Acoustic metamaterial structures based on multi-frequency vibration absorbers

This paper presents a new metamaterial beam based on multi-frequency vibration absorbers for broadband vibration absorption. The proposed metamaterial beam consists of a uniform isotropic beam and small two-mass spring-mass-damper subsystems at many locations along the beam to act as multi-frequency vibration absorbers. For an infinite metamaterial beam, governing equations of a unit cell are derived using the extended Hamilton principle. The existence of two stopbands is demonstrated using a model based on averaging material properties over a cell length and a model based on finite element modeling and the Bloch-Floquet theory for periodic structures. For a finite metamaterial beam, because these two idealized models cannot be used for finite beams and/or elastic waves having short wavelengths, a finite-element method is used for detailed modeling and analysis. The concepts of negative effective mass and effective stiffness and how the spring-mass-damper subsystem creates two stopbands are explained in detail. Numerical simulations reveal that the actual working mechanism of the proposed metamaterial beam is based on the concept of conventional mechanical vibration absorbers. For an incoming wave with a frequency in one of the two stopbands, the absorbers are excited to vibrate in their optical modes to create shear forces to straighten the beam and stop the wave propagation. For an incoming wave with a frequency outside of but between the two stopbands, it can be efficiently damped out by the damper with the second mass of each absorber. Hence, the two stopbands are connected into a wide stopband. Numerical examples validate the concept and show that the structure's boundary conditions do not have significant influence on the absorption of high-frequency waves. However, for absorption of low-frequency waves, the structure's boundary conditions and resonance frequencies and the location and spatial distribution of absorbers need to be considered in design, and it is better to use heavier masses for absorbers.