转动惯量对负载音叉固有频率的影响

Effect of rotational inertia on the natural frequency of loaded turing fork

在计算负载音叉的固有频率时,通常将负载视为附加在弹簧振子上的额外质量,此模型可以较好地描述音叉共振频率对负载质量的依赖关系.但实验发现负载的转动惯量对音叉的共振频率也有轻微的影响.从维里定理出发并考虑到负载的转动动能,得到推广的固有频率计算公式,相比简单的弹簧振子模型,该公式可以更好地描述实测数据的规律.

When calculating the natural frequency of a loaded tuning fork,the load is usually considered as an additional mass attached to the spring oscillator,and this model can better describe the dependence of the tuning fork resonant frequency on the load mass.However,it is found that the load moment of inertia also has a slight effect on the resonant frequency of the tuning fork.Starting from Virial theorem and taking into account the rotational kinetic energy of the load,a generalized formula for the calculation of the natural frequency was obtained,which could better describe the laws of the measured data than the simple spring oscillator model.