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17 April 2013 Actual working mechanisms of smart metamaterial structures
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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.
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P. Frank Pai and Mannur J. Sundaresan "Actual working mechanisms of smart metamaterial structures", Proc. SPIE 8695, Health Monitoring of Structural and Biological Systems 2013, 86952M (17 April 2013);

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