Vibration transmission through an impacting mass-in-mass unit, an analytical investigation

Impacting events are discontinuous and non-smooth in nature; thus, resulting in various forms of complex nonlinear dynamics. A numerical algorithm has been developed based on the analytical solution to distinguish different classes of impacting responses. The main advantages of the solver are that it can either stop the integration process after automatically identifying the steady state solution or continue until the maximum time is reached in case of the chaotic type response. To identify the frequency of higher periodic response, a periodicity coefficient has been defined as the frequency ratio of excitation and the system's response. The effect of coefficient of restitution on the different dynamic responses is also discussed within the scope of the paper. The amplitude of the vibration of the main mass is reduced due to the presence of the multi-periodic and chaotic impacting responses for a wide range of excitation frequencies. These characteristics make impact dampers ideal for applications in wideband vibration insulation and a unit of wideband nonlinear metamaterial.