浸液轴向运动板的非线性自由振动和内共振分析

摘要

以竖直浸没于液体中的轴向运动矩形板作为研究模型,根据经典薄板理论以及von Kámán非线性几何关系,得到流-固耦合系统的非线性振动微分方程.假定液体为无黏、无旋、不可压缩的理想流体,流体对板的动压力采用速度势函数及Bernoulli方程描述.然后应用直接多尺度法求解系统的非线性偏微分方程,根据可解性条件,获得系统的非线性频率.分析了浸液轴向运动板的1∶1内共振及1∶3内共振现象,并讨论了系统参数对该流-固耦合系统非线性动力学特性的影响.%A vertically moving rectangular plate immersed in liquid was investigated.Based on the classical thin plate theory and von Kámán nonlinear geometrical relationships,the nonlinear vibration differential equations of the fluidstructure coupling system were derived.It was assumed that the liquid is incompressible,inviscid and irrotational.The velocity potential and Bernoulli's equation were used to describe the fluid pressure acting on the moving plate.The system was solved by applying directly the method of multiple scales to the nonlinear partial-differential equations.Based on the solvable condition,the nonlinear frequency of the system was obtained.The 1 ∶ 1 and 1 ∶ 3 internal resonances of the moving plate-fluid system were investigated.The effects of system parameters on the nonlinear dynamic characteristics of the fluidstructure coupling system were discussed in detail.