Flexural wave motion in beam-type disordered periodic systems: Coincidence phenomenon and sound radiation

This paper deals with flexural wave motion in uniform beam-type periodic systems whose repeating units are identical finite beams with multiple beam-length disorders. A general expression derived for the propagation constants has been employed to study its variation with frequency for a beam system having 4-span disordered repeating units. This is helpful in understanding flexural wave motion in disordered periodic beams. Free flexural waves have been studied as wave groups consisting of a large number of harmonic components of different wavelengths, phase velocities and directions. Phase velocities have been computed and plotted for different frequencies in the propagation zones in which the free waves progress without attenuation. This has been found to be useful in understanding and predicting the coincidence phenomenon in disordered periodic beams under convected pressure field loading. The excitation of wave groups in disordered periodic beam-type systems by a slow (subsonic) convecting pressure field can include fast (supersonic) moving flexural wave components which can radiate sound. It has been pointed out that sound radiation from a disordered periodic beam (or plate) can be quite different as compared to that from a periodic beam under similar convected pressure field loading.     

Flexural waves in graphene and 2D supracrystals

A method has been proposed for the calculation of the phase and group velocities of flexural waves in one-atom-thick graphene-like structures. The method is based on the expression for the flexural modulus in terms of the two-dimensional Young??s modulus. The method is also applicable to studying the characteristics of swelling waves in single-walled nanotubes of a sufficiently large diameter.     

Calculation of the phase velocities of three-dimensional flexural waves in isotropic cylindrical bars and shells using the Debye and Debye-type potentials

Using the Debye and Debye-type potentials, two representations of the vector potential of the displacement vector are considered for isotropic cylindrical bars and shells. With this approach, characteristic equations are obtained for the wavenumbers of three-dimensional flexural waves propagating in the aforementioned bodies; the phase velocities of such waves are calculated.

     

Guided waves in a transversely isotropic cylinder immersed in a fluid

Propagation of flexural guided waves in a fluid-loaded transversely isotropic cylinder is studied. Numerical results are presented for a cobalt cylinder immersed in water. The phase velocities are not significantly affected except for several modes in which the energy leakage occurs into the fluid over certain frequency ranges. Attenuation spectra for the leaking modes are plotted.     

ANALYSIS OF THE FLEXURAL VIBRATION OF A THIN-PLATE BOX USING A COMBINATION OF FINITE ELEMENT ANALYSIS AND ANALYTICAL IMPEDANCES

Many practical built-up thin-plate structures, e.g., a modern car body, are essentially assemblies of numerous thin plates joined at their edges. The plates are so thin that they invariably support the weight of the structure and machinery using their substantial in-plane stiffness. Consequently, vibrational power injected into the structure from sources mounted at these stiff points is controlled by high impedance long-wavelength in-plane waves in the plates. As the long in-plane waves propagate around the structure, they impinge upon the numerous structural joints at which short-wavelength flexural waves are generated in adjoining plates. These flexural waves have much lower impedance than the in-plane waves. Hence, the vibration of thin-plate structures excited at their stiff points develops into a mixture of long in-plane waves and short flexural waves. In a previous paper by the same authors, a numerically efficient finite element analysis which accommodated only the long in-plane waves was used to predict the forced response of a six-sided thin-plate box at the stiff points. This paper takes that finite element analysis and, drawing on theory developed in two additional papers by the same authors, couples analytical impedances to it in order to represent the short flexural waves generated at the structural joints. The parameters needed to define these analytical impedances are identified. The vibration of the impedances are used to calculate estimates of the mean-square flexural vibration of the box sides which compare modestly with laboratory measurements. The method should have merit in predicting the vibration of built-up thin-plate structures in the so-called “mid-frequency” region where the modal density of the long waves is too low to allow confident application of statistical energy analysis, yet the modal density of the short flexural waves is too high to allow efficient finite element analysis.     

Effect of kinesin velocity distribution on slow axonal transport

The goal of this paper is to investigate the effect that a distribution of kinesin motor velocities could have on cytoskeletal element (CE) concentration waves in slow axonal transport. Previous models of slow axonal transport based on the stop-and-go hypothesis (P. Jung, A. Brown, Modeling the slowing of neurofilament transport along the mouse sciatic nerve, Physical Biology 6 (2009) 046002) assumed that in the anterograde running state all CEs move with one and the same velocity as they are propelled by kinesin motors. This paper extends the aforementioned theoretical approach by allowing for a distribution of kinesin motor velocities; the distribution is described by a probability density function (PDF). For a two kinetic state model (that accounts for the pausing and running populations of CEs) an analytical solution describing the propagation of the CE concentration wave is derived. Published experimental data are used to obtain an analytical expression for the PDF characterizing the kinesin velocity distribution; this analytical expression is then utilized as an input for computations. It is demonstrated that accounting for the kinesin velocity distribution increases the rate of spreading of the CE concentration waves, which is a significant improvement in the two kinetic state model.     

Natural beam focusing of non-axisymmetric guided waves in large-diameter pipes

The propagation of non-axisymmetric guided waves in larger diameter pipes is studied in this paper by treating the guided waves as corresponding Lamb waves in an unwrapped plate. This approximation leads to a simpler method for calculating the phase velocities of hollow cylinder guided waves, which reveals a beam focusing nature of non-axisymmetric guided waves generated by a partial source loading. The acoustic fields in a pipe generated by a partial-loading source includes axisymmetric longitudinal modes as well as non-axisymmetric flexural modes. The circumferential distribution of the total acoustic field, also referred as an angular profile, diverges circumferentially while guided waves propagate with dependence on such factors as mode, frequency, cylinder size, propagation distance, etc. Exact prediction of the angular profile of the total field can only be realized by numerical calculations. In particular cases, however, when the wall thickness is far less than the cylinder diameter and the wavelength is smaller than or comparable to the pipe wall thickness, the acoustic field can be analyzed based on the characteristics of Lamb waves that travel along a periodic unwrapped plate. Based on this assumption, a simplified model is derived to calculate the phase velocities of non-axisymmetric flexural mode guided waves. The model is then applied to discussions on some particular characteristics of guided-wave angular profiles generated by a source loading. Some features of flexural modes, such as cutoff frequency values are predicted with the simpler model. The relationship between the angular profiles and other factors such as frequency, propagation distance, and cylinder size is obtained and presented in simple equations. The angular profile rate of change with respect to propagation distance is investigated. In particular, our simplified model for non-axisymmetric guided waves predicts that the wave beam will converge to its original circumferential shape after the wave propagates for a certain distance. A concept of "natural focal point" is introduced and a simple equation is derived to compute the 1st natural focal distance of non-axisymmetric guided waves. The applicable range of the simplified equation is provided. Industrial pipes meet the requirement of wall thickness being far less than the pipe diameter. The approximate analytical algorithms presented in this paper provides a convenient method enabling quick acoustic field analysis on large-diameter industrial pipes for NDE applications.     

Processing an acoustic microscope’s spatiotemporal signal to determine the parameters of an isotropic layer

This paper presents a method for measuring the thickness and velocities of body waves and the density of an isotropic layer by a pulse scanning acoustic microscope. The method is based on recording the microscope signal as a function of the displacement magnitude of the focused ultrasonic transducer along its axis perpendicular to the sample surface and on the decomposition of the recorded 2D spatiotemporal signal into the spectrum of plane pulse waves. The velocities of the longitudinal and transverse waves and the layer’s thickness are calculated from the relative delays of the components of the spectrum of plane waves reflected from the surfaces of the layer and the density is computed by the amplitudes of these components. An experimental investigation of a test sample in the form of a glass plate carried out in the 50-MHz range shows that the error in measuring the thickness and velocities of body waves does not exceed 1% and the density measurement error does not exceed 10%.     

Excitation of chorus-like waves by temperature anisotropy in dipole research experiment (DREX): A numerical study

Due to their significant roles in the radiation belts dynamics, chorus waves are widely investigated in observations,experiments, and simulations. In this paper, numerical studies for the generation of chorus-like waves in a launching device,dipole research experiment(DREX), are carried out by a hybrid code. The DREX plasma is generated by electron cyclotron resonance(ECR), which leads to an intrinsic temperature anisotropy of energetic electrons. Thus the whistler instability can be excited in the device. We then investigate the effects of three parameters, i.e., the cold plasma density nc, the hot plasma density nh, and the parallel thermal velocity of energetic electrons, on the generation of chorus-like waves under the DREX design parameters. It is obtained that a larger temperature anisotropy is needed to excite chorus-like waves with a high nc with other parameters fixed. Then we fix the plasma density and parallel thermal velocity, while varying the hot plasma density. It is found that with the increase of nh, the spectrum of the generated waves changes from no chorus elements, to that with several chorus elements, and then further to broad-band hiss-like waves. Besides, different structures of choruslike waves, such as rising-tone and/or falling-tone structures, can be generated at different parallel thermal velocities in the DREX parameter range.     

无旋性前进重力波传递在均匀流中的Lagrangen解析解与试验验证Ⅱ.试验验证

针对文献[1]中的无旋性自由表面周期性规则前进重力波传递在均匀流中,本文以与前进波波向同向与反向的均匀流两种特例情况,进行试验测量,所得的波形曲线、流速分布、流体质点的运动轨迹与运动周期及其质量传输速率与Lagrange平均高程等特性,均与文献[1]中全以Lagrange方式所得的三阶解结果符合得很好.这证实本研究取定的标注流体质点的参数,正好为其在原静止水中的位置坐标值.同时亦证实波流场中由流体质点所构成的波形曲线,其波长皆同于(纯)前进波,而其传播速度为(纯)前进波波速与均匀流流速之和是具Doppler效应的;而流体质点的运动周期与其运动周期平均高程、及其质量传输速率扣掉均匀流流速等,都与(纯)前进波的相符.另外,亦揭示出流体质点的运动轨迹,在前进波波向与均匀流同向中,当流体质点在波谷断面处时沿前进波波向的流速分量为反向、零与正向时,则其形状分别为朝波向前进的扁长辐状余摆线、在波谷断面处成尖点朝下的滚轮状线与短辐形余摆线;而在前进波波向与均匀流反向中,当流体质点的质量传输速率为沿前进波波向为正向与零时,则其形状分别为朝波向前进的缩短的扁长辐形余摆线与长轴在前进波波向上椭圆形封闭曲线;而当流体质点的质量传输速率为反前进波波向,但质点在波峰断面处时沿前进波波向的流速分量分别为正向、零与反向时,则其形状分别为反波向前进的倒扁长辐形余摆线、在波峰断面处成尖点朝上的倒滚轮状线与倒短辐形余摆线.     

表面张力-重力短峰波作用的海底边界层速度二阶解

依据最近提出的三阶表面张力-重力短峰波理论,通过求解经典的Prandtl边界层方程,给出海底边界层速度的二阶解析解,为确定海底边界层的质量输运提供了一个必备的先行理论基础.     

Active control of the plate energy transmission in a semi-infinite ribbed plate

Active control of the plate flexural wave transmission through the beam in a semi-infinite beam-reinforced plate is analytically investigated. The ribbed plate is modeled as a continuous system, using equations of motion to describe the plate in flexure and the beam in both flexure and torsion. The maximum transmission of the plate flexural waves through the reinforcing beam is found to occur at resonance frequencies corresponding to the optimal coupling between the plate flexural waves and the flexural and torsional waves in the beam. A single control force is applied to the beam, and a cost function is developed to attenuate the far-field flexural energy transmission. It can be observed that the transmission peaks corresponding to the flexural resonances in the beam are reduced. Similarly, the transmission peaks corresponding to the torsional resonance conditions in the beam can be attenuated using a single control moment applied to the beam. Significant attenuation of all the resonance peaks in the flexural wave transmission can also be achieved with the application of a single force and a single moment collocated on the beam. In this paper, the feasibility of attenuating the flexural wave transmission due to both the flexural and torsional resonance conditions by using a single point force and point moment collocated on the beam is demonstrated.     

Faster-than-light particles: An alternative view

The existence of a wave motion analogous to the electromagnetic waves, but with wave velocity less than that of light, is postulated. It is suggested that these waves, which transport energy and momentum with subluminal velocities, could replace the concept of faster-than-light particles. The possibility of the neutrinos as being the source of the waves is suggested for further investigation.     

Crack detection in beams by wavelet analysis of transient flexural waves

In this paper, a method of crack detection in beam is provided by wavelet analysis of transient flexural wave. Firstly, we introduce a rotational spring in the cracked-beam model, and calculate the transient flexural wave propagation by the Reverberation Matrix Method. Secondly, at any point in this beam, the arrival time of waves with different group velocities can be identified by means of analysis of wavelet transform. From the signal of mid-frequency flexural wave extracted by wavelet transform, we can exactly determine the existence and position of crack in the beam. Here, a similar experiment is also produced to test the transient strain signal in beam, and the result after wavelet transform analysis is shown in accord with the theoretical one. Therefore, a powerful method is proved by the theoretical and experimental studies on the cracked beam, which can detect the crack accurately utilizing the wavelet analysis of the mid-frequency flexural wave.     

Stability of capillary waves with arbitrary symmetry on the surface of a jet in a longitudinal electric field periodically varying with time

The Mathieu differential equation for the evolution of the amplitudes of arbitrarily symmetric capillary waves (with arbitrary azimuthal numbers) propagating over the surface of a incompressible dielectric cylindrical liquid jet is analyzed. The jet is placed in a time-periodic uniform electric field that is parallel to the symmetry axis of the jet unperturbed by the wave flow. It is found that the time-varying electric field pressure parametrically builds up both axisymmetric waves on the jet surface, flexural waves, and flexural deformation waves. At a fixed frequency of the external field, waves with different wavelengths and symmetries (different azimuthal numbers) may build up simultaneously in the main demultiplication resonance, as well as in secondary and tertiary resonances. The parametric buildup of flexural deformation waves has a threshold relative to the external field frequency: it takes place at the field frequency exceeding a certain value depending on the jet radius and physicochemical properties of the liquid.     

Wave motion of incompressible turbulent fluid

Evolution of small disturbances in a fully developed incompressible turbulent flow is considered on the base of the transport equation for the single-point probability density function (PDF) of velocity fluctuations. It is shown that at high frequencies this equation is similar to the Vlasov equation for charged plasma in a self-consistent electromagnetic field having longitudinal wave solutions for turbulent stresses similar to Langmuir waves. It is found that the longitudinal waves of turbulent stresses have a constant phase velocity and can be damped, neutral, or growing waves, depending on the type of undisturbed probability density function of velocity fluctuations. The obtained result differs from the previously published solutions to this problem using the statistical moments closures according to which the wave disturbances should be neutral or damped. The possibilities of experimental observation of longitudinal waves of turbulent stresses are analyzed.     

A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation

A 2.5-dimensional method in frequency wave-number domain is developed to investigate the mode waves in a deviated borehole penetrating a transversely isotropic formation. The phase velocity dispersion characteristics of the fast and slow flexural mode waves excited by a dipole source are computed accurately at various deviation angles for both hard and soft formations. The sensitivities of the flexural mode waves to all elastic constants in a transversely isotropic formation are calculated. Numerical results show that, for a soft formation, the fast flexural mode wave is dominated by c66 at high deviation angles and low frequencies, while the slow flexural mode wave is dominated by c44 at the same conditions. Waveforms in time domain are also presented to support the conclusions.     

Collisions of solitons and vortex rings in cylindrical Bose-Einstein condensates

Interactions of solitary waves in a cylindrically confined Bose-Einstein condensate are investigated by simulating their head-on collisions. Slow vortex rings and fast solitons are found to collide elastically contrary to the situation in the three-dimensional homogeneous Bose gas. Strongly inelastic collisions are absent for low density condensates but occur at higher densities for intermediate velocities. The scattering behavior is rationalized by use of dispersion diagrams. During inelastic collisions, spherical shell-like structures of low density are formed and they eventually decay into depletion droplets with solitary-wave features. The relation to similar shells observed in a recent experiment by Ginsberg et al. [Phys. Rev. Lett. 94, 040403 (2005)] is discussed.     

Experimental analysis of flexural waves in river ice

Results of a full-scale experiment on reception of vibroacoustic signals excited in river ice by a pulsed source are discussed. The oscillograms of signals reveal the presence of air acoustic and bottom seismic waves, as well as flexural waves propagating in ice, which manifest themselves in the form of wave trains separated in arrival time. Experimental data are used to measure the group velocity and the damping decrement of flexural waves and the velocity of bottom-seismic waves. The theoretical estimate obtained for the group velocity of flexural waves in terms of the liquid-thin plate model agrees well with the value obtained from the experiment.     

Energy spreading,equipartition, and chaos in lattices with non-central forces

We numerically study a one-dimensional,nonlinear lattice model which in the linear limit is relevant to the study of bending(flexural)waves.In contrast with the classic one-dimensional mass-spring system,the linear dispersion relation of the considered model has different characteristics in the low frequency limit.By introducing disorder in the masses of the lattice particles,we investigate how different nonlinearities in the potential(cubic,quadratic,and their combination)lead to energy delocalization,equipartition,and chaotic dynamics.We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation.Beyond a certain energy threshold,when the cubic nonlinearity is present,the system is found to reach energy equipartition and total delocalization.On the other hand,when only the quartic nonlinearity is activated,the system remains localized and away from equipartition at least for the energies and evolution times considered here.However,for large enough energies for all types of nonlinearities we observe chaos.This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present,while the appearance of only quadratic nonlinearity leads to energy localization.Our results reveal a rich dynamical behavior and show differences with the relevant Fermi–Pasta–Ulam–Tsingou model.Our findings pave the way for the study of models relevant to bending(flexural)waves in the presence of nonlinearity and disorder,anticipating different energy transport behaviors.