Longitudinal waves in one dimensional non-uniform waveguides

Wave approach is used to analyze the longitudinal wave motion in one dimensional non-uniform waveguides.With assumptions of constant wave velocity and no wave conversion,there exist four types of non-uniform rods and corresponding traveling wave solutions are investigated.The obtained results indicate that the kinetic energy is preserved as a constant and the wave amplitude is inversely proportional to square root of the cross-sectional area of the rod.Under certain condition,there exists a cut-off frequency for the rod with variation in geometric or material properties,below which waves do not propagate along the non-uniform rod.For the rod with arbitrary variable cross-section, the conclusions are similar if the wave frequency is high enough.And a series solution of the wave motion is presented.

Dynamic symmetry breaking and structure-preserving analysis on thelongitudinal wave in an elastic rod with a variable cross-section

The longitudinal wave propagating in an elastic rod with a variable cross-section owns wide engineering background,in which the longitudinal wave dissipation determines some important performances of the slender structure.To reproduce the longitudinal wave dissipation effects on an elastic rod with a variable cross-section,a structure-preserving approach is developed based on the dynamic symmetry breaking theory.For the dynamic model controlling the longitudinal wave propagating in the elastic rod with the variable cross-section,the approximate multi-symplectic form is deduced based on the multi-symplectic method,and the expression of the local energy dissipation for the longitudinal wave propagating in the rod is presented,referring to the dynamic symmetry breaking theory.A structure-preserving method focusing on the residual of the multi-symplectic structure and the local energy dissipation of the dynamic model is constructed by using the midpoint difference discrete method.The longitudinal wave propagating in an elastic rod fixed at one end is simulated,and the local/total energy dissipations of the longitudinal wave are investigated by the constructed structure-preserving scheme in two typical cases in detail.

A family of solutions of the time–space fractional longitudinal wave equation

In this article,we have studied a nonlinear time–space fractional longitudinal wave equation in the context of the conformable fractional derivative.Through the soliton ansatz method and a direct integration approach with the symmetry condition,new soliton and solitary wave solutions are derived.Furthermore,the existing conditions of these obtained solutions are also given in this text.These new results add to the existing literature.We believe that they can provide a new window into the understanding of this model.

A study on stochastic longitudinal wave equation in a magneto-electro-elastic annular bar to find the analytical solutions

In this paper,we set up dynamic solitary perturb solutions of a unidirectional stochastic longitudinal wave equation in a magneto-electro-elastic annular bar by a feasible,useful,and influential method named the dual(G’/G,1/G)-expansion method.Computer software,like Mathematica,is used to complete this discussion.The obtained solutions of the proposed equation are classified into trigonometric,hyperbolic,and rational types which play an important role in searching for numerous scientific events.The technique employed here is an extension of the(G’/G)-expansion technique for finding all previously discovered solutions.To illustrate our findings more clearly,we provide 2D and 3D charts of the various recovery methods.We then contrasted our findings with those of past solutions.The graphical illustrations of the acquired solutions are singular periodic solitons and kink solitons which are added at the end of this paper.

SCATTERING OF A GRAZING LONGITUDINAL WAVE PULSE BY A RIBBON-TYPE CRACK—THE SECOND-ORDER APPROXIMATE SOLUTION

Scattering of an incident grazing longitudinal ultrasonic wave pulse by a traction - free ribbon - type crack in solid is theoretically analyzed. An exact series solution of the scattered field is obtained by iteration. Each term of the series corresponds roughly to one of the rescattering processes by the respective crack tips. The first two terms, which combine to form the second order approximate solution, are discussed in detail. This 2nd - order solution includes scattered cylindrical longitudinal waves, cylindrical shear waves , head waves and surface waves on the crack surfaces, and it gives good description of the early - time wave field.

SCATTERING OF A GRAZING LONGITUDINAL WAVE PULSE BY A RIBBON-TYPE CRACK—EXPERIMENTAL VERIFICATION BY THE PHOTOELASTIC METHOD

By using the dynamic photoelastic method and our technique of fabricating an internal crack in solid , the scattered waves of incident grazing longitudinal ultrasonic wave pulse by a ribbon-type crack are ob-served and analyzed . In particular, the distribution of the intensity of the scattered head wave is measured quantitatively . The experimental results fairly agree with the theoretical ones given in ref. [ 1 ] .

Linear Analysis of Obliquely Propagating Longitudinal Waves in Partially Spin Polarized Degenerate Magnetized Plasma

Linear analysis of low frequency obliquely propagating electrostatic waves in a partially spin polarized degenerate magnetized plasma is presented. Using Fourier analysis, a general linear dispersion relation is derived for low frequency electrostatic lower hybrid(LH) wave, ion acoustic(IA) wave and ion cyclotron(IC) wave in the presence of electron spin polarization. It is found that the electron spin polarization gives birth to a new spin-dependent wave(spin electron acoustic wave) in the spectrum of these waves. Further, the electron spin polarization also causes drastic shifts in the frequency spectrum of these waves. These effects would have a strong bearing on wave phenomena in degenerate astrophysical plasmas.

Wave-induced flow of pore fluid in a cracked porous solid containing penny-shaped inclusions

An aim of current study is to analyze the contribution of reflected longitudinal waves to wave-induced fluid flow(WIFF) in the cracked porous solid.Initially,we investigate the time harmonic plane waves in cracked porous solid by employing the mathematical model proposed by Zhang et al.(2019).The solution is obtained in form of the Christoffel equations.The solution of the Christoffel equations indicates that there exist four(three dilatational and one shear) waves.These waves are attenuated in nature due to their complex and frequency-dependent velocities.The reflection coefficients are calculated at the sealed pore stress-free surface of cracked porous solid for the incidence of P1 and SV waves.It is found that three longitudinal waves contribute to WIFF and the contribution of these waves to the induced fluid in the cracked porous solid is analyzed using the reflection coefficients of these longitudinal waves.We analytically show that the fluid flow induced by these longitudinal waves is linked directly to their respective reflection coefficients.Finally,a specific numerical example is considered to discuss and to depict the impact of various parameters on the characteristics of propagation like phase velocity/attenuation,reflection coefficients and WIFF of longitudinal waves.

DETECTION OF LONGITUDINAL DEFECT IN PIPES USING TORSIONAL MODES

The multi-modes and disperse characteristics of torsional modes in pipes are investigated theoretically and experimentally. At all frequencies, both phase velocity and group velocity of the lowest torsional mode T（0,1） are constant and equal to shear wave velocity. T（0,1） mode at all frequencies is the fastest torsional mode. In the experiments, T（0,1） mode is excited and received in pipes using 9 thickness shear vibration mode piezoelectric ceramic elements. Furthermore, an artificial longitudinal defect of a 4 m long pipe is detected using T（0,1） mode at 50 kHz. Experimental results show that it is feasible for longitudinal defect detection in pipes using T（0,1） mode of ultrasonic guided waves.

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase. The finite element formulation based on this variational principle is also derived. As the functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in the time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations and, as a numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide further understanding of the wave propagation in porous media.

High sensitive piezoelectric quartz crystal liquid density sensor

We report for the first time a cleavage phenomenon in the resonant peak of a piezoelectric quartz crystal(PQC) in liquid phase.In the presence of a strong longitudinal wave effect,an additional resonant peak appears in the conductance-frequency curve.With gradually increasing liquid density,the additional peak moves from low to high frequency region then disappears.The frequency of the additional resonant peak is sensitive to the change in liquid density.The frequency shift of the additional peak is linear with the liquid density in a given range.For a 5 MHz PQC with a reflection distance of 16 mm for longitudinal wave,the sensitivity to liquid density is 2.61×10^6 Hz g^-1 cm^3.The overlap between the primary resonant peak and the additional resonant peak causes a decrease in the intensity of the former and an increase in the intensity of the latter.In a combined impedance analysis method,the changes in surface mass loading,density and viscosity of the liquid were monitored simultaneously by a PQC sensor.

An Unexpected Frequency Response of A Piezoelectric Quartz Crystal Sensor to the Density and Viscosity of the Liquid

An unexpected frequency response for a piezoelectric quartz crystal (PQC) sensor to liquid density and viscosity was reported. For a PQC oscillating in a liquid phase, the frequency shifts (?f ) show a wave-shape response to liquid density (ρ) and viscosity (η) in fine structure, if the longitudinal wave effect was not eliminated. This result is different from the well-known linear relationship between of ?f and (ρη)1/2. An oscillating frequency-temperature curve of the sensor was observed and explained.

Neutrino Temporal Oscillation

We conjecture the existence of massless neutrinos that are in the line of Standard Model (unable to account for the neutrino mass) but have characteristics that are not accounted for the Standard Model: they use a shorter radial path than the photon and possess bosonic flavors, considered like bosons instead of fermions. We call this theory “neutrino temporal oscillation”. Faced with some experimental comparisons solar neutrinos, neutrinos from SN 1987A, cosmological neutrinos, the theory gives better results, explanations and sense than the complicated theory of neutrino oscillations (transformism). The deficit of detection of solar neutrinos would have been blindly attributed to the “neutrino oscillation” by physicists who quickly concluded that the neutrino and the photon follow the same transverse path. The “OPERA” experiment which measured the speed of neutrinos in 2011 resulted, after a “superluminal” saga, in neutrino speeds consistent with the speed of light, in data that the three existing types of neutrinos cannot explain, with the final outcome of a fourth “sterile” neutrino with non-standard interaction. OPERA findings aren’t just in conflict with existing theory, but other measurements as well. For example, a study from the Kamiokande II experiment in Japan of the supernova SN1987A found that light and neutrinos that departed this exploded star arrived at Earth within hours of each other. Even though measurements of the neutrinos emitted by this supernova strongly suggest that their speeds differ from light by less than one part in a billion, the fact remains that two types of data were collected, and that only one was retained to be consistent with the existing theory. Thus, the OPERA observation is in conflicts with the result of SN1987A, which itself is highly doubtful. And what about the neutrinos and antineutrinos born during the big bang, except that they were never detected and there is nothing to indicate that their speed could be other than that of light. Neutrino physics seems sick, belief is transformed into evidence. The theory of “Neutrino temporal oscillation” shows hint that massless neutrinos can take a shortcut through the three spatial dimensions of the space-time that we know. It represents within the Standard Model an open window on a “new physics” that has a connection with physical reality.

Momentum Transfer on Underwater Shock Generation Induced by Pulsed Laser Irradiation with Thin Metal

The present paper has investigated the momentum transport phenomena of underwater shock wave generation in terms of photo-acoustic wave with a very thin metal. The shock wave was induced by a pulsed-laser irradiation. In order to clarify the momentum transport mechanics in this phenomenon, we have been considered the momentum and energy transport from laser to metal, and metal to water. A numerical solution of thermo-elastic wave in metal has been obtained to estimate a fundamental gain of the longitudinal wave. Then, the underwater shock wave phenomena have been analyzed by adapting compressible fluid dynamics with suitable boundary condition between the solid and liquid. We had performed an experiment as well and observed the shock wave with optical system. The aim of the research is to estimate the underwater shock wave strength theoretically. The metal region was calculated by Laplace transformation of heat conduction and wave equations. The water region was simulated by MacCormack’s method. Some of boundary conditions have been examined and the acceleration condition has been adopted at the interface. The simulated results show a good agreement with experimental result, consequently the momentum transfer mechanism from longitudinal wave to underwater shock wave has been cleared in the present report.

RAPID AND NONDESTRUCTIVE MEASUREMENT SYSTEM FOR WELDING RESDlUAL STRESS BY ULTRASONIC METHOD

Traditional methods of residual stress measurement are generally destructive or semi-destructive, as well as expensive, time-consuming and complex to implement. With the new development of welded structure, traditional methods can not satisfy the need of full life task management. So the acoustical theory is introduced, since the ultrasonic technique provides a useful nondestructive tool in the evaluation of stresses. In this study an ultrasonic stress measurement experimental installation is established, which consists of a special transducer, a signal emission unit and a signal recipient processing unit. Longitudinal critically refracted wave is selected as the measurement wave mode. The supporting software is programmed by Labview software. The longitudinal residual stress and transverse residual stress of twin wire welded plate are measured by this installment, in which the measuring process is real-time, quick and nondestructive. The experiment results indicate that the system can satisfy the need of life evaluation for welded structure. The system is light and portable.

Nonlocal Theory of High-Temperature Superconductivity

The Boltzmann local physical kinetics forecasts the destruction of SC regime because of the heat movement of particles. Then, the most fundamental distinction between a strange metal and a conventional metal is the absence of well-defined quasi-particles. Here, we show that the mentioned “quasi-particles” are solitons, which are formed as a result of self-organization of ionized matter. Shortcomings of the Boltzmann physical kinetics consist in the local description of the transport processes on the level of infinitely small physical volumes as elements of diagnostics. The non-local physics leads to the theory superconductivity including the high temperature diapason. The generalized non-local non-stationary London’s formula is derived.

Role of the spin anisotropy of the interchain interaction in weakly coupled antiferromagnetic Heisenberg chains

In quasi-one-dimensional(q1D) quantum antiferromagnets, the complicated interplay of intrachain and interchain exchange couplings may give rise to rich phenomena. Motivated by recent progress on field-induced phase transitions in the q1D antiferromagnetic(AFM) compound YbAlO3, we study the phase diagram of spin-1/2 Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations,and investigate the role of the spin anisotropy of the interchain coupling on the ground state of the system. We find that the Ising anisotropy of the interchain coupling can significantly enhance the longitudinal spin correlations and drive the system to an incommensurate AFM phase at intermediate magnetic fields, which is understood as a longitudinal spin density wave(LSDW). With increasing field, the ground state changes to a canted AFM order with transverse spin correlations. We further provide a global phase diagram showing how the competition between the LSDW and the canted AFM states is tuned by the Ising anisotropy of the interchain coupling.

Longitudinal leaky surface acoustic wave on Y-rotated cut quartz substrates

The properties of Quasi-longitudinal leaky surface acoustic wave(QLLSAW) on Y-rotated cut quartz substrates were presented. The phase velocity of QLLSAW on the quartz substrate along some orientations can be up from 6200 m/s to 7100 m/s, circa 100% above that of regular SAW. Both theoretical and experimental results show that QLLSAW propagating along some promising orientations for SAW devices are of small power flow angle and low tem-perature coefficient, for example, along the Euler angle (0°155.25°? 42°?, the measurements of phase velocity and temperature coefficient of delay of QLLSAW are 6201 m/s and 12.9 ppm/℃. The experimental results show that QLLSAW had little absorption by liquid loading on the substrate surface, which proved that the direction of particle motion is the same as wave vector and parallel to the surface of the substrates, i.e., the wave is of the properties of longitudinal wave.

The effect of type waves on vibroseismic implementation of changes properties of rock, oil viscosity, oil compound composition, and enhanced oil recovery

Based on the results of laboratory studies,the frequency of 35 Hz in longitudinal waves and 20 Hz in circular waves is the optimum frequency that can increase the maximum oil recovery.Coreflooding test results before the vibration effect can increase oil production by 51.96%and reduce the residual oil saturation by 59.03%The surprising results when the vibration effect was applied to the coreflooding test method with P wave types continuously succeeded in increasing oil production by 60.54%,inter-mittent P waves by 63.53%and circular waves by 64.76%,while also reducing Sor by 48.49%in continuous P waves,intermittent P waves at 44.81%and C waves at 43.3%,The P wave type vibrational method has an increase in oil gain by 16%,intemittently by 22%,Sor reduction by 18%and 24%,in circular wave oil gain increases by 25%,and Sor decreases by 27%from before the vibration effect given.Besides vibration can change the physical properties of rocks,among others;permeability has increased by 7%using P waves continuously,intermittently by 31%and C waves by 4%;porosity of 5.88%with P waves contin-uously,intermittently of 6.46%and circular waves of 4.63%;grain size before vibration of 45.16 um after vibration using continuous P waves of 42.01μum,intermittently of 4798μum,and circular of 50.46μum;changes in oil composition to contain more alkanes,and lack of aromatic compounds;oil viscosity increased by 3%with continuous P waves,intermittent of 5%,and circular 61%.The new point from this paper is analyzing the vibroseismic effect by using SEM images in terms of the watershed segmentation of the Rabbani algorithm compared to lab results,which have an error rate of under 2%,and a review of oil composition by the GC-MS method.

Influence of the connecting condition on the dynamic buckling of longitudinal impact for an elastic rod

The stress wave propagation law and dynamic buckling critical velocity are formulated and solved by considering a general axial connecting boundary for a slender elastic straight rod impacted by a rigid body. The influence of connecting stiffness on the critical velocity is investigated with varied impactor mass and buckling time. The influences of rod length and rod mass on the critical velocity are also discussed. It is found that greater connecting stiffness leads to larger stress amplitude, and further results in lower critical velocity. It is particularly noteworthy that when the connecting stiffness is less than a certain value, dynamic buckling only occurs before stress wave reflects off the connecting end. It is also shown that longer rod with larger slenderness ratio is easier to buckle, and the critical velocity for a larger-mass rod is higher than that for a lighter rod with the same geometry.