Damping of flexural vibrations in thin plates using one and two dimensional acoustic black hole effect

The reduction of flexural vibration in thin plates is examined using the acoustic black hole effect associated with nearly zero reflection of quasi-plane waves from a lightly damped wedge or tapered hole where the profile varies according to a power-law. The flexural wave propagation can be determined through the application of geometrical acoustics approximation or exact analytical solutions. For a plate of thickness of power-law profile, the wave slows down and grows in amplitude. In the ideal case of no truncation of the quadratic (or higher) profile, the phase speed asymptotically decreases to zero and the wave never reaches the end. Manufactured plates always have a truncation, leading to relatively high reflection coefficients, however, the application of small damping layers leads to substantial decreases in the reflection coefficients and thus large reductions in mobility amplitudes. This paper contains the results of numerical models and experimental measurements of point mobility for structural plates incorporating tapered holes for validation. A rectangular plate with a 1D wedge on one end is examined, in addition to a circular plate with a quadratic profile in the centre. In both cases, the measurements show significant reductions in resonant peaks of mobility, in good agreement to numerical predictions

Damping of flexural vibrations in plates containing ensembles of tapered indentations of power-law profile

In this work, we report experimental results on damping flexural vibrations in rectangular plates containing tapered indentations (pits) of power-law profile, the centres of which are covered by a small amount of absorbing material. In the case of quadratic or higher-order profiles, such indentations materialise two-dimensional acoustic 'black holes' for flexural waves. Initially, the effects of single pits have been investigated. It has been found that, in order to increase the damping efficiency of power-law profiled indentations, their absorption crossections should be enlarged by drilling a central hole of sufficiently large size (14 mm), while keeping the edges sharp. Such pits, being in fact curved power-law wedges, result in substantially increased damping. The next and the major part of this investigation involved using multiple indentations in the same rectangular plates to increase damping. Plates with combinations from two to six equal indentations have been investigated. The results show that, when multiple indentations are used, the associated damping increases substantially with the increase of a number of indentations. For the plate with 6 indentations, the resulting damping becomes comparable if not greater than that achieved by a wedge of power-law profile

Point mobility of a cylindrical plate incorporating a tapered hole of power-law profile

The paper describes the results of experimental measurements of point mobility carried out on circular plates containing tapered holes of quadratic power-law profile with attached damping layers. The obtained results are compared to the developed numerical model, as a means of validation. The profiles of the tapered hole in the plates are designed to replicate near zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation, also known as acoustic black hole effect. The driving point mobility measurements are provided, showing a comparison of the results for a constant thickness circular plate, a constant thickness plate with a layer of damping film applied and a plate with a quadratic power-law profile machined into the center, which is tested with a thin layer of elastic damping material attached. The results indicate a substantial suppression of resonant peaks, agreeing with a numerical model, which is based on the analytical solution available for the vibration of a plate with a central quadratic power-law profile. The paper contains results for the case of free boundary conditions on all edges of the plates, with emphasis placed on the predictions of resonant frequencies and the amplitudes of vibration and loss factor. (c) 2011 Acoustical Society of America. [DOI: 10.1121/1.3585844

Effect of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power law profile

In the present paper, an efficient method of damping structural vibrations using the acoustic black hole effect is further investigated experimentally. This method is based on some specific properties of flexural wave propagation in tapered plates (wedges) of power-law profile that have to be partially covered by narrow thin strips of absorbing layers. Ideally, if the power-law exponent of the profile is equal or larger than two, the flexural wave never reaches the sharp edge and therefore never reflects back, which constitutes the acoustic black hole effect. It has been previously established theoretically and confirmed experimentally that this method of damping structural vibrations is very efficient even in the presence of edge truncations. The present work describes the results of the experimental studies of the effects of manufacturing intolerances on damping flexural vibrations in wedge-like structures of power-law profile. In particular, the effect of mechanical damage resulting from the use of cutting tools to wedge tips is investigated, including tip curling and early truncation, as well as the placement of absorbing layers on different wedge surfaces. Also, the effects of welded and glued bonding of wedge attachments to basic rectangular plates (strips) are investigated. The results show that, although the above-mentioned geometrical and material imperfections reduce the damping efficiency by varying degrees, the method of damping structural vibrations using the acoustic black hole effect is robust enough and can be used widely without the need of high precision manufacturin

Experimental study on damping of flexural waves in rectangular plates by means of one-dimensional acoustic 'Black Holes'

In this paper we present some recent experimental results on new lightweight and broad-band damping treatment for rectangular plates based on the so-called acoustic ‘black hole’ effect [1-5], which represents one of the most efficient ways of creating graded impedance interfaces [6] to reduce edge reflections of flexural waves. These acoustic black holes, or vibration 'traps', use elastic wedges of variable thickness defined by a power-law relationship h(x) = ε·xm (with m ≥ 2) to reduce edge reflections. In the ideal case of no edge truncations, bending wave velocities decrease to zero in such a way that the waves never reach the end and hence do not reflect back. They thus represent one-dimensional acoustic ‘black holes’ for flexural waves. It was predicted [2,3] that very low values of reflection coefficient can be achieved even in the presence of truncations and imperfections when a narrow layer of absorbing material is attached to its surface in order to dissipate the remaining energy (note that direct application of thin layers of absorbing materials to the surfaces of rectangular plates has a negligible influence on damping, which has also been demonstrated during the tests). (Continues...

Experimental investigation of damping flexural vibrations in plates containing tapered indentations of power-law profile

In the present paper, experimental results are reported on damping flexural vibrations in rectangular plates containing tapered indentations (pits) of power-law profile, with the centres of the indentations covered by a small amount of absorbing material. In the case of quadratic or higher-order profiles, such indentations materialise two-dimensional acoustic ‘black holes’ for flexural waves that can absorb almost 100% of the incident elastic energy. In the present investigation, pits have been made in different locations of rectangular plates, and the corresponding frequency response functions have been measured. It has been found that basic power-law indentations, with no or very small central hole, result in rather low reduction in resonant peak amplitudes, which may be due to the relatively small effective absorption area in this case. To increase the damping efficiency of power-law profiled indentations, this absorption area has been enlarged by increasing the size of the central hole in the pit, while keeping the edges sharp. As expected, such pits, being in fact curved power-law wedges, result in substantially increased damping. When multiple indentations are used, the resultant damping increases substantially, as expected, and may become comparable if not greater than that achieved by one-dimensional wedges of power-law profile

Experimental investigation of damping flexural vibrations using two-dimensional acoustic ‘black holes’

In the present paper, we report the results of the experimental investigation of damping flexural vibrations in rectangular plates containing tapered indentations (pits) of power-law profile, with the addition of a small amount of absorbing material. In the case of quadratic or higher-order profiles, such indentations materialise two-dimensional ‘black holes’ for flexural waves. In the present investigation, pits have been made in different locations of rectangular plates. It has been found that basic power-law indentations that are just protruding over the opposite surface cause rather small reduction in resonant peak amplitudes, which may be due to their relatively small absorption crossection. To increase damping in the present investigation, the absorption crossection has been enlarged by increasing the size of the central hole in the pit, while keeping the edges sharp. As expected, such pits, being in fact curved power-law wedges, result in substantially increased damping comparable with that achieved by one-dimensional wedges of powerlaw profile

Angular momenta creation in relativistic electron-positron plasma

Creation of angular momentum in a relativistic electron-positron plasma is explored. It is shown that a chain of angular momentum carrying vortices is a robust asymptotic state sustained by the generalized nonlinear Schrodinger equation characteristic to the system. The results may suggest a possible electromagnetic origin of angular momenta when it is applied to the MeV epoch of the early Universe.Comment: 20 pages, 6 figure

Compaction of Hyaloclastite from the Active Geothermal System at Krafla Volcano, Iceland

Hyaloclastites commonly form high-quality reservoir rocks in volcanic geothermal provinces. Here, we investigated the effects of confinement due to burial following prolonged accumulation of eruptive products on the physical and mechanical evolution of surficial and subsurface (depths of 70 m, 556 m, and 732 m) hyaloclastites from Krafla volcano, Iceland. Upon loading in a hydrostatic cell, the porosity and permeability of the surficial hyaloclastite decreased linearly with mean effective stress, as pores and cracks closed due to elastic (recoverable) compaction up to 22-24 MPa (equivalent to ~1.3 km depth in the reservoir). Beyond this mean effective stress, denoted as P∗, we observed accelerated porosity and permeability reduction with increasing confinement, as the rock underwent permanent inelastic compaction. In comparison, the porosity and permeability of the subsurface core samples were less sensitive to mean effective stress, decreasing linearly with increasing confinement as the samples compacted elastically within the conditions tested (to 40 MPa). Although the surficial material underwent permanent, destructive compaction, it maintained higher porosity and permeability than the subsurface hyaloclastites throughout the experiments. We constrained the evolution of yield curves of the hyaloclastites, subjected to different effective mean stresses in a triaxial press. Surficial hyaloclastites underwent a brittle-ductile transition at an effective mean stress of ~10.5 MPa, and peak strength (differential stress) reached 13 MPa. When loaded to effective mean stresses of 33 and 40 MPa, the rocks compacted, producing new yield curves with a brittle-ductile transition at ~12.5 and ~19 MPa, respectively, but showed limited strength increase. In comparison, the subsurface samples were found to be much stronger, displaying higher strengths and brittle-ductile transitions at higher effective mean stresses (i.e., 37.5 MPa for 70 m sample, >75 MPa for 556 m, and 68.5 MPa for 732 m) that correspond to their lower porosities and permeabilities. Thus, we conclude that compaction upon burial alone is insufficient to explain the physical and mechanical properties of the subsurface hyaloclastites present in the reservoir at Krafla volcano. Mineralogical alteration, quantified using SEM-EDS, is invoked to explain the further reduction of porosity and increase in strength of the hyaloclastite in the active geothermal system at Krafla

Perturbative Effects in the Form Factor \gamma\gamma^*\to \pi and Extraction of the Pion Wave Function from CLEO Data

We study the pion form factor F^{\pi \gamma\gamma^*}(Q^2) in the light-cone sum rule approach, accounting for radiative corrections and higher twist effects. Comparing the results to the CLEO experimental data on F^{\pi \gamma\gamma^*}(Q^2), we extract the the pion distribution amplitude of twist-2. The deviation of the distribution amplitude from the asymptotic one is small and is estimated to be a_2(\mu) = 0.12 \pm 0.03 at \mu=2.4 GeV, in the model with one non-asymptotic term. The ansatz with two non-asymptotic terms gives some region of a_2 and a_4, which is consistent with the asymptotic distribution amplitude, but does not agree with some old models.Comment: 21 pages, LaTeX, 7 eps figures; (v2): Phys. Rev. D versio