失谐叶盘受迫响应的灵敏度分析方法

Sensitivity analysis method for forced response of mistuned bladed discs

针对失谐叶盘结构的受迫响应与叶片失谐之间的敏感性问题,提出了一种失谐叶盘最大响应幅值分别关于叶片频率失谐参数和叶片节点失谐质量的一阶和二阶灵敏度系数计算方法,以探究叶盘结构失谐参数对其最大响应幅值的影响。该方法立足于高保真失谐叶盘减缩建模和响应分析技术,直接对失谐叶盘结构的动力学方程进行推导获取其一阶和二阶灵敏度系数的数学表达式,未引入任何其他近似和简化计算措施,可以有效地求解高保真失谐叶盘最大响应幅值在不同激励频段、激励阶次和失谐形式下的灵敏度系数。该灵敏度分析方法在大规模高保真失谐叶盘结构模型上验证了其有效性。结果表明,与常规的数值差分灵敏度近似计算方法相比,本文提出的灵敏度分析方法在计算精度和计算效率方面具有巨大的优势,对进一步的失谐叶盘响应分析具有广泛的应用前景和通用性。

The forced response of bladed discs is very sensitive to random blade mistuning.This paper proposes an effective sensitivity analysis method to explore the impact of blade mistuning parameters on the maximum vibrational amplitude of mistuned bladed discs.This method is constructed based on the reduced-order model and a subsequent forced response analysis of mistuned bladed discs.Mathematical expressions of the first and second order sensitivity coefficients for the maximum blade vibrational amplitude with respect to blade frequency mistuning parameters and mistuning nodal mass are derived from the equations for motion of mistuned bladed discs,without any hypothesis or numerical simplification.The method proposed can be used to perform effective sensitivity analysis for bladed discs with any random blade mistuning pattern vibrating in different frequency bands under an engine order excitation.The method is numerically validated in a high-fidelity mistuned bladed disc model.It is shown that the proposed method has the advantages of high accuracy and computational efficiency over the method of finite difference approximation of the sensitivity coefficients.Benefiting from its versatility,the method proposed is expected to further contribute to the forced response analysis of mistuned bladed discs.