On inner resonance in highly contrasted composites Design of media with negative mass or stiffness
Invited paper
ENTPE - LGCB/LTDS CNRS UMR 5513
Tuesday 2 june, 2015, 11:40 - 12:00
0.7 Lisbon (47)
Abstract:
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.