A dynamic model of vibration system with single degree of freedom with dry friction-rigidity constraint was established

and the dynamic constraint conditions of piecewise smooth vibration system considering the coupling conditions of dry friction and collision were given.At the same time

the nonlinear stiffness factor was introduced

and the response periodic motion types and distribution regions of the system were obtained by co-simulation method.The dynamic characteristics of motion viscosity and displacement viscosity of mass blocks were discussed

and the basic periodic transition rule in the low frequency and small clearance parameter domain was quantitatively characterized.The results show that the velocity viscosity response between the mass block and the belt is mainly affected by the excitation frequency.Due to the existence of dry friction

the velocity of the first collision between the mass block and the restraint surface is more complicated.The crash-vibration response between the mass block and the rigid constraint has a strong correlation with the clearanceδand excitation frequencyω

and abundant dynamic response characteristics appear in the parameter domain of low frequency and small clearance.