Wave propagation in magneto-electro-elastic nanobeams via two nonlocal beam models

This paper makes the first attempt to investigate the dispersion behavior of waves in magneto-electro-elastic (MEE) nanobeams. The Euler nanobeam model and Timoshenko nanobeam model are developed in the formulation based on the nonlocal theory. By using the Hamilton’s principle, we derive the governing equations which are then solved analytically to obtain the dispersion relations of MEE nanobeams. Results are presented to highlight the influences of the thermo-electro-magnetic loadings and nonlocal parameter on the wave propagation characteristics of MEE nanobeams. It is found that the thermo-electro-magnetic loadings can lead to the occurrence of the cut-off wave number below which the wave can’t propagate in MEE nanobeams.     

Wave propagation in stereo-lithographical (STL) bone replicas at oblique incidence

Comparisons between predictions of a Biot-Allard model allowing for angle-dependent elasticity and angle-and-porosity dependent tortuosity and transmission data obtained at normal incidence on water-saturated replica bones are extended to oblique incidence. The model includes two parameters which are adjusted for best fit at normal incidence. Using the same parameter values, it is found that predictions of the variation of transmitted waveforms with angle through two types of bone replica are in reasonable agreement with data despite the fact that scattering is not included in the theory.     

Wave propagation through a dielectric layer containing densely packed fibers

This paper presents the theoretical formulation for the propagation of electromagnetic wave through a dielectric layer containing a random dense distribution of fibers. The diameter of the fibers is comparable to the inter-fiber spacing and wavelength of the incident radiation, but is much smaller than the thickness of the layer. Discontinuity of refractive index across the boundaries of the dielectric layer resulted in multiple internal reflection of both the primary source wave and the scattered waves. As a result the incident waves on the fibers consist of the multiply-reflected primary waves, scattered waves from other fibers, and scattered-reflected waves from the boundaries. The effective propagation constant of the dielectric fiber layer was developed by utilizing the Effective field-Quasicrystalline approximation. The influence of the refractive index of the dielectric medium on the radiative properties of a dense fiber layer was examined by means of numerical analyses.     

Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory

The governing equation of wave motion of viscoelastic SWCNTs (single-walled carbon nanotubes) with surface effect under magnetic field is formulated on the basis of the nonlocal strain gradient theory. Based on the formulated equation of wave motion, the closed-form dispersion relation between the wave frequency (or phase velocity) and the wave number is derived. It is found that the size-dependent effects on the phase velocity may be ignored at low wave numbers, however, is significant at high wave numbers. Phase velocity can increase by decreasing damping or increasing the intensity of magnetic field. The damping ratio considering surface effect is larger than that without considering surface effect. Damping ratio can increase by increasing damping, increasing wave number, or decreasing the intensity of magnetic field.     

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.     

Reprint of : Connection between wave transport through disordered 1D waveguides and energy density inside the sample: A maximum-entropy approach

We study the average energy – or particle – density of waves inside disordered 1D multiply-scattering media. We extend the transfer-matrix technique that was used in the past for the calculation of the intensity beyond the sample to study the intensity in the interior of the sample by considering the transfer matrices of the two segments that form the entire waveguide. The statistical properties of the two disordered segments are found using a maximum-entropy ansatz subject to appropriate constraints. The theoretical expressions are shown to be in excellent agreement with 1D transfer-matrix simulations.     

Wave propagation analysis in nonlinear curved single-walled carbon nanotubes based on nonlocal elasticity theory

Theoretical predictions are presented for wave propagation in nonlinear curved single-walled carbon nanotubes (SWCNTs). Based on the nonlocal theory of elasticity, the computational model is established, combined with the effects of geometrical nonlinearity and imperfection. In order to use the wave analysis method on this topic, a linearization method is employed. Thus, the analytical expresses of the shear frequency and flexural frequency are obtained. The effects of the geometrical nonlinearity, the initial geometrical imperfection, temperature change and magnetic field on the flexural and shear wave frequencies are investigated. Numerical results indicate that the contribution of the higher-order small scale effect on the shear deformation and the rotary inertia can lead to a reduction in the frequencies compared with results reported in the published literature. The theoretical model derived in this study should be useful for characterizing the mechanical properties of carbon nanotubes and applications of nano-devices.     

Alternative method for wave propagation within bounded linear media: Conceptual and practical implications

This paper uses an alternative approach to study the monochromatic plane wave propagation within dielectric and conductor linear media of plane-parallel faces. This approach introduces the time-averaged Poynting vector modulus as field variable. The conceptual implications of this formalism are that the nonequivalence between the time-averaged Poynting vector and the squared-field amplitude modulus is naturally manifested as a consequence of interface effects. Also, two practical implications are considered: first, the exact transmittance is compared with that given by Beer's Law, employed commonly in experiments. The departure among them can be significative for certain material parameter values. Second, when the exact reflectance is studied for negative permittivity slabs, it is shown that the high reflectance can be diminished if a small amount of absorption is present.     

含气泡液体中声传播的解析解及其强非线性声特性

声波在含气泡的液体中传播时,气泡的受迫振动会引起强的声散射,并且由于振动的非线性,使得气泡产生的次级波不仅含有基频成分,而且还会有高次谐波。本文从理论上描述了气泡个数随尺并给出了含气泡液体的等效非线性声参数Ｂ／Ａ的计算公式理论与已有的实验观测符合较好,文中对含气泡水的声速和声衰减等特性也进行了讨论。     

一种时延范德波尔电磁系统中的复杂行为(Ⅰ)——分岔与混沌现象

建立了一种可积的无穷维系统——时延范德波尔电磁系统，采用Poincaré映射分析了系统随参数E和λ变化发生的分岔与混沌现象，发现这种时延系统具有复杂的非线性动力学特性，例如吸引子共存、间歇性混沌、类似边界碰撞分岔通向混沌以及周期增加的现象.在研究系统时间混沌行为的同时，还对空间混沌行为进行了初步分析，通过描绘空间分布图发现时延范德波尔电磁系统随参数E和λ变化时，在空间中会呈现出周期和混沌等不同的图案. 关键词： 分岔 混沌 无穷维系统 时延范德波尔电磁系统     

Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation

In this paper,the generalized Boussinesq wave equation u tt-uxx+a(um) xx+buxxxx=0 is investigated by using the bifurcation theory and the method of phase portraits analysis.Under the different parameter conditions,the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained.     

Front propagation in chaotic and noisy reaction-diffusion systems: a discrete-time map approach

We study the front propagation in reaction-diffusion systems whose reaction dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We have examined the influence of chaos and noise on the front propagation speed and on the wandering of the front around its average position. Assuming that the reaction term acts periodically in an impulsive way, the dynamical evolution of the system can be written as the convolution between a spatial propagator and a discrete-time map acting locally. This approach allows us to perform accurate numerical analysis. They reveal that in the pulled regime the front speed is basically determined by the shape of the map around the unstable fixed point, while its chaotic or noisy features play a marginal role. In contrast, in the pushed regime the presence of chaos or noise is more relevant. In particular the front speed decreases when the degree of chaoticity is increased, but it is not straightforward to derive a direct connection between the chaotic properties (e.g. the Lyapunov exponent) and the behaviour of the front. As for the fluctuations of the front position, we observe for the noisy maps that the associated mean square displacement grows in time as t ^1/2 in the pushed case and as t ^1/4 in the pulled one, in agreement with recent findings obtained for continuous models with multiplicative noise. Moreover we show that the same quantity saturates when a chaotic deterministic dynamics is considered for both pushed and pulled regimes. Received 17 July 2001     

Interaction of a Hopf bifurcation and a symmetry-breaking bifurcation: Stochastic potential and spatial correlations

The multivariate master equation for a general reaction-diffusion system is solved perturbatively in the stationary state, in a range of parameters in which a symmetry-breaking bifurcation and a Hopf bifurcation occur simultaneously. Thestochastic potential U is, in general, not analytic. However, in the vicinity of the bifurcation point and under precise conditions on the kinetic constants, it is possible to define a fourth-order expansion ofU around the bifurcating fixed point. Under these conditions, the domains of existence of different attractors, including spatiotemporal structures as well as the spatial correlations of the fluctuations around these attractors, are determined analytically. The role of fluctuations in the existence and stability of the various patterns is pointed out.     

Superluminal propagation and information transfer: A statistical approach in the microwave domain

Signal velocity is calculated in a medium with negative group delay (NGD). By accounting for the medium and the detector noise sources, the time varying probability of error at the detector [Pe(t)$\mathit{Pe}(t)$] is evaluated in the NGD channel and a normal dispersion channel. The scheme in which Pe(t)$\mathit{Pe}(t)$ falls below a threshold at earlier time, implies faster information transfer. It is found that the signal velocity depends on the detector type and the relative noise strength of the detector with respect to the channel. Finally, it is shown that NGD channels can be useful in applications that are limited by the detector noise.     

Sound absorption of a double-leaf micro-perforated panel with an air-back cavity and a rigid-back wall: Detailed analysis with a Helmholtz-Kirchhoff integral formulation

So far the electro-acoustical equivalent circuit analysis has been widely used to analyse micro-perforated panel (MPP) absorbers, however, as for the double-leaf MPP the equivalent circuit analysis inevitably includes an approximation. In this paper, the sound absorption characteristics of a double-leaf MPP absorber backed by a rigid wall are analysed by wave theory using Helmholtz-Kirchhoff integral formulation to obtain a strict solution. The present wave theory is experimentally validated with existing measured results. The theory is also compared with the equivalent circuit solutions so that the differences between the two theories appear and the effect of the approximation is clarified. The comparison shows that the difference mainly appears in the vicinity of the resonance peaks: the differences occur in the resonance frequencies and the absorption coefficient at frequencies between the two resonance peaks.     

Fermi Resonances and Vibrational Spectrum of a Polyatomic Molecule XY4: an Algebraic Approach

A U(2) algebraic model is introduced for the spectrum of a molecule XY₄, where the interactions between the stretch and bend modes are described by T_d symmetric Fermi resonance terms. The presented algebraic model in a limit corresponds to another model in recent literature. The vibrational spectrum of methane (CH₄) measured recently with modern spectroscopy techniques is employed to test those models. The obtained standard deviation between the observed and the calculated vibrational energy levels in the algebraic model is smaller than that in the corresponding model.     

Wave propagation in a waveguide with continuous right-angled corners: Numerical simulations and experiment measurements

This paper studied the acoustic wave propagation in a waveguide with continuous right-angled corners, with emphasis on the effect brought by the distance between the corners. The numerical analyses showed that at middle to high frequencies, the transmission loss (TL) of a multi-cornered waveguide was 2–5 dB higher than that of single-cornered and varied with frequency. To explain the performance at peaks and dips in the TL curve, analyses on eigenmodes and sound intensity distribution were conducted. The performance of multi-cornered waveguides was experimentally investigated, which fit well with the numerical results. The present study indicates that, for a waveguide with continuous corners, its acoustic performance is not simply a “summation” of two individual single-cornered ones. Both the standing wave modes and the evanescent modes between the corners lead to its complicated frequency performance.     

A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation

The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main harmonic part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium.     

Dual energy time reversed elastic wave propagation and nonlinear signal processing for localisation and depth-profiling of near-surface defects: a simulation study

Nonlinear Elastic Wave Spectroscopy (NEWS) relies on the activation of defects by wave energy that propagates through the medium. In general, the response of activated defects will not scale linearly with the excitation amplitude, and the resulting nonlinear signatures can be identified and used for quality inspection. The efficiency of NEWS based inspection methods is therefore intrinsically linked to the locally deposited activation energy at the defect zone and the ability to generate nonlinear signatures that exceed the noise level of acquisition. Time Reversal techniques allow focusing of high levels of energy in small areas, and are consequently very useful for the local activation of defected zones. In this report, numerical simulations are reported showing the potential of a combination consisting of dual energy reciprocal Time Reversal and nonlinearity filtering using the Scaling Subtraction Method. The method is applied to the detection of planar near-surface defects parallel to the surface in a 2D domain. The results are evaluated for sweep excitation at different frequency ranges; for point-like receiver as well as extended transducers, and for in-plane as well as out-of-plane focusing. The observable nonlinear response at the surface is linked to an effective nonlinearity within the medium based on the defect geometry and the distribution of the local stresses.     

Adsorption and interfacial phenomena of a Lennard-Jones fluid adsorbed in slit pores: DFT and GCMC simulations

ABSTRACT

Confinement of fluids in porous media leads to the presence of solid–fluid (SF) interfaces that play a key role in many different fields. The experimental characterisation of SF interfacial properties, in particular the surface tension, is challenging or not accessible. In this work, we apply mean-field density functional theory (DFT) to determine the surface tension and also density profile of a Lennard-Jones fluid in slit-shaped pores for realistic amounts of adsorbed molecules. We consider the pore walls to interact with fluid molecules through the well-known 10-4-3 Steele potential. The results are compared with those obtained from Monte Carlo simulations in the Grand Canonical Ensemble (GCMC) using the test-area method. We analyse the effect on the adsorption and interfacial phenomena of volume and energy factors, in particular, the pore diameter and the ratio between SF and fluid–fluid dispersive energy parameters, respectively. Results from DFT and GCMC simulations were found to be comparable, which points to their reliability.