Dynamic simulation model of gear transmission shaft considering forced vibration

In the study of multi degree of freedom system, the influence of viscous damping should be considered. The differential equation corresponding to the forced vibration of the system is expressed in the following form

M, C and K of the formula belong to diagonal matrix

The formula is the corresponding motion equation in n degrees of freedom, which is calculated according to the vibration theory.

Hi (τ) is the unit impulse response function. The expression is as follows:

The formula is the response result of the multi degree of freedom system under the excitation force, and each mode will have different degrees of effect on the excitation force.