Title: Lattice oscillations of square patterns in a vertically vibrated granular layer
Speaker: Dan Goldman
Speaker Info: U. Texas, Austin
Brief Description:
Special Note:
Abstract:
Square spatial patterns form in a layer of vertically vibrated granular material for a range of container drive frequencies and accelerations. The time-averaged square lattice pattern is stationary, but individual peaks of the lattice, visualized by strobing at the subharmonic of the drive frequency, oscillate with frequencies lower than the strobe frequency. We examine the dynamics of this lattice for layers that are typically 1000x1000 particles with a depth of 4 particle diameters. We find that the oscillations of the peaks are coupled and can be written as a sum of lattice normal modes. The amplitude and frequency of the oscillations of the two-dimensional lattice are a function of the drive frequency and the peak container acceleration. We find a transition to a single excited normal mode at a constant value of wavelength x frequency, where the wavelength of the pattern increases monotonically with increasing acceleration. In addition, dispersion relations for the lattice are measured by resonantly pumping individual normal modes and recording the corresponding wavenumber of the excited mode. The dispersion relations follow those for a two-dimensional array of masses and springs.Date: Friday, February 25, 2000