为求解边界条件为弹支的多跨传动轴弯曲振动响应，基于第二类拉格朗日方程，建立了瑞利连续轴动力学模型，并使用伽辽金法将偏微分方程转化为常微分方程。提出了多跨传动轴振型函数的多项式拟合方法，通过传递矩阵法计算得到了传动轴有限截面的振型值，据此用多项式分别拟合振型函数及其高阶导数。以直升机尾传动轴为算例,将拟合得到的前三阶振型函数及相应的高阶导数代入到动力学方程组中，通过振型叠加法计算得到了尾传动轴在偏心激励下的弯曲振动响应。算例结果表明，该方法具有较好的收敛性和可靠性。
Abstract
In order to solve the bending vibration response of multi-span shaft with the elastic support boundary condition, a dynamic model of the Rayleigh continuous shaft was established based on the second Lagrange equation, and the partial differential equations were transformed into the ordinary differential ones by using Galerkin's method. A polynomial fitting method for the mode shape function of multi-span shaft was proposed, the mode shape values of the finite section of the shaft were calculated by means of transfer matrix method, and the mode shape functions and their higher order derivatives were fitted by polynomial. The helicopter tail drive shaft for example, fitting functions of three order mode shapes and their higher-order derivatives were substituted into dynamic equations, and the bending vibration response of the tail drive shaft under eccentric excitation was calculated by mode superposition method. The study results revealed that the method has good convergence and reliability.
关键词
多跨传动轴 /
弹性支承 /
弯曲振动 /
振型 /
多项式拟合
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Key words
multi-span shaft /
elastic support /
bending vibration /
mode shape /
polynomial fitting
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