Soil Plate Oscillator Research Articles

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

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.

Demonstration of acoustic landmine detection using a clamped soil plate oscillator with airborne sound excitation

Landmine detection in gravel road beds, soil, or sand for some mines (constructed out of plastic) are difficult to detect using ground penetrating radar. In acoustic landmine detection, one would like to remotely detect a vibration profile across the surface of the soil (sand or gravel) due to the interaction between a large soil column and the localized elastic top plate. In an idealized laboratory experiment, the soil plate oscillator (SPO) apparatus models an idealization of an acoustic landmine detection experiment. The clamped circular acrylic plate (1/8 in. thick) models the top plate of a plastic buried mine while the soil column (350 g dry sifted masonry sand) supported by the plate models the burial depth. A constant current amplified sinusoidal chirp from a sweep spectrum analyzer drives two three inch diam speakers (placed above the column) generating airborne excitation. A laser Doppler vibrometer (LDV) measured the rms particle velocity at 15 scan locations across the 4.5 inch diameter soil surface in sweeps between 50 Hz and 1250 Hz. The LDV-microphone frequency response vs. scan position is used to extract a response profile at any individual frequency. These mixed mode shapes are compared for both in-phase and out-of-phase excitation.

Classroom demonstration of nonlinear tuning curve vibration and two-tone tests using a column of glass beads vibrating over a clamped elastic plate

A soil plate oscillator (SPO) apparatus consists of two circular flanges sandwiching and clamping a thin circular elastic plate. The apparatus can model the acoustic landmine detection problem. Here, 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. A magnetic disk centered and fastened below the plate is driven by an AC coil placed below the magnet. Nonlinear tuning curves of the magnet’s acceleration are measured by driving the coil with a swept sinusoidal signal applied to a constant current amplifier. Ten (separate) tuning curve experiments are performed using a fixed column of 350 grams of beads using 1,2,3,…,10 mm diameter beads. The backbone curves (peak acceleration vs. corresponding resonant frequency) exhibit a linear region with comparable slopes, while the detailed curvature vs. bead diameter reveals more structure. A bilinear hysteresis model is useful for characterizing results. In two-tone tests, air-borne sound from two 3 inch diameter speakers drives the bead column surface at closely spaced frequencies near the fundamental resonance. Nonlinearly generated combination frequency tones are compared for each of the ten bead diameter experiments.A soil plate oscillator (SPO) apparatus consists of two circular flanges sandwiching and clamping a thin circular elastic plate. The apparatus can model the acoustic landmine detection problem. Here, 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. A magnetic disk centered and fastened below the plate is driven by an AC coil placed below the magnet. Nonlinear tuning curves of the magnet’s acceleration are measured by driving the coil with a swept sinusoidal signal applied to a constant current amplifier. Ten (separate) tuning curve experiments are performed using a fixed column of 350 grams of beads using 1,2,3,…,10 mm diameter beads. The backbone curves (peak acceleration vs. corresponding resonant frequency) exhibit a linear region with comparable slopes, while the detailed curvature vs. bead diameter reveals more structure. A bilinear hy...

Classroom demonstration of acoustic landmine detection using a clamped soil plate oscillator

In landmine detection some mines (constructed out of plastic) are difficult to detect using ground penetrating radar. In acoustic landmine detection, one can detect a vibration profile across the surface of the soil (sand) due to the interaction between the soil column and the elastic top plate. Table top classroom demonstrations can bring to life idealized field experiments. The soil plate oscillator (SPO) apparatus models an idealization of an acoustic landmine detection experiment. The clamped circular elastic plate models the top plate of a plastic buried mine while the soil column supported by the elastic plate models the burial depth. An amplified sinusoidal chirp from a sweep spectrum analyzer drives an AC coil placed below a small magnet attached to the underside of the clamped plate—causing vibration. A laser Doppler vibrometer measured the rms particle velocity at 13 scan locations across the 4.5 inch diameter soil surface in sweeps between 50 Hz and 850 Hz. Results show a fundamental mode shape...

The soil plate oscillator: Nonlinear mesoscopic elasticity of layers of glass beads in flexural vibration

The soil plate oscillator (SPO) apparatus consists of two circular flanges sandwiching and clamping a thin circular elastic plate. In this presentation, uniform spherical glass beads—representing a nonlinear mesoscopic elastic material—are supported at the bottom by the plate and stiff cylindrical sidewalls of the upper flange. A small magnetic disk centered and fastened below the plate is driven by an AC coil placed below the magnet. Nonlinear tuning curves of the magnet’s acceleration are measured by driving the coil with a swept sinusoidal signal applied to a constant current amplifier. Experiments are first performed to measure the peak resonant frequency vs. mass loading as glass beads are added to make a level column above the plate. Experiments are repeated using 1,2,3,…,10 mm diameter beads to demonstrate how the frequency first decreases and then eventually increases for each bead diameter. Next, ten (separate) tuning curve experiments are performed using a fixed column of 350 grams of beads for ...

The importance of tuning curves and two-tone tests in nonlinear acoustic landmine detection

During the 1990s through ∼2010, Jim Sabatier’s group (Univ. Mississippi and NCPA) had made significant progress in understanding airborne acoustic landmine detection. In particular, using their development of scanning laser Doppler vibrometry, plastic anti-tank landmines could be detected in soil along roadbeds. Research on the nonlinear acoustic detection of buried landmines by Dimitry Donskoy (Stevens Tech) lead to lumped element models of the target which included a nonlinear spring-like mechanism. Tom Muir studied seismic excitations. Sabatier and Korman suggested that the soil nonlinearity and the soil interaction with the flexural vibration of the top-plate of the landmine or drum-like simulant were both significant factors in nonlinear landmine detection. Nonlinear tuning curves of the soil vibration response vs. frequency (directly over the target) along with rich combination frequency generation in two-tone tests suggested that the vibration was similar to Paul Johnson’s group results on mesoscopic nonlinear elasticity found in geomaterials. Recent airborne acoustic nonlinear landmine detection experiments compare drum-like simulant tuning curves to results using a soil plate oscillator apparatus (two circular flanges sandwiching and clamping a thin circular elastic plate that supports a cylindrical level column of sand above the plate) to help model flexural mesoscopic nonlinear hysteretic behavior.

Modeling nonlinear acoustic landmine detection using a soil plate oscillator apparatus

In modeling nonlinear acoustic landmine detection, there will be a cylindrical drum-like buried target. This target, which has a clamped thin elastic plate, rigid sidewalls, and bottom plate, is buried in an open concrete “soil tank” containing dry sifted masonry sand. Subwoofers located 40 cm above the surface are driven with a swept tone from 50 to 450 Hz to generate airborne sound that couples into the sand exciting vibration in the buried target. A small geophone is used to measure the “ground” vibration profile across the buried target. Nonlinear tuning curves of vibration particle velocity vs. frequency are used to compare “over—off the target” results. The backbone curves (peak velocity vs. corresponding resonant frequency) are different in these cases—such that resonances due to soil alone or soil over a compliant buried target can be distinguished. Next, a soil plate oscillator SPO (consisting of two circular flanges sandwiching and clamping a thin circular elastic plate that supports a cylindrical level column of sand above the plate) is driven by airborne sound. Nonlinear tuning curve vibration at points across the sand are compared with the results in the “idealized” landmine detection experiment to develop a lumped element model of the system.

Demonstration of nonlinear tuning curve vibration of granular medium supported by a clamped circular elastic plate using a soil plate oscillator

A demonstration will be conducted in order to show how a soil plate oscillator (SPO) filled with granular material will create a nonlinear system due to shifting peaks in a tuning curve with incremental increases in the swept drive amplitude. An SPO has two flanges clamping an elastic plate which supports a circular column of granular material. The plate (with a magnet and accelerometer fastened to the underside) is driven below by an amplified swept sinusoidal current applied to an AC coil. Past results have used masonry sand, granular edible uncooked materials, and glass beads in order to study the nonlinear tuning curve response near a resonance with (1) a fixed soil column while changing drive amplitude and (2) mass loading of a soil column versus the resonant frequency response of the system at a fixed drive amplitude. When the experiments are performed at a fixed drive but with a changing mass layer the resonant frequency increases then decreases with increased added mass due to an increase in flexural rigidity of the granular media disk layer which dominates the effect of adding mass. SPO tuning curves resemble the nonlinear mesoscopic elastic behavior of resonant effects of geomaterials such as sandstone.

Nonlinear behavior of different sized granular bead media on a vibrating clamped circular elastic plate

This experiment uses a soil plate oscillator (SPO), or a circular acrylic (elastic) plate clamped into place using flanges, to study the nonlinear oscillatory behavior of a column of granular media (with selected diameters) that is supported by the plate. Secured on the underside of the plate's center is a rare earth magnet that is driven by an AC coil which is controlled by an amplified swept sinusoidal chirp. An accelerometer is fastened to the magnet and a spectrum analyzer measures the plate's acceleration versus frequency. In separate measurements of nonlinear tuning curve response, the plate is loaded with 350 grams of spherical soda lime beads of diameters 2, 3, 4, 5, 6, 7, and 10 mm. The driver current is changed in 40 evenly spaced increments, holding other parameters fixed, during each sweep. A study of the backbone curve (rms acceleration a(f) peak versus frequency f) for each bead diameter exhibits a frequency “softening” vs. amplitude—similar to the nonlinear mesoscopic elasticity observed in resonance experiments in geo-materials. After some initial curvature, the plot has a negative linear slope with increasing amplitude. Smaller beads show significantly more acceleration response than larger beads while the slopes have somewhat comparable values.

The soil plate oscillator: Measuring nonlinear mesoscopic elasticity of granular medium in flexural vibration

The soil plate oscillator apparatus (SPO) consists of two circular flanges (5 inch ID, 8 inch OD, 2.5 inch thick) sandwiching and clamping a thin (1/8 inch) circular elastic acrylic plate. Granular media (soil, masonry sand, glass beads, or even edible granular material) is supported at the bottom by the plate and side walls of the upper flange. A magnetic disk (1 cm) fastened below the plate (on center) is driven by a swept sinusoidal current in a coil placed below the magnet. This electrodynamic SPO, placed in a Wheatstone bridge, was used to measure the on-axis motional electrical impedance Zmot with and without granular loading. Nonlinear tuning curves near resonance exhibit softening with increasing drive amplitude. Measurements of Real{Zmot} and Imag{Zmot} were used to predict the nonlinear mechanical point impedance (Zmech = constant / Zmot) behavior of the SPO system. A lumped element model (granular media and elastic plate system) help determine the mesoscopic nonlinear properties of the granular media alone. Nonlinear tuning curves of the magnet’s acceleration were also measured. A bilinear hysteresis model fits the tuning curve results. See I. T. Perez-Miravete et al., JASA 125, 1302 (2009) for a nonlinear mesoscopic analysis of a flexural bar.

Modeling acoustic landmine detection using a soil-plate oscillator

In laboratory acoustic landmine detection experiments a plastic cylindrical drum-like simulant is buried in a soil (or sand) tank. Airborne sound, generated from two subwoofer loudspeakers (located above the soil), drive the soil particles and subsequent particle vibration over the compliant top plate of the simulant. Measurements of tuning curve soil surface vibration particle velocity versus frequency are recorded for various scan locations across the soil surface in an effort to profile the buried simulant. Measurements of resonances “off the target” are also included in this study. The results can be modeled using a soil-plate-oscillator (SPO) apparatus. The SPO involves a vertical thick-wall cylindrical column of granular medium (sand, soil, pebbles, light density edible granular material like wheat germ or even uncooked brown rice) that is supported by a thin circular elastic (acrylic) plate (8 in. diameter, 1/8 in. thick) that is rigidly clamped at the bottom of the column. A small accelerometer placed on the granular surface (or a laser Doppler vibrometer) measures tuning curve results across the surface using a sweep spectrum analyzer. Profiles are compared for both the SPO and the simulant in an effort to model the results in the later—more complicated case.

Vibration experiments using a clamped circular elastic plate with edible granular material loading

An apparatus called the soil-plate-oscillator (SPO), designed to study flexural vibration of a soil loaded plate, consists of a thin circular elastic (acrylic) plate (8 in. diam, 1/8 in. thick) clamped below a thick-wall cylindrical aluminum tube supporting a vertical soil (or sand) column or other granular material. A small accelerometer attached to a 1 cm diam rare earth magnet (which is fastened to the center of the plate from below) is used to detect the plate vibration response. The plate is driven from below by an AC coil (located coaxially below the plate and securely fastened) using an amplified swept sinusoidal current. The charge amplified accelerometer signal is measured versus frequency by a spectrum analyzer. With interest in studying light density granular media (with various grain sizes) experiments were performed with uncooked brown rice, quick oats, un-popped popcorn kernels pretzel gold fish crackers, and pretzel nuggets. The resonant frequency reaches a minimum and then increases with i...

Nonlinear vibration experiment: Clamped circular elastic plate with granular material loading

Experiments using a soil-plate-oscillator (SPO) involve a vertical cylindrical column of granular medium (masonry sand, glass spheres, uncooked brown rice, un-popped popcorn kernels, or even “Toasty Oats” ™ cereal) that is supported by an air-backed thin circular elastic acrylic plate (20.3 cm diameter and 3.2 mm thick) that is rigidly clamped to the bottom of a thick-walled aluminum tube. The soil column is driven from below using an electrodynamic system. Here, an AC coil placed on axis and below the plate, drives a 1 cm diameter 1.5 cm long rare earth magnet that is fastened to the underside center of the plate. The coil is electrically driven by an amplified swept sinusoidal slowly varying chirp. A small accelerometer attached to the magnet is used to measure the vibration. In nonlinear tuning curve experiments the resonant frequency decreases significantly with increased amplitude—representing a softening in the nonlinear system. For fixed amplitude the resonant frequency vs. the granular medium mass loading (over the plate) reaches a minimum and then increases with increased loading due to the granular medium’s flexural stiffness—which overcomes the mass loading effects. For water loading, the frequency always decreases since there is no bending stiffness.

Soil-plate oscillator: A model for nonlinear acoustic landmine detection

A soil-plate oscillator (SPO) apparatus involves a cylindrical column of granular medium (sand, soil, and pebbles) supported by a thin circular elastic plate (acrylic) that is rigidly clamped to the bottom of a thick walled aluminum tube. The plate is air-backed. The soil column is driven from above by two subwoofers electrically connected to an amplified swept sinusoidal slowly varying chirp. In nonlinear tuning curve experiments, the resonant frequency decreases with increased amplitude—representing a softening in the nonlinear system. Hysteresis effects can be observed along with slow dynamic behavior (associated with mesoscopic nano-scale nonlinear elasticity). In two tone tests, numerous combination frequencies are observed in the surface vibration of the soil along with the sum frequency (typically 200 Hz) and second and higher harmonics. Soil surface vibrations and plate vibrations show similar effects when the soil layer is even 30 times the plate thickness. SPO results compare well when an inert VS 1.6 anti-tank mine is buried in a large concrete soil box. Nonlinear hysteresis models of the soil alone and for the soil-plate interaction are useful in understanding these results, since off-the mine vs. on-the mine tuning curves shapes behave significantly different, indicating some false alarms can be eliminated.

Soil plate oscillator: Modeling nonlinear mesoscopic elastic behavior and hysteresis in acoustic landmine detection, Part II

An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The mechanical impedance Zmech (force/particle velocity, at the plate's center) versus frequency is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Resonant oscillation measurements (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. “Tuning curve” behavior of real Zmot and imaginary Zmot at successively higher vibration amplitudes exhibit a decrease “softening” in the resonance and an increase in the quality Q factor. A bilinear hysteresis model [T. K. Caughey, ASME, J. Applied Mech. Trans. 640 (1960)] predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior.

Soil plate oscillator: Modeling nonlinear mesoscopic elastic behavior and hysteresis in acoustic landmine detection.

An experimental apparatus, designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic plate clamped at the boundary between thick round flanges. The soil column is supported by the plate and upper cylindrical wall. A small magnet attached to the center of the plate is driven by a rigid ac coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator (SPO) design. Measurements of the electrical motional impedance Zmot of the SPO versus frequency are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. The mechanical impedance Zmech (force/particle velocity, at the plate’s center) is inversely proportional to Zmot. Experiments, with and without mass loading at the plate’s center, verify Snowden’s theory for a clamped plate [J. Acoust. Soc. Am. (1971)] and help establish mechanical parameters. Resonant oscillations (for various point mass loadings) provided effective mass, spring, damping and coupling constant parameters of the system. “Tuning curve” behaviors of real {Zmot} and imaginary {Zmot} at successive vibration amplitudes (for various soil column heights) are used to develop a general mesoscopic nonlinear elastic model for granular media.

Nonlinear acoustic landmine detection: Comparison of soil nonlinearity with soil-interface nonlinearity

To model the soil-top plate interface in nonlinear acoustic landmine detection, the soil-plate oscillator was developed [J. Acoust. Soc. Am. 116, 3354–3369 (2004)]. A Lexan plate (2.39 mm thick, 18.5 cm diameter) is clamped at an inside diameter of 11.8 cm between two metal flanges. Dry sifted masonry sand (2-cm layer) is placed over the plate. Turning curves experiments are performed by driving a loudspeaker (located over the sand) by a swept sinusoid. The acceleration versus frequency is measured near resonance on a swept spectrum analyzer using an accelerometer centered on the surface. The corresponding backbone curve exhibits a linear decrease in resonant frequency f versus increasing acceleration, where a=−ao(f−fo)/fo. Define a nonlinear parameter α=1/ao. When the elastic plate is replaced by a ‘‘rigid’’ plate, α decreased from 0.128 to 0.070 (s2/m), while fo increased from 191 to 466 Hz. When a cylindrical drumlike mine simulant (rigid walls, thin acrylic top-plate) was buried 2 cm deep in a concrete sand box, ‘‘on the mine’’ results yielded α=0.30 (s2/m) with fo=147 Hz, while ‘‘off the mine,’’ α∼0.03 (s2/m) at fo=147 Hz. [Work supported by ONR.]