Suppression of Rayleigh-Benard Convection with Proportional-Derivative Controller

We study theoretically (linear stability) and experimentally the use of proportional and derivative controllers to postpone the transition from the no-motion state to the convective state in a circular cylinder heated from below and cooled from above. The heating is provided with an array of individually controlled actuators whose power is adjusted in proportion to temperatures measured in the cylinder\u27s interior. As the proportional controller\u27s gain increases, so does the critical Rayleigh number for the onset of convection. Relatively large proportional controller gains lead to oscillatory convection. The oscillatory convection can be suppressed with the application of a derivative controller, allowing further increases in the critical Rayleigh number. The experimental observations are compared with theoretical predictions

EXPERIMENTAL STUDY ON THE STABILIZATION OF THE NO-MOTION STATE IN THE RAYLEIGH-BENARD CONVECTION PROBLEM

ABSTRACT We demonstrate experimentally that through the use of proportional-differential control, it is possible to stabilize the nomotion state of a fluid layer heated from below, cooled from above, and confined in an upright, circular cylinder (the Rayleigh-Bénard problem). An array of 24 independently controlled heaters (thermal actuators), microfabricated on a silicon wafer, constitutes the bottom boundary of the test cell. A cooling system maintains the top boundary at a constant temperature. Silicon diodes located at the midheight of the cell, above the actuators, measure the fluid's temperature. The multi-input, multi-output controller adjusts the heaters' power in proportion to the deviation of the fluid's temperatures, as recorded by the diodes, from preset values associated with the no-motion, conductive state. First, a set of experiments was conducted in the absence of a controller to determine the uncontrolled, reference state. Advantage is taken of the linear dependence of the mid-height temperature on the power input in the no-motion state. The preset temperatures are determined by extrapolating the mid-height temperatures to the desired input power values. A proportional controller is then engaged. We show that as the controller's gain increases so does the critical Rayleigh number for the onset of convection. The proportional controller allows us to increase the critical Rayleigh number by as much as a factor of 1.4. When the controller's gain is larger than a critical value, the system becomes time-wise oscillatory (Hopf bifurcation) and the controller's performance deteriorates. The oscillatory convection can be significantly damped out by engaging a proportional-differential (PD) controller. The PD controller allows us to further increase the critical Rayleigh number for the onset of convection to as much as a factor or 1.7 compared to the uncontrolled case. Further increases in the critical Rayleigh number were not possible due to the actuators' saturation. We also compared the supercritical flow patterns at the mid-height of the test cell in the presence of the controller with the flow patterns in the absence of a controller. The proportional controller modified the flow pattern from a single convective cell with ascending fluid in one half of the cell and descending in the other half, to fluid ascending at the center of the cell and descending at near the lateral wall. Our work represents an improvement over previous experimental investigations on the stabilization of Rayleigh-Bénard convection in which the critical Rayleigh number was increased by only a factor of 1.2. Almost uniform temperature distribution at the mid-height is obtained through the combined action of proportional and derivative controllers. The Rayleigh-Bénard convection is suppressed under conditions when, in the absence of a controller, flow would persist

Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types

International audienceIn this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elasticmaterials is evidenced via multimode resonance experiments. In these experiments the dynamic response,including the spatial variations of velocities and strains, is carefully monitored while the sample is vibratedin a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments candecouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying thenonequilibrium dynamics of the material differ substantially for a compressional wave and for a shearwave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise innatural systems as well as to the design and engineering of nonlinear acoustic metamaterials

Advanced nonlinear ultrasonic methods for health monitoring of composite structures

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Resonant Ultrasound Spectroscopy for Materials with High Damping and Samples of Arbitrary Geometry

International audienceResonant ultrasound spectroscopy (RUS) is a powerful and established technique for measuring elastic constants of a material with general anisotropy. The first step of this technique consists of extracting resonance frequencies and damping from the vibrational frequency spectrum measured on a sample with free boundary conditions. An inversion technique is then used to retrieve the elastic tensor from the measured resonance frequencies. As originally developed, RUS has been mostly applicable to (i) materials with small damping such that the resonances of the sample are well separated and (ii) samples with simple geometries for which analytical solutions exist. In this paper, these limitations are addressed with a new RUS approach adapted to materials with high damping and samples of arbitrary geometry. Resonances are extracted by fitting a sum of exponentially damped sinusoids to the measured frequency spectrum. The inversion of the elastic tensor is achieved with a genetic algorithm, which allows searching for a global minimum within a discrete and relatively wide solution space. First, the accuracy of the proposed approach is evaluated against numerical data simulated for samples with isotropic symmetry and transversely isotropic symmetry. Subsequently, the applicability of the approach is demonstrated using experimental data collected on a composite structure consisting of a cylindrical sample of Berea sandstone glued to a large piezoelectric disk. In the proposed experiments, RUS is further enhanced by the use of a 3D laser vibrometer allowing the visualization of most of the modes in the frequency band studied