A 2D metamaterial cellular system inspired by lightweight honeycombs and spider webs is investigated. The hexagonal cells of the honeycomb act as hosting substructures for spider-web-like or cantilever resonators with added lumped masses which can vibrate, in principle, in any of the infinitely many modes. Contrary to traditional approaches utilizing discrete mass-spring resonators, here the infinite-dimensional (full spectrum) resonators are intentionally tailored to generate multiple, complete or incomplete, stop bands across which wave propagation is either totally or partially suppressed along preferential directions. The Plane Wave Expansion method is employed to obtain the dispersion curves and the bandgap sensitivity with respect to the design parameters. Experimental results based on laser scanning vibrometry corroborate the theoretical predictions and confirm the robustness of the stop band behavior with a wealth of results which pave the way towards suitable optimization strategies and a closer understanding of these formidable stop band cellular material systems.

The unusual features of the nonlinear dynamic response of nanocomposite beams made of polybutylene terephthalate (PBT) and branched carbon nanotubes (bCNTs) are documented experimentally. The frequency response curves for cantilever specimens with different bCNTs weight fractions (wt%) are obtained under harmonic base excitations by measuring the free tip displacement via 3D scanning laser vibrometry. The steady-state response acquired for different excitation levels exhibits a surprising nonlinear softening trend which is switched into hardening for higher bCNTs wt% and increasing oscillation amplitudes. The stick-slip hysteresis, caused by the interaction of the bCNTs with the thermoplastic hosting matrix, determines a softening nonlinearity of the material that counteracts the well-known geometric hardening associated with the nonlinear curvature of the first mode of the cantilever. However, for bCNTs weight fractions greater than 1%, the bridging of the branched CNTs gives rise to the formation of a strong network which contributes to the hardening response at higher oscillation amplitudes. This mechanical behavior is detected by the trend of the nonlinear harmonic spectra and by the estimation of the equivalent damping ratio using the half power bandwidth method. A nonlinear mathematical model of the nanocomposite cantilever samples derived from a 3D mesoscale hysteretic model of the PBT/bCNT material is shown to predict the observed unusual experimental behavior. The presence of bCNTs in a thermoplastic matrix seems to be the main driver of the highly tunable nonlinear stiffness and damping capacity.

In this experimental study, we investigate the nonlinear dynamic response of nanocomposite beams composed of polybutylene terephthalate (PBT) and branched carbon nanotubes (bCNTs). By varying the weight fraction of bCNTs, we obtain frequency response curves for cantilever specimens under harmonic base excitations, measuring the tip displacement via 3D scanning laser vibrometry. Our findings reveal a surprising nonlinear softening trend in the steady-state response of the cantilevers, which gets switched into hardening for higher bCNT weight fractions and increasing oscillation amplitudes. The interaction of bCNTs with the thermoplastic hosting matrix results in stick-slip hysteresis, causing a softening nonlinearity that counteracts the geometric hardening associated with the nonlinear curvature of the first mode of the cantilever. However, when the weight fraction of bCNTs is greater than 1%, the bridging of the branched CNTs leads to the formation of a strong network that contributes to the hardening response at higher oscillation amplitudes. This mechanical behavior is detected by the trend of the nonlinear harmonic spectra and the equivalent damping ratio estimated using the half-power bandwidth method. To predict the observed unusual experimental behavior, we use a nonlinear mathematical model of the nanocomposite cantilever samples derived from a 3D mesoscale hysteretic model of the PBT/bCNT material. Our results suggest that the presence of bCNTs in a thermoplastic matrix is the main driver of the highly tunable nonlinear stiffness and damping capacity of the material. The reported experimental and modeling results provide valuable insights into the nonlinear dynamic behavior of PBT/bCNT nanocomposites and have potential applications in the design of advanced materials with tailored mechanical properties.