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在文献［３］的基础上，进一步探讨了高速旋转时，离心惯性力产生的旋转软化效应对增压器涡轮叶 片模态特性的影响。介绍了旋转软化效应的理论基础，给出了考虑旋转软化效应的三维振动方程有限元 列式。在一维情形下，进行了旋转软化及应力刚化模态问题的讨论。对文献［３］中的涡轮进行了仅考虑旋 转软化效应及同时考虑旋转软化和应力刚化的模态分析。计算结果表明，仅考虑旋转软化时，旋转状态 涡轮叶片的固有频率较零速时低；但与应力刚化相比，旋转软化对涡轮叶片模态特性的影响较小，因此 综合考虑旋转软化和应力刚化时涡轮叶片的固有频率仍较零速时高。
On the basis of [3], the effect of rotational softening effect caused by centrifugal inertial force on the turbocharger turbine blade’s modal characteristics is further discussed. The theoretical basis of spin-softening effect is introduced, and the finite element formulation of three-dimensional vibration equation considering spin-softening effect is given. In the one-dimensional case, the problems of rotational softening and stress-hardening modes are discussed. For the turbine in [3], the modal analysis considering only the rotational softening effect and considering both the rotational softening and the stress stiffening was carried out. The calculation results show that the rotational frequency of the turbine blade is lower than that of the zero-speed turbine blade only when the rotational softening is considered. However, the effect of rotational softening on the modal characteristics of the turbine blade is smaller than that of the rigid blade. Therefore, The natural frequency of the turbine blade is still higher than zero speed when the stress is rigidified.