Reaction Force and Power Flow Analysis of an Acoustic Metamaterial Beam with Multi-band Gaps

A model of a novel metamaterial beam with periodically attached spring-mass combinations is presented. Dispersion relation, reaction forces and power flow are calculated and aided by the finite element method, to help understand the actual band gap generation and wave attenuation mechanism. Results show that multiple large low-frequency band gaps are generated and can be overlapped to form a broad gap with reasonable damping. Reaction force analysis and energy distribution reveal the actual wave attenuation working mechanism of multiple translational absorbers on the beam: some of the resonators create negative inertia, 180 degrees out of phase with the host beam, to counterbalance the positive inertia of some resonators in phase with the host beam, plus the shear force induced by flexural waves, and the different combinations of the resonance open different band gaps. Damping effect on the transmitted power flow is complicated. Therefore, the specific effect of damping needs to be identified in practical engineering when the metamaterial beam is applied.