Click on images for details

Bandgap formation in IAIR and chiral lattices Local resonances provide an opportunity for generating bandgaps in periodic media. Producing wide bandgaps in the low frequency range is typically challenging. However, inertial amplification is an effective way to tune the wave attenuation range to low frequencies without adding an excessive amount of mass to the system. A preliminary investigation of this possibility has been carried out by modeling structural assemblies of interest as composed by simple point-mass and 1D-beam elements. Matlab software has been developed for structural response computation using a finite element (FEM) approach. An example is shown in Figure 1. The Frequency Response function (FRF) plotted in Figure 1(a) results from a simulation of the IAIR-based lattice in Figure 1(b), where the applied harmonic load is indicated, along with the recording point at which the FRF is computed. A wide bandgap is visible from Figure 1(a) in the low frequency range. Wave propagation along the structure is impeded in this stop-band, as further confirmed by the acceleration distribution at the frequency associated with point ‘A’ in the FRF: such distribution is shown in Figure 1(c), highlighting energy confinement around the loading point. In contrast, Figure 1(d) demonstrates how vibrational energy spreads through the whole lattice at frequencies outside the bandgap (e.g. at the frequency of point ‘B’ in the FRF). Similar bandgaps can be produced through chiral lattices, as discussed below.
Figure 1: (a) Frequency Response Function (FRF) computed for the IAIR lattice in (b) at the indicated recording point. (c)-(d) Acceleration distribution within the lattice at frequency points ‘A’ and ‘B’ in (a), respectively.
Parametric analysis and design Several parameters of IAIR and chiral unit cells can be varied to tune the position and width of generated bandgaps. An important design option is the characteristic angle θ of IAIR resonators. Figure 2 shows how smaller values of θ have the effect of shifting the bandgap to lower frequencies, although the attenuation bandwidth is shrunk.
Figure 2: FRFs computed for the lattice in Figure 1(b) in combination with two different values of the characteristic IAIR angle (associated unit cells are shown to the right of the plots).
A number of design parameters are available for the chiral configuration, including length and angle of ligaments, radius of the nodal rings, and size of mass insertions within them. Impact of mass inclusions is investigated in Figure 3 and seen to consist in enhancement of existing bandgaps as well as formation of new ones at lower frequencies. These simulations thus demonstrate viability of low-frequency vibration control through IAIR and chiral lattices, and they provide an efficient computational tool for initial design of structural assemblies with desired properties.
Figure 3: FRFs computed for chiral lattices with and without nodal mass inclusions (associated unit cells are shown to the right of the plots).
Impact of viscoelastic IAIR inclusions Integrating viscoelastic components into IAIR resonators provides an effective combination of vibration cancellation due to internal resonances and energy dissipation through viscoelastic damping. This is demonstrated in Figure 4, which illustrates the effect of inserting an IAIR lattice with viscoelastic ligaments into a backbone truss structure. The tip response of the damped structure exhibits a deep and broad attenuation region right in the frequency range where the backbone structure has its first resonance. In addition, the damped resonators are found to suppress higher-frequency resonances of the truss, thus confirming effectiveness of combining local resonances and viscoelastic damping for vibration mitigation purposes.
Figure 4: (a) Truss backbone structure before and after insertion of viscoelastic IAIR resonators. (b) Tip FRF of the backbone structure (black line) and structural assembly with visco-IAIRs (red line), under clamped-free boundary conditions.
Georgia Institute of Technology – School of Aerospace Engineering Atlanta, Georgia 30332-0150 Contact Us:
Massimo Ruzzane Emanuele Baravelli	ruzzene@gatech.edu ebaravelli@gatech.edu