Nonlinear tuning curve vibration using a column of dry or wetted granular material vibrating over a clamped elastic plate

摘要

A soil plate oscillator (SPO) apparatus consists of two circular metal flanges sandwiching and clamping a thin circular elastic plate. The apparatus can model the acoustic landmine detection problem, in particular the vibration interaction between a column of granular media and the elastic plate supporting the column. Uniform spherical soda-lime glass beads - representing a nonlinear mesoscopic elastic material - are supported at the bottom by the acrylic plate (4.5 inch diam, 1/8 inch thick) and cylindrical sidewalls (1/4 inch thick) of the upper flange. A 6 inch diam loud speaker placed 2 inches above the bead column is driven with a swept sinusoidal signal applied to a constant current amplifier to generate air-borne sound excitation from 50 - 1250 Hz. A small accelerometer fastened to the underside of the plate at the center measures the response using a spectrum analyzer. Nonlinear tuning curves of the plate vibration are measured using 350 g of dry beads for separate experiments with 2, 4, 6, and 8 mm diam beads. Experiments are repeated with beads wetted by mineral oil. Results show less frequency "softening" in the backbone curves (peak acceleration vs. corresponding resonant frequency) for wetted beads compared with dry beads. Nonlinear tuning curves are compared using (a) 6 mm diam beads, then (b) dry sifted masonry sand.