On inner resonance in highly contrasted composites Design of media with negative mass or stiffness

Invited paper

Claude Boutin


Tuesday 2 june, 2015, 11:40 - 12:00

0.7 Lisbon (47)

We analyze the dynamics of composites in view of using inner resonance effects to design media of negative effective mass or stiffness. The study is performed by multiscale asymptotic approach, considering periodic media and phenomena varying at large scale compared to the period size. In Weakly contrasted composites a transition between two regimes occurs at the scattering frequency fR : when f < fR, the dynamics occurs at macroscale, and weak local dynamic effects arise as correctors ; when, f > fR, the dynamics occurs at microscale. Thus, unconventional macrodynamic regimes involving local resonance seems impossible except considering Highly contrasted composites. In elastic composites made of a stiff matrix and soft inclusions, at the same frequency, the stiff matrix (C) carry long wavelength while short waves propagates in the soft inclusion (R). Thus, inner resonance occurs and a dynamic regime coexist at micro and macro scales ("co-dynamics" regime) : the stiff component (C) moves uniformly in the period, while R experiences a non uniform, frequency dependant motion. Hence, the effective inertia is positive or negative around the eigen-frequencies of R. Such “co-dynamics” regime is possible in porous media with inner resonators. Around resonance, the resonator brought a negative contribution to the effective gas stiffness [9]. This results in a broad band gap along with strong dispersion. The similarities of the results related to different physics, show that inner resonance requires highly contrasted microstructures. It imposes R to respond in forced regime imposed by C. Then, the effective constitutive law is determined by C, while R acts as a source term in the balance equations. This analysis provides design rules to build up composites with negative effective mass or stiffness, which are of prime interest for their unusual properties.

ICS file for iCal / Outlook

[ Close ]