Theoretical Relationship Between Combustion Pressure and Engine Vibration

A theoretical equation relating a simplified mathematical pressure-time model to vibration of a spring-mass system is presented as an aid to understanding the relationship between engine noise and combustion. The equation shows that the intensity of low frequency vibrations is proportional to the pressure rise due to combustion. At slightly higher frequencies the intensity is proportional to the maximum slope of the pressure-time curve. At the highest frequencies (characteristic of rumble), the intensity is proportional to the maximum rate of change of the slope.