Model of two-degree-of-freedom system and natural frequency for car seat vibrator

Models of a two-degree-of-freedom spring mass system for the car seat vibrator are created for two states of typical application scenarios, including free vibration and non-free vibration. By solving the vibration equation of the two-degree-of-freedom system, the theoretical formula for the natural frequency of the vibrator can be derived. Finite element models are established for both free and non-free vibration states of the vibrator, and experimental systems are designed to suspend the vibrator in air or place it on foam. The accuracy of the theoretical formula is verified. The results also indicate that in non-free vibration state, the second-order natural frequency of the vibrator is always greater than the natural frequency when it is free or its shell is fixed; however, this difference becomes less obvious if there is a larger external mass. Additionally, increasing the external mass will reduce the natural frequency.