine and double bottom tank, and the steps for this study are illustrated as follows.
1. A pressure-displacement numerical model to address the coupled interaction between liquid and structure is developed, and a finite element method is employed to solve the vibration equation of a simply supported beam coupled with liquid. The whole modal is in the form of beam-dominated vibration, and the coupled frequencies are fewere than the liquid's frequencies, as well as the beam's Eigen values. The same problem is solved by modal representation method, and the counterpart equations are deduced in the right and left eigenvector sets. It also shows that a limited set of eigenvectors can make higher order frequencies increas. On the accuracy of the messages transfer, the right Eigen vector set has more advantages.
2. The coupled equations in the form of potential-displacement and symmetric are deduced. It is solved by FEM based on matrix block method, for a2D partially filled liquid tank's Eigen value problem. The liquid height reduction make the whole frequencies decrease, but affect the modals little. Increasing liquid height affect some order modals significantly. The frequencies are in the reverse relation with filling ratio. When the filling ratio is small, there is obvious displacement on the bottom in higher order modals. When the filling ratio is large, due to the liquid impulsive effect, there is a displacement even in lower order modals.
3. The sloshing model of liquid in a rigid tank is constructed, which is solved by FEM and analytic method separately. Sloshing frequencies increase in proportional to the liquid height, and the fundamental frequency increases significantly. The free surface shapes show symmetric and anti-symmetric waves, the sloshing modals adjoin with the relative shift of the liquid center-of mass as well. The coupled vibration problem of a beam with one side attached to liquid is solved by Galerkin method, and the results agree well with FEM results. Coupled frequencies are lower than liquid sloshing frequencies, and are far lowere than the beam's frequencies. The liquid sloshing modal is dominated in lower frequencies vibration, and the beam elastic modulus affects lower order coupled frequencies significantly. The coupled Eigen values show an increase for increasing the liquid height. For the coupled vibration equation of a beam with two side fluid, it is solved by FEM, and the results are compared with experiment data, which are in good agreement. The liquid sloshing modes in3D liquid tank with-or-without baffles are observed. The existence of baffles cause sloshing frequencies down, which cut the liquid surface into many free surfaces, and there are similar free surface waves and equal Eigen frequencies.
4. A numerical model is constructed based on DMU's'Yu-kun'ship, and that the coupled vibration of the main engine and the double bottom tank is solved, in different filling ratio conditions, where the sloshing effect is considered or not. The liquid height has no effect on lower order frequencies, and there are double bottom dominated modals in lower orders vibration with filling ratio increasing, while the double bottom displacement is reduced. When the sloshing effect is not considered, there is no obvious displacement in main engine and the double bottom tank. The first16frequencies are equal, so the obtained results are liquid sloshing frequencies, when the sloshing effect is considered. The coupled vibration system of main engine and double bottom tank are investigated under main engine's excitation. The main engine vibrates in X form. The filling ratio almost has no effect on the main engine's vibration, but it has significant effect on the double tank's nodes. The free surface effect has no effect on the coupled vibration, and the displacement directions of liquid nodes near the lube oil cabin wall are opposite, while the most relative displacements are in the time of two cylinder's biggest side thrust.
It has an important significance in science and engineering.
本文的研究工作针对上述问题展开,采用矩阵分块方法求解了部分充液箱体振动方程,给出了结构两侧同时存在液体的情况下,耦合矩阵的形成过程和方法。建立了箱体内多个自由液面并存的晃动模型。分析了充液箱体在外部激励下的响应问题,最后将理论分析的结果应用到实船的主机和双层底结构的耦合振动分析,具体的工作如下。
1.构建了压力-位移形式的流体和结构耦合振动的数学模型,采用有限元法对简支梁与流体耦合振动问题进行求解,整体振型以梁振动为主导,耦合频率远远小于流体单独振动的频率,也低于简支梁单独振动频率。采用缩减法对同一问题进行分析,给出了左侧和右侧特征值解法的具体表达形式,采用较少数量的特征向量进行运算时,会导致系统高阶次频率值略有升高,在耦合界面的信息的准确传递上,右侧特征值解法拥有更明显的优势。
2.给出了势函数-位移形式的流固耦合振动方程以及对称形式的方程,针对二维部分充液箱体的振动问题,采用矩阵分块的方法对该问题的特征方程进行了求解。当箱内液面高度较低时,仅导致整体频率下降,对振型影响不大；当液面升高到一定程度时,整体的某些阶次振型出现变化。对十字型隔板液箱的自由振动进行了实验与仿真对比分析,二者的结果吻合良好,整体的固有频率与充液高度成反比,充液高度较低时,箱体底板在较高阶次出现明显的模态位移。充液高度较高时,液体的脉冲作用得到了加强,在较低阶次也能引起底板产生模态位移。
3.建立了刚性箱体内液体晃动模型,采用有限元法和解析法对该模型进行求解,二者结果吻合良好,液体低频晃动频率随着液体高度升高而增加,基频增加的幅度最大,自由液面波形交替呈现对称和非对称形式,低频晃动伴随着液体质心在水平方向的变化。采用伽辽金法求解了简支梁与单侧液体的耦合振动问题,与有限元法求解的结果吻合良好,但耦合振动的频率略低于液体自由晃动的频率,与简支梁单独振动的频率值相差较大,低频振动中以液体晃动为主导,梁的弹性模量对较低阶次耦合振动频率影响较大,液面的升高导致系统的频率上升。推导了梁与双侧液体耦合振动方程,应用有限元法进行了求解,计算结果与已有的试验数据吻合良好。分析了三维液箱内液体低频晃动问题,隔板的存在使箱内液体晃动频率下降,隔板使液体出现多个自由液面,得到了相似表面波和相同特征频率的结果。
4.以大连海事大学校船“育鲲”轮为参考建立模型,求解了船用主机与充液双层底之间的耦合振动,通过改变充液的高度来研究二者之间的自由振动特性,其中的液体分为带有自由液面晃动效应和不带有自由液面晃动效应两种。考虑液体的高频振动情况下,充液高度的改变对系统的较低阶次的频率没有影响,充液比的上升使双层底主导的振型在较低阶次出现,双层底的模态位移有所减少。考虑液体低频晃动的情况时,主机和双层底结构均没有出现明显的模态位移,求得的前16阶次频率值相同,表明结果为液体晃动的频率。考虑主机的激励的情况,对主机与双层底的流固耦合系统进行了强迫振动分析。主机出现X型振动,充液高度的变化对主机上的节点振动响应影响较小,而对双层底结构上节点节点振动响应影响明显,自由液面对整体在强迫作用下的响应影响不大。考虑液面晃动的情况下,靠近滑油舱壁两侧的液体节点的位移方向相反,最大相对位移出现在两缸侧推力最大的时刻。本文具有一定的科学和工程意义。
The zone where the marine main engine's forces exciting at directly is the engine room. As the foundation of the main engine, the double bottom tank does not only affect the vibration of main engine, but also is the key part which influence the coupled vibration between main engine and the hull. Take the DMU ship'Yu-kun'for example; to gain the overall longitudinal strength and the part strength of the bottom, the double bottom tank is equipped with wash and transverse plates, ribbed slabs, main engine oil tank, bilge tank, fuel oil overflow, etc. There are many kinds of liquid in cabins, and the height of the liquid is usually changed, which may affect the coupled vibration. The ribbed slabs cut the liquid surface into many zones, and many free surfaces exist in the mean time. Parts of the ribbed slabs immerse in the liquid, so there is coupled vibration of structure with two sides liquid. All these problems should beconsidered in the analysis of the coupled vibration of main engine and double bottom tank.
Based on the problems mentioned above, this paper solves the partially filled liquid tank's vibration equations by matrix block method. The coupled matrix is given under the condition of the structure coupled with two-side liquid. The sloshing model of liquid tank with many free surfaces is constructed. The liquid tank's response under excitation is analysed. Finally, the results of the analysis are applied in the coupled vibration of 'Yu-kun'ship's main engine and double bottom tank, and the steps for this study are illustrated as follows.
1. A pressure-displacement numerical model to address the coupled interaction between liquid and structure is developed, and a finite element method is employed to solve the vibration equation of a simply supported beam coupled with liquid. The whole modal is in the form of beam-dominated vibration, and the coupled frequencies are fewere than the liquid's frequencies, as well as the beam's Eigen values. The same problem is solved by modal representation method, and the counterpart equations are deduced in the right and left eigenvector sets. It also shows that a limited set of eigenvectors can make higher order frequencies increas. On the accuracy of the messages transfer, the right Eigen vector set has more advantages.
2. The coupled equations in the form of potential-displacement and symmetric are deduced. It is solved by FEM based on matrix block method, for a2D partially filled liquid tank's Eigen value problem. The liquid height reduction make the whole frequencies decrease, but affect the modals little. Increasing liquid height affect some order modals significantly. The frequencies are in the reverse relation with filling ratio. When the filling ratio is small, there is obvious displacement on the bottom in higher order modals. When the filling ratio is large, due to the liquid impulsive effect, there is a displacement even in lower order modals.
3. The sloshing model of liquid in a rigid tank is constructed, which is solved by FEM and analytic method separately. Sloshing frequencies increase in proportional to the liquid height, and the fundamental frequency increases significantly. The free surface shapes show symmetric and anti-symmetric waves, the sloshing modals adjoin with the relative shift of the liquid center-of mass as well. The coupled vibration problem of a beam with one side attached to liquid is solved by Galerkin method, and the results agree well with FEM results. Coupled frequencies are lower than liquid sloshing frequencies, and are far lowere than the beam's frequencies. The liquid sloshing modal is dominated in lower frequencies vibration, and the beam elastic modulus affects lower order coupled frequencies significantly. The coupled Eigen values show an increase for increasing the liquid height. For the coupled vibration equation of a beam with two side fluid, it is solved by FEM, and the results are compared with experiment data, which are in good agreement. The liquid sloshing modes in3D liquid tank with-or-without baffles are observed. The existence of baffles cause sloshing frequencies down, which cut the liquid surface into many free surfaces, and there are similar free surface waves and equal Eigen frequencies.
4. A numerical model is constructed based on DMU's'Yu-kun'ship, and that the coupled vibration of the main engine and the double bottom tank is solved, in different filling ratio conditions, where the sloshing effect is considered or not. The liquid height has no effect on lower order frequencies, and there are double bottom dominated modals in lower orders vibration with filling ratio increasing, while the double bottom displacement is reduced. When the sloshing effect is not considered, there is no obvious displacement in main engine and the double bottom tank. The first16frequencies are equal, so the obtained results are liquid sloshing frequencies, when the sloshing effect is considered. The coupled vibration system of main engine and double bottom tank are investigated under main engine's excitation. The main engine vibrates in X form. The filling ratio almost has no effect on the main engine's vibration, but it has significant effect on the double tank's nodes. The free surface effect has no effect on the coupled vibration, and the displacement directions of liquid nodes near the lube oil cabin wall are opposite, while the most relative displacements are in the time of two cylinder's biggest side thrust.
It has an important significance in science and engineering.
引文
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