For an impact system of an Euler beam with interior inlaid freely moving steel ball

under a complicated operating condition

the impact damping characteristic of the steel ball was investigated for residual damped vibrations of the Euler beam acted by inertia forces.A linear spring-damping model was employed to simulate the impact between the steel ball and interior beam walls.Then the linear piecewise dynamic equations for the impact system were established

and the dimensionless state-space equations with finite degrees of freedoms were derived by introducing dimensionless variables

and assuming modes and truncating high order modes.Numerical calculations sufficiently indicate that

under this operating condition

the steel ball has a significant impact damping effect on suppressing the beam residual damped vibrations in amplitudes

and moreover

the impact damping exhibits a strong stage character.The impact damping of the ball is enhanced with increase of its mass.