ON THE CONTROL OF IMPACT RINGING NOISE （I）——THE IMPACT VIBRATION OF A GENERALIZED DISTRIBUTED SYSTEM

Ringing noise is radiated by the vibrational parts when they impact with each other. In the first part of this paper, the vibration equation of the generalized distributed system is solved. Using the expression of vibration, the total vibration energy of the system impacted is obtained. The energy of every normal mode of vibration is proportional to the square of the spectra! component of the impact force at the frequency, and to the square of the value of the normal function of this mode at the impact point. The total vibration energy E is the sum of,energy of all the normal modes.
E = \frac2\pi ^2M\sum\limits_n \varphi _n²(x₀)|F(ω _n)|²
According to the physical model of the statistical energy analysis, the work done by the impact force is calculated. The result indicates that the total vibration energy induced by impact is related to the average conductance 〈G〉at the impact point.
E = 4π\sum\limits_i〈G〉|F(ω_t)|²Δω_t