气轮机叶片振动响应的数值分析

求解叶片强迫振动方程的难点在于定量确定叶片的激振力和选用合适的计算模型·针对这一问题,应用薄壳理论,建立了气轮机叶片的应变 位移非线性关系,给出了激振力的形式;应用虚功原理得到了带有较大弯曲和扭转变形的叶片受迫振动方程,再应用振型迭加法求出叶片的振动响应方程,得到了叶片的共振响应条件·结合具体算例,分析了叶片的振动响应及共振响应,结果表明,气轮机叶片振动响应主要取决于叶片固有频率、振动模态、激振频率、激振力(谐波分量)等因素,叶片的非共振响应曲线为拍,当固有频率ω、激振力频率ωe和激振力沿叶片周向移动的角速度ωN间的关系为ω=ωe=nωN(n=1,2,…,∞)时,叶片发生共振·

Numerical Analysis of Response to Vibration of Turbine Blades

The difficulties found in solving the forced vibration equation of turbine blades are mainly the problem how to determine the exciting force acted on blades and the choice of an appropriate computation model. A nonlinear strain-displacement relationship is therefore developed in terms of the exciting force acted on turbine blades. Then, based on virtual work principle, a forced vibration equation of the blades which were twisted and bended to a certain degree is given. Further, a response function to blades' vibration is given by iterative process for relevant vibration mode, thus showing the response conditions to resonance of blades. A practical question is exemplified to analyze the response to blades' vibration/resonance. The results reveal that the response to blades' vibration depends mainly on such factors as the natural frequency of blades, vibration mode, frequency of exciting shock and exciting force or a harmonic component and, if taking beat frequency from the non-resonant response curve and the relationship among blades' natural frequency ω, exciting shock frequency ωe and the angular velocity of exciting force moving peripherally around blades, ωN, is ω = ωe = nωN(n = l,2,&mellip;,∞), the blades resonate.