【摘要】 本文构造具有线弹性和线阻尼的弹性支承上的van der Pol振子模型,试图从较一般的意义上研究弹性支承对自激振动的抑制机理。文中给出了这一非线性振动模型的微分方程,并用奇异摄动法求得了渐近解。研究结果表明,在支承质量远小于振子质量,支承刚度远小于振子刚度的情况下,弹性支承具有不大的线阻尼,就能完全抑制振子的自激振动。这一结论,同A.C.(?)和B.(?)用弹性支承抑制滑轴承中油膜振荡的实验所得的结果完全相符。但由于油膜涡动问题的复杂性,他们的理论分析没有体现出相应的结论。上述理论上的结论,是我们从分析弹性支承上的van der Pol振子模型获得的,可望在实际中推广应用。更多还原

【Abstract】 In this paper, we construct the van der Pol vibrator model upon theelastic supporting with linear elasticity and linear damping, and try toresearch from more general meaning the mechanism for the elastic sup-porting to restrain self-excited vibration. This paper also gives the dif-ferential equation of the nonlinear vibration model, and obtains its asym-ptotic solution by means of singular perturbation methods. It is clearlyshown in our results researched that self-excited vibration of the vibratorwill be wholly restrained if only the elastic supporting possesses slightlya bit of linear damping on condition that the mass of the supporting isfar small to the mass of the vibrator, and the rigidity of the supportingis far small to the rigidity of the vibrator. This conclusion accords per-fectly with the experiment results which were obtained by A.C.and through the experiments of the ela-stic supporting restraining oil whip in the sliding bearing. However theirtheoretical analysis did not embody out corresponding conclusion becauseof complexity of the oil film whirl problems. The above-mentioned con-clusion in theory is obtained by us from the analysis of the van der Polvibrator model upon the elastic supporting, and it will be hopeful ofextension and application in practice.更多还原