Nonlinear tuning curve vibration using a column of non-wetted or wetted glass beads vibrating over a clamped elastic plate: Case for air-borne sound excitation

Abstract

A soil plate oscillator (SPO) apparatus consists of two circular flanges sandwiching and clamping a thin circular elastic plate. The apparatus can model certain aspects of the nonlinear acoustic landmine detection problem which involves the interaction of granular material with an elastic plate in flexural vibration. Uniform spherical 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 stiff cylindrical sidewalls of the upper flange. Two 3 in. diam loud speakers placed above the bead column are driven with a swept sinusoidal signal applied to a constant current amplifier to generate air-borne sound excitation from 50 to 1250 Hz. A small accelerometer fastened to the underside of the plate at the center measures the response. Separate tuning curve experiments are performed using a fixed column of 350 grams using 2,3,…,10 mm diameter soda-lime glass beads—wetted or non-wetted (mineral-oil). With dry beads, backbone curves (peak acceleration vs. corresponding resonant frequency) exhibit a linear region with comparable slopes, while detailed back-bone curvature vs. bead diameter reveals more structure. Wet beads exhibit less non-linear tuning curve behavior.