Plane wave expansion and extended plane wave expansion formulations for Mindlin-Reissner elastic metamaterial thick plates

The plane wave expansion (PWE) and the extended plane wave expansion (EPWE) formulations are derived in order to obtain the complex dispersion relation of flexural waves in a metamaterial Mindlin-Reissner thick plate with multiple periodic resonators. These new formulations are useful to obtain more accurate results at higher frequencies than those based on Kirchhoff-Love thin plate theory. Multiple periodic resonators with multiple degrees of freedom (M-DOF) attached to metamaterial thick plates broaden the applications for wave attenuation in high frequencies.     

Wave propagation in anisotropic turbulent superfluids

In this work, a hydrodynamical model of Superfluid Turbulence previously formulated is applied to study how the presence of a non-isotropic turbulent vortex tangle modifies the propagation of waves. Two cases are considered: wave front parallel and orthogonal to the heat flux. Using a perturbation method, the first-order corrections due to the presence of the vortex tangle to the speeds and to the amplitudes of the first and second sound are determined. It is seen that the presence of the quantized vortices couples first and second sound, and the attenuation of second sound is proportional to the line density L if the wave propagates orthogonal to the heat flux, while it is proportional to the square root of L if the wave propagates parallel with the heat flux.     

Second sound near lambda transition in presence of quantum vortices

In this paper, temperature waves (also known as second sound) are considered, with their respective coupling with waves in the order parameter describing the transition from normal phase to superfluid phase, and with waves in the vortex length density. We analyze the coupling between these three kinds of waves and explore its relevance in situations not far from the lambda transition. In particular, the expressions for the second sound speed and second sound attenuation are explicitly obtained within some approximations, showing the influence of the order parameter and the vortex length density, which is decisive close to the transition.

     

Sonofusion: EA optimisation of acoustic resonator

We present a novel recipe combining evolutionary algorithm (EA) concepts, robust against local optima, for high-dimensional multimodal optimisation problems, which we developed for the purpose of optimising piezo-driven liquid-filled acoustic resonators for future sonofusion experiments. In contrast to other resonators (e.g. mirrors for laser, flute), the structure bounding the oscillating medium cannot be assumed to be static. Instead, the vibration response of the whole fluid-structure setup to a periodic driving force is considered. Manufacturing and reproducibility criteria exclude trivial spherical or cylindrical shapes leading to many design parameters to be optimised. With maximising the sound pressure amplitude in the center of the fluid volume being the primary goal, one faces a competition of an increased number of resonances varying in amplitude and frequency, and interacting with other resonances. In this smooth, yet high-dimensional search space scattered with many local optima, an EA approach is efficient. Evaluating a solution candidate corresponds to calculating a harmonic response over a frequency band of a 2D-axisymmetric FE model of the piezo-driven structure filled with acoustic fluid elements (modeled in Ansys). Thus, more than 10⁴ evaluation calls per run cannot be afforded. Serving those needs we developed an EA combining elements from genetic algorithms (GA), evolution strategies (ES), differential evolution (DE), and simulated annealing (SA). (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sound waves in two-fraction polydispersed bubbly media

The propagation of sound waves in two-fraction mixtures of a liquid with polydisperse gas bubbles of different composition is investigated. A system of differential equations of the perturbed motion of the mixture is presented, and a dispersion relation is derived. The equilibrium velocity of sound, and the low-frequency and high-frequency asymptotic forms of the linear attenuation factor are obtained. The characteristic mean radii of the bubbles are determined. The theory is compared with existing experimental data.     

On the use of Helmholtz resonators as sound attenuators

Summary In the present paper a nonlinear acoustic theory is proposed, to accurately describe the properties of a generalized type of Helmholtz resonators. The theory may be used as a layout tool to design sound attenuators for combustion facilities. The present investigation shows that, in addition to the nonlinear effects, the effects due to thermoacoustic boundary layers and the first frequency correction to the Helmholtz approximation should be taken into account, in order to predict the frequency-dependent attenuation properties of Helmholtz attenuators with the accuracy required by typical technical applications. A series of experiments is presented which is used to validate the theoretical predictions.

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Zusammenfassung In der vorliegenden Abhandlung wird eine nichtlineare akustische Theorie vorgeschlagen, mit der das Verhalten einer verallgemeinerten Art von Helmholtzresonatoren beschrieben werden kann. Die Theorie kann als Werkzeug zur Auslegung von Schalldämpfern für Verbrennungsanlagen benutzt werden. Die vorliegende Arbeit zeigt, dass neben den nichtlinearen Effekten auch die Einflüsse der thermoakustischen Grenzschichten und der ersten Frequenzkorrektur zur Helmholtzapproximation berücksichtigt werden müssen, damit die frequenzabhängigen Eigenschaften von Helmholtzdämpfern mit technisch ausreichender Genauigkeit beschrieben werden können. Mit einer Reihe von Experimenten werden die theoretischen Ergebnisse untermauert.

     

Dissipative terms of thermal nature in the theory of an ideal monoatomic superfluid

A dissipative model of helium II was built up in previous works, using a 13-field extended thermodynamic theory formulated by Liu and Müller. In this work a generalization of such model is presented, where an extended thermodynamics with 14 fields due to Kremer is used. It is shown that the fourteenth field is able to account for the experimental data concerning the second sound attenuation. Further, the proposed theory is able to explain the Osborne experiment. Finally, a comparison with the two-fluid model is performed, emphasizing the different ways in which the dissipative phenomena are explained by the two theories.     

基于Green-Naghdi模型与三相延迟模型的耦合热弹性波传播

研究了基于G-N模型与三项延迟模型的热弹性波的传播特征.在各种广义热弹性理论中,热位移概念的引入使得G-N模型具有独特性质而引起广泛的关注和应用.基于G-N模型,最近一个三相延迟模型被提出.主要研究了这两种模型下第一和第二声波(耦合热弹性波)的色散和衰减特性,分析了温度场和位移场在两种模型下的振幅比和相位差.结果发现三相延迟模型更为通用和灵活,应得到更多的关注与应用.     

Attenuation and Diffraction of Bending Waves at Gaps in Fluid Loaded Plates

The scattering of a bending wave by a finite number of parallelrectilinear gaps in an infinite fluid-loaded plate is discussed.For the purpose of analysis, the widths of the gaps are assumedto be infinitesimal, but there is no physical contact betweenabutting edges of neighbouring sections of the plate. A sectionedge may be restrained by resilient supports or loadings, eitherindividually or jointly with the neighbouring edge. The theorydetermines the attenuation of the bending wave by the gaps andthe sound radiated into the ambient fluid during the interaction.Specific results are given for a steel plate which has a singlegap in air and in water, such that either (1) the abutting edgesare free to vibrate independently, (2) both edges are clamped,or (3) one edge is clamped and the other free. In each of thesecases the coupling between the two halves of the plate is providedsolely by the fluid loading: the bending wave would be totallyreflected at the gap in vacuo. The results are relevant to thecontrol and suppression of structure-borne sound     

Finite element modeling of the nonlinear oscillations in axisymmetric acoustic resonators

Oscillation of a gas in closed resonators has gained considerable interest in the past years. In this paper, the nonlinear equations governing the behavior of the gas oscillations inside the resonator are formulated in a weak form and then modeled using the finite element method. The pressure ratios, predicted by the proposed model, are in close agreement with the exact solutions available for simple geometries such as cylindrical, exponential and linearly varying area resonators. The presented comparisons validate the accuracy of the finite element model and emphasize its potential for predicting the performance or resonators of more complex geometries which are necessary for generating high pressures from the standing waves. Also, gas flow through the boundaries of the resonator is implemented in the proposed model. The presented finite element model presents an invaluable tool for designing a new class of acoustic compressors which can be used, for example, in refrigeration and vibration control applications.     

耳蜗毛细胞活动的神经动力学分析

为了更深刻地了解耳蜗毛细胞活动的神经动力学机制，建立了基于Hodgkin-Huxley方程的毛细胞模型，通过数值模拟对不同声音频率刺激时的毛细胞膜电位、功率和能量消耗进行了神经动力学分析.研究结果表明:声音频率在0.1~20 kHz范围内，外毛细胞膜电位的衰减低于内毛细胞，而外毛细胞功率和能量消耗的增益远高于内毛细胞.外毛细胞膜电位的低衰减、功率和能量消耗的高增益支持了外毛细胞的放大作用是由电致运动驱动的.对耳蜗毛细胞膜电位、功率和能量消耗的研究结果有助于深刻了解毛细胞活动的神经动力学性质.     

Mass‐in‐mass lattices with small internal resonators

We consider the mass‐in‐mass (MiM) lattice when the internal resonators are very small. When there are no internal resonators the lattice reduces to a standard Fermi‐Pasta‐Ulam‐Tsingou (FPUT) system. We show that the solution of the MiM system, with suitable initial data, shadows the FPUT system for long periods of time. Using some classical oscillatory integral estimates we can conclude that the error of the approximation is (in some settings) higher than one may expect.     

Method for Analyzing the Influence of the Quantum Nonlocal Effect on the Characteristics of a Plasmonic Nanolaser

Doklady Mathematics - Based on the discrete source method, a rigorous approach has been developed and implemented that allows one to analyze light scattering by models of resonators of plasmonic...     

Coupling Boundary Elements to a Raytracing Procedure using the Singular Indirect Method

The coupling of Boundary Elements and a raytracing procedure is presented here. Such a hybrid method is best suited to the study of realistic outdoor sound propagation problems: The noise often acts in a domain where many objects like buildings or sound insulation walls scatter the sound. Thus, diffraction has to be taken into account. BEM is well suited. To study the effects of this noise on a sound receiver far away, raytracing may be preferable for such application, because refraction can be implemented more easily. Hence, a Boundary Element Analysis is performed in noisy nearfield regions, a raytracing procedure at a larger distance from the sound sources. First, the direct Boundary Element algorithm is applied to determine the sound pressure at interface points. Second, a singular indirect Boundary Element formulation is used to find intensities of point sources on the same interface which produce the previously determined sound pressure. Finally, these sound intensities are the input data for the raytracing procedure. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dispersion of elastic waves in a micropolar metamaterial plate with periodical arranged resonators

The wave propagation in a micropolar elastic metamaterial is investigated in this paper. The elastic metamaterial is composed of the micropolar elastic host material and the periodically arranged local resonators. Compared with the classical elastic metamaterial, the micropolar elastic metamaterial has more material parameters that can be elaborately designed to manipulate the elastic wave propagation. By introducing additional displacement fields, a multi-displacement continuum model of the micropolar elastic metamaterial is presented to characterize the resonance behavior of the resonators and the microstructure effects of the unit cell. According to this continuum model, two independent wave systems exist: one is a longitudinal system and the other is a shear and rotation coupled transversal system. The dispersive curves and band gaps of the longitudinal and transversal systems are numerically discussed and the influences of the resonators are mainly considered.     

The eskolemization of universal quantifiers

This paper is a sequel to the papers Baaz and Iemhoff (2006, 2009) [4] and [6] in which an alternative skolemization method called eskolemization was introduced that, when restricted to strong existential quantifiers, is sound and complete for constructive theories. In this paper we extend the method to universal quantifiers and show that for theories satisfying the witness property it is sound and complete for all formulas. We obtain a Herbrand theorem from this, and apply the method to the intuitionistic theory of equality and the intuitionistic theory of monadic predicates.     

Dual-phase-lag thermoelastic damping models for micro/nanobeam resonators

Thermoelastic damping (TED) affects the quality factors of vacuum-operated micro/nanobeam resonators significantly. In this work, by adopting the non-Fourier theory of dual-phase-lag (DPL) model, an analytical formula of TED in micro/nanobeam resonators with circular cross-section is first developed. Moreover, for micro/nanobeam resonators with rectangular cross-section, the series-form type of DPL-TED model is also proposed and compared with the modified existing model. The characteristics of TED spectra with the single-peak, dual-peak, and multiple-peak phenomena are explored. The simulation results reveal that the ratio of dual-phase-lag times and the characteristic dimension of beams such as the radius and thickness have significant influences on TED behaviors. In addition, temperature distributions in micro/nanobeams exhibit an apparent distinction under the DPL non-Fourier effect.     

Attenuation correction in positron emission tomography

We describe a mathematical method for computing the attenuation distribution from Positron emission tomography (PET) data. The method renders possible the correction of PET data for attenuation without a transmission scan. It can be applied if the attenuation distribution is sufficiently simple (abdomen and bead). We give the results for computer-generated data and for data on patients.     

Localization of acoustic sources in subsonic jets

The sound in the acoustic far–field of a round jet is generated by a multitude of unsteady flow structures with different length and time scales. Most likely, different components of the noise spectrum are created by different structures in the jet which emit sound in different directions. Based on Lighthill's acoustic analogy, we present a method for relating flow structures of the jet with far–field noise spectra and their associated directivity patterns. The method allows to determine what kind of noise (with respect to frequency and emission direction) is generated at a given streamwise location. We illustrate the method with numerical results for a round isothermal jet. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)