摘要
本文研究了带有环形刚性隔板的部分充液刚性圆柱罐中液体在水平简谐激励作用下的晃动响应。引入人工界面将复杂的液体域分割为若干个形状简单的子域,基于叠加原理利用分离变量法研究自由晃动时各子域内液体速度势函数的解析解,在自由液体面与人工界面处利用Galerkin法即可求得液体晃动的固有频率和模态。将水平激励下的液体速度势函数设为刚体运动速度势与相对运动速度势两部分的和。引入广义坐标,利用模态叠加法即可得到相对运动速度势表达式。将刚体运动速度势与相对运动速度势分别代入自由表面方程即可得到含有广义坐标的动力响应方程。求得广义坐标并将其代入势函数表达式即可得到水平激励下的速度势响应。数值结果与有限元法的结果分别进行了比较,显示出很好的一致性。
The sloshing response of liquid in cylindrical tank with a rigid annual baffle under horizontal loads was studied.The complicated liquid domain was separated into several simple subdomains by introducing artificial interfaces.The analytical solutions of velocity potential corresponding to every subdomain were obtained by method of separation of variables based on the superposition principle.The natural frequencies and modes were calculated by using Galerkin method on the free surface and artificial interfaces.The total potential function under horizontal loads was assumed to the sum of the rigid potential and the relative potential.The generalized coordinates were introduced and the relative potential expressions were obtained by mode superposition method.After substituting the rigid potential and the relative potential into the free surface wave conditions,the dynamic response equations with generalized coordinates were established.The responses of fluid potential can be obtained by solving the dynamic response equations and substituting the generalized coordinates into potential expressions.The results were compared with those obtained by finite element method.Excellent agreement has been achieved.
出处
《力学季刊》
CSCD
北大核心
2011年第2期166-172,共7页
Chinese Quarterly of Mechanics
关键词
液体子域
波高方程
广义坐标
刚体速度势
相对速度势
fluid sub-domain
wave height function
generalized coordinates
rigid velocity potential
relative velocity potential
