Wave Propagation in a Strongly Nonlinear Locally Resonant Granular Crystal

In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment

Energy equipartition in two-dimensional granular systems with spherical intruders

We study the effects of a line of spherical interstitial particles (or intruders) placed between two adjacent uncompressed chains of larger particles in a square packing of spheres, using experiments and numerical simulations. We excite one of the chains of particles adjacent to the intruders with an impact and show how energy is transmitted across the system until equipartition is reached from the excited (or impacted) chain to the absorbing (or adjacent) chain. The coupling of the two chains, although a purely two-dimensional effect, is modeled by a simplified one-and-a-half-dimensional system in which transverse motions of the particles are neglected

Sequential phosphorylation of SLP-76 at tyrosine 173 is required for activation of T and mast cells.

Cooperatively assembled signalling complexes, nucleated by adaptor proteins, integrate information from surface receptors to determine cellular outcomes. In T and mast cells, antigen receptor signalling is nucleated by three adaptors: SLP-76, Gads and LAT. Three well-characterized SLP-76 tyrosine phosphorylation sites recruit key components, including a Tec-family tyrosine kinase, Itk. We identified a fourth, evolutionarily conserved SLP-76 phosphorylation site, Y173, which was phosphorylated upon T-cell receptor stimulation in primary murine and Jurkat T cells. Y173 was required for antigen receptor-induced phosphorylation of phospholipase C-γ1 (PLC-γ1) in both T and mast cells, and for consequent downstream events, including activation of the IL-2 promoter in T cells, and degranulation and IL-6 production in mast cells. In intact cells, Y173 phosphorylation depended on three, ZAP-70-targeted tyrosines at the N-terminus of SLP-76 that recruit and activate Itk, a kinase that selectively phosphorylated Y173 in vitro. These data suggest a sequential mechanism whereby ZAP-70-dependent priming of SLP-76 at three N-terminal sites triggers reciprocal regulatory interactions between Itk and SLP-76, which are ultimately required to couple active Itk to its substrate, PLC-γ1

Dynamic analysis of externally excited NES-controlled systems via a mixed Multiple Scale/Harmonic Balance algorithm

"A general, nonlinear, multi-d.o.f. structure,. excited by harmonic external force in 1:1 resonance. with one of the modes of the system, is considered.. The structure is attached to an essentially nonlinear. oscillator, with small mass and damping (Nonlinear. Energy Sink, NES). The scope of the NES is to passively. control the amplitude of vibrations of the main. structure. A mixed Multiple Scale\/Harmonic Balance. Method (MSHBM) is proposed to get the differential. equations describing the slow- and fast-flow dynamics. of the whole structure. The main advantage of the. procedure is that no complexification-averaging is required,. so that the analysis is reconducted in the framework. of the classical perturbation techniques.

Performance comparison between a nonlinear energy sink and a linear tuned vibration absorber for broadband control

The performance of a linear tuned vibration absorber (LTVA) and a nonlinear energy sink (NES) for the vibration mitigation of an uncertain linear primary system is investigated. An analytic tuning rule for the LTVA when the primary system contains uncertainty is derived. The behavior of the linear system coupled to the NES is analyzed theoretically. A tuning methodology for the NES in the deterministic as well as for the uncertain case is presented. © The Society for Experimental Mechanics, Inc. 2016