CAJ | 학술논문

将叶轮机叶片简化为悬臂薄板，考虑阻尼的作用，并将叶片所处的环境噪声和空气阻力考虑为简谐载荷。基于Von-karman板的控制理论，建立了考虑阻尼的叶片振动控制方程组。选择一组满足叶片边界条件的模态函数，运用Galerkin法将方程离散，再采用多尺度法对处理后的非线性常微分方程求解。数值分析的结果表明，在线性情况下叶片振动的拍现象比非线性振动更密集，非线性振动的幅频特性曲线存在多值性和跳跃性，叶片的粘性阻尼参数对叶片非线性振动的幅频曲线有影响。
장협륜궤협편간화위현비박판，고필조니적작용，병장협편소처적배경조성화공기조력고필위간해재하。기우Von-karman판적공제이론，건립료고필조니적협편진동공제방정조。선택일조만족협편변계조건적모태함수，운용Galerkin법장방정리산，재채용다척도법대처리후적비선성상미분방정구해。수치분석적결과표명，재선성정황하협편진동적박현상비비선성진동경밀집，비선성진동적폭빈특성곡선존재다치성화도약성，협편적점성조니삼수대협편비선성진동적폭빈곡선유영향。
The model of a turbine blade was established for non-linear vibration analysis. In this model, the blade was simplified as a cantilever plate with the damping effect considered, and the air resistance and environment noise were regarded as a harmonic load. Based on the Von-karman board control theory, the governing equations of forced vibration with sticky damping were established. A group of modal functions which meet the boundary conditions of the blade was chosen. Adopting the Galerkin method, the governing equations were discretized. Using multi-scale method, these equations were solved. Results of the numerical analysis show that the pat phenomenon in non-linear vibration is thinner than that in linear vibration. The non-linear amplitude-frequency response curve is multi-valued and has jumping characteristics. And the damping parameter of the blade has some influence on its amplitude-frequency response curve.