Oscillations Of Plate Research Articles

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.

Analysis of Heat Transfer of a Flat Plate Oscillating Heat Pipe, for Different Surfaces

Analysis of Heat Transfer of a Flat Plate Oscillating Heat Pipe, for Different Surfaces

Nonlinear oscillations of shape-morphing submerged structures: Control of hydrodynamic forces and power dissipation via active flexibility

Abstract In this paper, we consider nonlinear oscillations of a shape-morphing plate submerged in a quiescent, Newtonian, viscous fluid. We investigate the two-dimensional problem arising from two prescribed concurrent periodic motions of the plate: a rigid oscillation along its transverse direction coupled to a shape-morphing deformation to an arc of a circle with prescribed maximum curvature. As opposed to existing literature concerned with passive flexible structures, this study focuses on actively prescribed deformations of the structure as a means to manipulate the vortex-shedding and convection patterns responsible for hydrodynamic forces and power dissipation during underwater oscillations. We elucidate the potential of the proposed shape-morphing strategy in regulating the added mass and damping effects along with the hydrodynamic power dissipation both in the linear and nonlinear hydrodynamic regime, by utilizing a linear boundary integral formulation as well as computational fluid dynamics simulations. Results show the possibility of minimizing the hydrodynamic power dissipation for optimal values of the imposed curvature, along with significant reduction of the hydrodynamic forces. A simplified semianalytical argument relates these novel effects to specific geometric properties of the plate motion. Findings from this study are directly relevant to cantilever-based sensing and actuation systems operating in fluids, where control and modulation of oscillation quality factors, hydrodynamic forces, and power losses is beneficial.

Coupled effects of phase transitions and rheology in 2‐D dynamical models of subduction

AbstractObservations of seismicity and seismic tomography provide a present‐day constraint on the geometry of slabs within the mantle. However, it is challenging to directly relate the observed shape of slabs to their time evolution. Phase transitions modify the buoyancy forces within slabs, affecting how slabs deform as they sink into the lower mantle and how forces are transmitted to the surface plates. Here we show that if the crustal shear zone is sufficiently weak (1020 Pa s), then the coupled effects of a compositionally dependent phase transition model and a stress‐dependent rheology lead to oscillatory plate speeds and trench motion in response to buckling and folding of the slab. On average, subducting plate velocity is 4 cm/yr and trench motion is ±0.7 cm/yr. However, during folding, subducting plate speed and trench motion increases by a factor of 3 and trench motion switches from advance to retreat. In models with a higher‐viscosity shear zone (1021 Pa s), average plate speed is lower (2 cm/yr) and there is only trench advance. Stress‐dependent weakening due to increasing driving stresses can also cause unexpected changes in plate velocity (i.e., decrease or no change). In addition, due to the added negative buoyancy from the phase transitions, slab breakoff occurs in models with a yield stress ≤500 MPa. Because of the oscillatory motion of the trench, long flat slabs do not form in the transition zone: this suggests that other factors, such as interaction of the slab with deep mantle flow, may be required to create long flat slabs.

Behavior of Nonlinear Flutter-Type Oscillations of Flexible Plates in Supersonic Gas Flow

AbstractThe behavior of nonlinear oscillations of isotropic rectangular plate fluttering in a supersonic gas flow is examined. The study was conducted taking into account both types of nonlinearity...

The Stokes’ second problem for nanofluids

Abstract In this paper, a nanofluid version of the Stokes’ second problem is investigated. For this purpose, a homogeneous model is considered with nano-sized Cu particles suspended in water. The governing equations are first transformed in dimensionless form and then solved by Laplace transform. Exact solutions corresponding to the dimensionless velocity and temperature due to both cosine and sine oscillations of an infinite flat plate are presented. It is concluded that both skin friction coefficient and density of nanofluids increases with an increase of nanoparticles volume fraction. Also the dimensionless temperature increases by increasing the Eckert number and solid volume fraction of nanoparticles.

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.

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.

The influence of the noise field on parametric oscillations of flexible square plates

This paper examines the impact of the external field intensity of white noise on the nonlinear dynamics of square plates under the longitudinal load. It is shown that in some cases, the noise of high intensity is able to reduce the number of frequencies in the oscillation spectrum of the system.

Design and study of a Flat Plate Oscillating Heat Pipe. Flow Pattern analysis and Heat Transfer Performance

Design and study of a Flat Plate Oscillating Heat Pipe. Flow Pattern analysis and Heat Transfer Performance

A coupled WC-TL SPH method for simulation of hydroelastic problems

ABSTRACTA coupled weakly compressible (WC) and total Lagrangian (TL) smoothed particle hydrodynamics (SPH) method is developed for simulating hydroelastic problems. The fluid phase is simulated using WCSPH method, while the structural dynamics are solved using TLSPH method. Fluid and solid components of the method are validated separately. A sloshing water tank problem is solved to test the WCSPH method while oscillation of a thin plate and large deformation of a cantilever beam are simulated to test the TLSPH method. After validating each component, the coupled WC-TL SPH scheme is used to simulate two benchmark hydroelastic problems. The first test case shows the evolution of water column with an elastic boundary gate, and the second one investigates the breaking water column impact on elastic structures. The agreement between WC-TL SPH results and literature data shows the ability of the proposed method in simulating hydroelastic phenomena.

Influence of vortical structure impingement on the oscillation and rotation of flat plates

Abstract Wind tunnel experiments were performed to study the impact of coherent vortical structures, shed from a cylinder, on the oscillations and rotations of vertical flat plates with thickness ratio b / c = 1 / 16 , 3/16 and 5/16. Various combinations of cylinder diameter to plate chord ratio of d / c = 1.1 , 0.8 and 0.5, and cylinder-plate spacing L d / c ∈ [ 1 , 14 ] were studied to determine the role of the strength and scale of the vortices on the motion of the plates. The plate motion was characterized with high-temporal resolution accelerometer, gyroscope sensor and a laser tachometer. High temporal- and spatial-resolution flow measurements were performed using hotwire and planar particle image velocimetry (PIV). Plates were found to oscillate around two distinctive equilibrium positions depending on the strength of the vortices shed from the cylinder. For comparatively low cylinder-plate spacing L d / c , the frequency of the shed vortices dominates the plate oscillation and the plate aligns with the mean direction of the flow. However, the plate motion transitions to an oscillation around an axis perpendicular to the mean flow with larger L d / c and, eventually, the oscillation become dominated by the vortices shed by the plate. Given an initial impulse, the plates are also able to sustain multi-frequency rotations for large L d / c ratios. In addition to governing the plate oscillations and equilibrium position, the spacing L d / c is found to significantly modify the characteristics of the recirculation bubble and turbulence levels in the wake of the plate.

A novel magnetic fluid shock absorber with levitating magnets

The paper presents a shock absorber whose working element includes two magnetic fluid rings around a group of magnets. The damping efficiency of this shock absorber is investigated by the free oscillations of an elastic plate and can be well explained with the classical equations of motion. In the shock absorber, a nonlinear equivalent stiffness is provided by the magnetic repulsion force, which controls the movement of the working element and varies in conformity to a power law. Through the theoretical and experimental study on the magnetic repulsion force, the nonlinear equivalent stiffness is determined and depends on the initial distance between the working element and the repulsion magnet. For an oscillation with the amplitude of 1mm and frequency of 1.1 Hz, the damping efficiency is inversely proportional to the nonlinear equivalent stiffness.

Investigation of natural oscillations of inhomogeneous orthotropic circular plate lying on an inhomogeneous viscoelastic foundation

In the building of large engineering complexes, bridges and overpasses for various purposes and in many other areas the plates of widely different configurations are used. These plates are made of natural and artificial orthotropic materials. Among them, rectangular and circular plates are the most common. According to the above mentioned natural oscillations, engineer-designer and calculator need to properly assess real property of construction element and the influence of the environment, which is in contact during the operation. Therefore, the object of this study is inhomogeneous circular plate lying on inhomogeneous viscoelastic foundations. It is assumed that the moduli of elasticity and the plate density are continuous functions of the current radius. In this case, unlike homogeneous plates, the motion equation is complex differential equation with variable coefficients. In this regard, there is need to build an approximate analytical solution method. In the course of the study we used methods of separation of variables and Bubnov-Galerkin orthogonalization method, which gives effective results with homogeneous boundary conditions. An axisymmetric form of natural oscillations of orthotropic circular plate with inhomogeneous radius lying on an inhomogeneous viscoelastic foundation is considered. The case, when the contour around the plate is rigidly clamped, is studied in detail. Numerical analysis for concrete values of the characteristic parameters is carried out. The motion equation is obtained taking into account inhomogeneity of the plate and the foundation, as well as partial variable coefficients of the fourth order.

Light-Induced Pulling and Pushing by the Synergic Effect of Optical Force and Photophoretic Force.

Optical force, coming from momentum exchange during light-matter interactions, has been widely utilized to manipulate microscopic objects, though mostly in vacuum or in liquids. By contrast, due to the light-induced thermal effect, photophoretic force provides an alternative and effective way to transport light-absorbing particles in ambient gases. However, in most cases these forces work independently. Here, by employing the synergy of optical force and photophoretic force, we propose and experimentally demonstrate a configuration which can drive a micron-size metallic plate moving back and forth on a tapered fiber with supercontinuum light in ambient air. Optical pulling and oscillation of the metallic plate are experimentally realized. The results might open exhilarating possibilities in applications of optical driving and energy conversion.

Destabilizing effect of damping on the post-critical flutter oscillations of flat plates

In the framework of energy harvesting from flow-induced vibrations, understanding the behaviour of dynamic systems under high levels of damping is a key issue. In particular, this work refers to two-degree-of-freedom elongated rectangular plates prone to the aeroelastic instability of classical flutter. The effect of heaving damping was studied through systematic linear analyses and wind tunnel tests, developing specific aeroelastic setups for both large-amplitude motion and high viscous forces. Some configurations clearly showed a destabilizing effect of damping, both in terms of earlier instability onset and larger post-critical motion amplitudes. For high-inertia systems with low pitching damping, still-air frequency ratios of the uncoupled system away from unity and small mass unbalance downstream of the elastic axis are the key parameters to observe this phenomenon. Both analytical and experimental results suggest that this destabilizing effect relates to the tendency of any configuration to approach the behaviour of the system with unit still-air uncoupled frequency ratio while increasing the heaving damping.

Dynamic impact on a frozen support caused by natural and quasinatural oscillations of an ice plate

This paper presents the results of the numerical and analytical study of natural and quasinatural bending-gravitational oscillations of a circular elastic ice plate floating on the fluid surface and frozen onto a cylindrical vertical support. In the framework of the shallow water theory for bounded and unbounded reservoirs, the dependence of natural and quasinatural frequencies of geometrical parameters of the oscillation region is studied.

Stability analysis of the interface between two weak viscoelastic liquids under periodic oscillations

We consider the motion and the linear hydrodynamic instabilities of two immiscible viscoelastic liquids above a horizontal solid surface induced by the periodic oscillations of the horizontal plate along its plane. A planar interface, parallel to the oscillating plate, separates the lower layer from the other viscoelastic fluid that extends vertically to infinity. The two-dimensional motion of these fluids is studied together with the conditions under which the flow becomes unstable, deforming the planar interface and promoting the mixing of both liquids. The study extends the previous work by Isakova et al. [“A model for the linear stability of the interface between aqueous humor and vitreous substitutes after vitreoretinal surgery,” Phys. Fluids 26, 124101 (2014)] by considering non-Newtonian fluids, particularly liquids with weak viscoelasticity (neglecting normal stress differences), which may model more accurately the physical behavior of the aqueous humor and, especially, the vitreous humour substitute in the vitreous chamber of the eye after vitrectomy. A novel approach to the quasi-steady stability analysis of unsteady flows of Maxwell liquids is developed in the present paper. We focus on the effect of the small Deborah numbers on the motion and on the hydrodynamic instability of the two fluids as the other non-dimensional parameters are varied within the range of interest for the biofluiddynamics of the eye. The special case in which the lower layer modelling the aqueous humor is a Newtonian liquid and the upper vitreous substitute is a Maxwell liquid is considered with detail. We find that, even for a very small Deborah number of the vitreous substitute, the dynamics and the hydrodynamic stability of the two fluids can be qualitatively very different to the Newtonian case, especially as the viscosity ratio is varied, showing that weak viscoelasticity may change dramatically the dynamics of the eye. An exhaustive characterization of the influence of the different parameters on the hydrodynamic stability is given, which may be useful also for the study of the dynamics of other systems where two viscoelastic liquids in contact are subjected to periodic oscillations.

Limit periodic motions in systems with after-effect in a critical case*

Abstract Systems with after-effect are considered, whose states are described by Volterra integro-differential equations. The critical case of one zero root of the characteristic equation is investigated (where all the other roots have negative real parts) along with the question of the existence in this case of limit periodic motions of the system, i.e., motions which tend exponentially to periodic regimes with unbounded increase of time. A time-dependent, small, piecewise-continuous limit periodic perturbation, generated by external factors, is present in the system. It is shown that in the system under the perturbation, limit periodic motions arise that are represented by power series in fractional powers of a small parameter characterizing the perturbation magnitude. As an example, rotational limit periodic oscillations of a solid plate in an air flow are considered with time dependence of the flow about the plate taken into account by introducing integral terms into the aerodynamic torque.

Control of Complicated Stress Oscillations in FGPM Thin Plates

Abstract Analytical solutions to one-dimensional electro-elastodynamic problems in functionally graded piezoelectric material thin plates subjected to impact pressure are obtained. In the case where both surfaces of the thin plate are free of electric charge, the stress oscillation is periodic when the mechanical impedance is independent of the space-variable, whereas it is complicated when the impedance depends on the space-variable. In the case where the voltage between both surfaces of the thin plate is zero, the stress oscillation is complicated whether the impedance is independent of or dependent on the space-variable. The complicated stress oscillations are found to be suppressed completely by applying specific voltages determined from the analytical solution.