|
Here we present methods for modeling, analysis, and design of metamaterial beams for broadband vibration
absorption/isolation. The proposed metamaterial beam consists of a uniform isotropic beam with many small spring-mass-
damper subsystems integrated at separated locations along the beam to act as vibration absorbers. For a unit cell of
an infinite metamaterial beam, governing equations are derived using the extended Hamilton principle. The existence of
stopband 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. However, these two idealized models
cannot be used for finite beams and/or elastic waves having short wavelengths. For finite metamaterial beams, a linear
finite element method is used for detailed modeling and analysis. Both translational and rotational absorbers are
considered. Because results show that rotational absorbers are not efficient, only translational absorbers are
recommended for practical designs. The concepts of negative effective mass and stiffness and how the spring-mass-damper
subsystems create a stopband 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.
It uses the incoming elastic wave in the beam to resonate the integrated spring-mass-damper absorbers to vibrate in their
optical mode at frequencies close to but above their local resonance frequencies to create shear forces and bending
moments to straighten the beam and stop the wave propagation. This concept can be easily extended to design a
broadband absorber that works for elastic waves of short and long wavelengths. Numerical examples validate the
concept and show that, for high-frequency waves, the structure’s boundary conditions do not have significant influence
on the absorbers’ function. However, for absorption of low-frequency waves, the boundary conditions and resonant
modes of the structure need to be considered in the design. With appropriate design calculations, finite discrete spring-mass-
damper absorbers can be used, and hence expensive micro- or nano-manufacturing techniques are not needed for
design and manufacturing of such metamaterial beams for broadband vibration absorption/isolation.
|
