船舶推进轴系纵横耦合非线性动力学分析—叶频激励下横向主共振响应

在考虑Von Karman非线性位移—应变关系下,基于Hamilton变分原理建立了船舶推进轴系纵横耦合非线性动力学方程。利用Galerkin方法,导出系统第一阶模态振动微分方程,采用多尺度法求解该方程。获得了叶频激励下横向主共振响应方程组,利用伪弧长延拓法数值求解了该方程组的平衡解并分析了其稳定性。探讨了支承刚度、激励载荷、螺旋桨质量、阻尼比以及细长比对轴系纵横耦合效应的影响。研究表明:细长比越小,激励载荷越大,阻尼比越小,系统纵横耦合效应越强;增加后艉轴承刚度可以抑制纵横耦合效应,增加前艉轴承以及推力轴承刚度则增强纵横耦合效应,而中间轴承对其没有明显影响;与线性模型相比,纵横耦合效应使轴系横向共振时的频率大于其线性固有频率,在某些激励频率处,幅频响应曲线上存在多解使幅值出现跳跃现象。分析结果对船舶推进轴系的设计有指导意义。

Coupled longitudinal-transverse nonlinear dynamics of a marine propulsion shafting—Primary resonance under blade frequency excitation

Based on Hamilton's principle and considered the Von Karman's nonlinear strain-displacement relationship, a coupled longitudinal-transverse nonlinear dynamic model of a marine propulsion shafting is established. The first mode equations are obtained by Galerkin method and are solved by the method of multiple scales. The primary resonance equations are derived under the blade frequency excitation. Then, these equations are numerically solved by pseudo-arclength continuation method to obtain the steady-state response and the stabilities are analyzed. The influence to the nonlinear effect is discussed about the support stiffness, load, mass of propeller, damping ration and slender ration. Research shows the smaller the slen-der ration, the bigger the load and the smaller the damping ration is, then the bigger the nonlinear effect is. The nonlinear effect is reduced by increasing the back stern bearing stiffness and increased by increasing the front stern bearing and thrust bearing stiffness. While the middle bearing makes no influence to it. Com-pared with the linear model, the lateral resonant frequency is bigger than the linear natural frequency. Insome frequencies, there are multiple solutions in amplitude-frequency curve and has jump phenomena. These analyses have a reference and guidance to the design of marine propulsion shafting.