Vibration transmission through the frictional mass-in-mass metamaterial: An analytical investigation

The aim of this paper is to present a unified method to simulate the dynamics of systems having friction. Linear complementary based approach is adopted along with Euler’s discretization method to compute the time domain displacement and velocity response of several systems associated with frictional contacts. The method develops an insight comprehension about the stick–slip phenomenon perceived in the frictional vibration. To validate the developed method, first, a block resting on the frictional surface is solved. Using the method, the dynamic response of a single spring mass and mass-in-mass system having internal frictional contact is analysed. Further, the mass-in-mass unit has been used in a metamaterial chain and the dynamic response is studied for the same having several unit cells. The transmittance spectrum has been developed for a frictional mass-in-mass system to study the effect of varying frictional forces on the attenuating potential of the system. Interestingly, through the transmission spectrum for the frictional mass-in-mass unit, used in a metamaterial chain, it can be observed that a wide low frequency attenuation band gap can be achieved for medium range of frictional force. This finding enables the frictional mass-in-mass unit to qualify as a good prospect for vibration reduction, due to energy dissipation resulting from medium frictional force acting between the two masses. •Linear complementary (LCP) based approach for frictional contact is presented.•Euler’s discretization method considering LCP is developed to compute time domain response.•Several simultaneous frictional contact in the metamaterial units can be solved.•Frictional metamaterial removes 2nd propagation band and shifts attenuation band.•Maximum dimensionless friction force 0.3 shifts the attenuation band to lowest frequency.