Nonlinear Waves in Granular Lattices
نویسندگان
چکیده
We present a numerical study of solitary waves in one dimensional (1D) granular lattices. Our system consists of an array of deformable spheres which we model using Hertzian interactions between neighbouring bodies. A general discussion of the origin of solitary waves is presented. We then provide an analysis of the Hertz force. For the case of a uniform chain of spheres, we derive an approximate solution in the asymptotic limit to the system equations. The solution is a solitary wave and numerical simulations verify this result. A scaling analysis is used to determine a relation between wave speed and amplitude. We find vs ∝ F 1/6 peak, where vs is the wave speed and Fpeak the amplitude and this is corroborated using simulations. We then proceed from uniform chains to those containing a defect. A study of the effect of defect size and material properties (i.e. Young’s modulus E and Poisson ratio ν) on a propagating solitary wave is performed. Finally, we outline the origin of intrinsic localised modes in granular lattices. These objects cause the scattering of incoming waves which can lead to interesting resonance phenomena. We probe the interaction of both solitary and plane waves with these modes. The transmission coefficient for plane waves is measured as a function of wavenumber q in order to observe whether the system permits behaviour analogous to Fano resonance. The results obtained do not clearly correspond to the Fano resonances observed in other systems. Thus, further studies are required to explain the mechanism of a plane wave’s interaction with a localised mode.
منابع مشابه
Nonlinear Waves in Granular Crystals
The properties and stabilities of various wave types are investigated in nonlinear lattices with a ‘Hertz’ type potential. In particular the interaction of intrinsic localized modes with other waves is studied. Evidence is provided that Fano-like resonances, observed in other nonlinear systems, cannot occur in Hertzian lattices.
متن کاملHighly nonlinear solitary waves in heterogeneous periodic granular media
We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (threemass) cell structures in one-dimensional granular lattices. To vary the composition of the fundamental periodic units in the granular chains, we utilize beads of different materials (stainless steel, b...
متن کاملDissipative Solitary Waves in Periodic Granular Crystals
We provide a quantitative characterization of dissipative effects in one-dimensional granular crystals. We use the propagation of highly nonlinear solitary waves as a diagnostic tool and develop optimization schemes that allow one to compute the relevant exponents and prefactors of the dis-sipative terms in the equations of motion. We thereby propose a quantitatively-accurate extension of the H...
متن کاملPhotonic crystals for matter waves: Bose-Einstein condensates in optical lattices.
We overview our recent theoretical studies on nonlinear atom optics of the Bose-Einstein condensates (BECs) loaded into optical lattices. In particular, we describe the band-gap spectrum and nonlinear localization of BECs in one- and two-dimensional optical lattices. We discuss the structure and stability properties of spatially localized states (matter-wave solitons) in 1D lattices, as well as...
متن کاملFrequency- and Amplitude-Dependent Transmission of Stress Waves in Curved One-Dimensional Granular Crystals Composed of Diatomic Particles
We study the stress wave propagation in curved chains of particles (granular crystals) confined by bent elastic guides. We report the frequencyand amplitude-dependent filtering of transmitted waves in relation to various impact conditions and geometrical configurations. The granular crystals studied consist of alternating cylindrical and spherical particles pre-compressed with variable static l...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009