一种求解含围带阻尼成圈叶片振动响应的高效方法

An Efficient Method for Solving Vibration Response of Continuous Covered Blades with Damped Shroud

针对含围带阻尼成圈叶片的非线性振动响应计算时自由度多、迭代求解计算量大的问题,综合波传动法、高阶谐波平衡法及Receptance法推导了一种求解含围带阻尼成圈叶片振动响应的高效方法。根据成圈叶片结构周期对称的特点,采用波传动法,将含围带阻尼成圈叶片降阶为一个基本扇区进行振动分析,接触面的非线性摩擦力可由单个扇区的位移结合干摩擦模型求得;将降阶后单个扇区的时域振动微分方程由高阶谐波平衡法转化为频域代数方程,通过叶片正则振型的正交性对频域的振动方程进行解耦,并利用叶片局部非线性的特点对非接触面上的线性自由度进一步缩聚,从而减少非线性迭代的规模,提高计算效率。算例结果表明:采用所提求解方法的响应计算结果与采用整体模型的结果相差小于0.33%,计算时间缩短为原来的10%,验证了该方法的正确性、高效性,同时采用该方法研究了真实围带阻尼叶片的非线性振动响应。

An efficient solution method based on wave propagation method, multi-harmonic balance method and Receptance method was developed to solve the problem with overlarge degrees of freedom and computational complexity in calculating the nonlinear vibration response of continuous covered blades with damped shroud. According to the cyclic symmetry property of blade, the vibration analysis of a whole blade can be reduced to one of its basic sector using wave propagation method and the nonlinear friction force can be solved from the displacement of the basic sector and friction contact model; the differential equations in time domain of the reduced basic sector can be transformed into algebraic equations in frequency domain by multi-harmonic balance method. The orthogonality of normalized modes is used to decouple the vibration equation of blade in frequency domain and the local nonlinear characteristics of the blade system are used to condense the linear DOFs in non-contact interfaces. So that the scale of nonlinear iteration can beeffectively reduced and the computation efficiency is improved. The results showed that the relative error obtained with the developed method was 0.33%and the calculation time was reduced to 10%, which verifies the accuracy and efficiency of the proposed method. The nonlinear vibration response of a real shrouded blade was investigated by this method.