Nonlinear tuning curve demonstration: Comparing a buried mine simulant with a clamped elastic plate—Cylindrical soil column oscillator

Abstract

Experiments using soil-plate-oscillators (SPO) involve a cylindrical column of granular media (masonry sand) supported by a clamped circular elastic acrylic plate (12.7 cm diameter, 3.2 mm thick). The plate is clamped between two 20.3 cm O.D., 12.7 cm I.D., 6.4 cm thick flat toroidal brass “rings.” Two 15 cm diameter subwoofers (10 cm above the soil) are driven by an amplified swept sinusoidal chirp which drives the 2.5-cm soil column. A spectrum analyzer measures the laser Doppler vibrometer particle velocity versus frequency near the center of the column. The resonant frequency decreases with the increasing amplitude—representing softening in the nonlinear system. The back-bone curve (locus of the resonant frequency versus corresponding peak velocity coordinates) has a distinct arching shape where the slope of the velocity increases with the decreasing frequency. Here, the resonant frequency goes from 247 to 203 Hz. A lumped element bilinear hysteresis model describes the shape of the tuning curves and backbone curve. Next, a drum-like simulant (made by replacing the upper toroidal ring by a 0.64-cm thick ring) is buried 2.5-cm deep in an open square concrete tank (57 cm). Nonlinear tuning curve experiments “on” and “off” the mine are compared with the SPO results. Experiments using soil-plate-oscillators (SPO) involve a cylindrical column of granular media (masonry sand) supported by a clamped circular elastic acrylic plate (12.7 cm diameter, 3.2 mm thick). The plate is clamped between two 20.3 cm O.D., 12.7 cm I.D., 6.4 cm thick flat toroidal brass “rings.” Two 15 cm diameter subwoofers (10 cm above the soil) are driven by an amplified swept sinusoidal chirp which drives the 2.5-cm soil column. A spectrum analyzer measures the laser Doppler vibrometer particle velocity versus frequency near the center of the column. The resonant frequency decreases with the increasing amplitude—representing softening in the nonlinear system. The back-bone curve (locus of the resonant frequency versus corresponding peak velocity coordinates) has a distinct arching shape where the slope of the velocity increases with the decreasing frequency. Here, the resonant frequency goes from 247 to 203 Hz. A lumped element bilinear hysteresis model describes the shape of the tuning curves and ...