Showing papers on "Longitudinal wave published in 2021"

Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with Pochhammer-Chree equation

Abstract: In this article, propagation of solitary wave solutions to the Pochhammer-Chree equation(PC) are investigated. Different kinds of solutions like bright-dark, kink, singular, hyperbolic, rational, trigonometric as well as Jacobi elliptic function solutions are obtained. The innovative methodology used to extract the solitary wave is known as Φ6-model expansion method. Moreover, the modulation instability (MI) analysis of governing equation is also discussed. Against the appropriate choices of parameters, two and three dimensional and contour graphs are also sketched. The obtained outcomes are more general and fresh and show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations.

Ray methods for nonlinear waves in fluids and plasmas

Abstract: Physical framework introductory concepts for wave motions Ray methods for linear waves Ray methods for nonlinear hyperbolic waves Ray method for the propagation of discontinuities generalized wavefront expansion for weak shocks small time analysis and shock stability Ray methods for nonlinear dispersive waves Ray methods for nonlinear dissipative waves interaction of dispersive waves interaction of hyperbolic waves.

Elastic bound state in the continuum with perfect mode conversion

Abstract: The partial or complete confinement of waves in an open system is omnipresent in nature and in wave-based materials and technology. Here, we theoretically analyze and experimentally observe the formation of a trapped mode with perfect mode conversion (TMPC) between flexural waves and longitudinal waves, by achieving a quasi-bound state in the continuum (BIC) in an open elastic wave system. The latter allows a quasi-BIC in a semi-infinite background plate when Fano resonance hybridizes flexural and longitudinal waves and balances their radiative decay rates. We demonstrate that when the Fabry-Perot resonance of the longitudinal wave is realized simultaneously, the TMPC formed by the elastic BIC approaches infinite quality factor. Furthermore, we show that quasi-BIC can be tuned continuously to BIC through the critical frequency of mode conversion, which offers the possibility of TMPC with an arbitrarily high quality factor. Our reported concept and physical mechanism open new routes to achieve perfect mode conversion with tunable high quality factor in elastic systems.

Morphology of oblique detonation waves in a stoichiometric hydrogen–air mixture

Abstract: Although the morphology of oblique detonation waves (ODWs) has been widely studied, it remains impossible to predict the wave systems in the initiation region, which is a critical component in promoting engine applications. Such wave systems are usually viewed as secondary ODWs or compression waves (CWs), introducing some structural ambiguities and contradictions with recent observations. In this study, ODWs are simulated numerically in a stoichiometric hydrogen–air mixture and their morphological features are analysed. To cover a wide range of flight conditions physically, the control parameters are the flight altitude , within which two special wave systems arise. One wave system indicates that the CW might induce an abrupt transition, and the other indicates that the classical secondary ODW might evolve into a normal detonation wave, another illustration of the well-known ‘detonation-behind-shock’ wave configurations. To clarify the mechanism of wave system variation, a geometric analysis of two characteristic heights demonstrates that the wave system could be predicted from the viewpoint of CW convergence. Moreover, analysis of the induction zone Mach number, compared with the corresponding Chapman–Jouguet Mach number, provides a criterion for the normal detonation wave formation. These semi-theoretical approaches collectively enhance our understanding of the wave system physically.

A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams:

Abstract: This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large-deformation ...

Reflection of plane harmonic wave in rotating media with fractional order heat transfer and two temperature

Abstract: The aim of the present investigation is to examine the propagation of plane harmonic waves in transversely isotropic homogeneous magneto thermoelastic rotating medium with fractional order heat transfer and two temperature. It is found that, for two dimensional assumed model, there exist three types of coupled longitudinal waves (quasi-longitudinal, quasi-transverse and quasi-thermal) in frequency domain. The amplitude ratios, energy ratios, phase velocities, specific loss, penetration depth, attenuation coefficients of various reflected waves are computed and depicted graphically. The conservation of energy at the free surface is verified. The effects of two temperature and fractional order parameter by varying different values are represented graphically

Analysis of plane wave propagation under the purview of three phase lag theory of thermoelasticity with non-local effect

Abstract: Present study characterizes the propagation of harmonic plane waves in Eringen's non-local thermoelastic medium. Three phase lag (TPL) theory of thermoelasticity has been applied to account for the interactions between elastic and thermal fields. Two sets of coupled longitudinal waves (elastic and thermal) and one independent vertically shear wave have been achieved. Longitudinal waves are found to be dispersive and experience attenuation. All these waves are found to be influenced by the elastic non-local parameter. Further shear-type wave obtains a critical frequency while the coupled longitudinal waves may face critical frequencies conditionally. High and low frequency asymptotes of physical fields have been calculated. By considering an illustrative example, numerical results have been computed to explore the physics of the problem. The results for the TPL model have been compared with those for the dual phase lag theory. The study reveals that the distribution of phase velocities and attenuation coefficients for the TPL model are significantly different from those of the dual phase lag models with respect to the frequency as well as non-local elastic parameter. TPL theory is found to be capable in predicting better results as compare to the dual phase lag theory of thermoelasticity.

Solitary dynamics of longitudinal wave equation arises in magneto-electro-elastic circular rod

Abstract: This paper examines the effectiveness of an integration scheme, which called the extended modified auxiliary equation mapping method in exactly solving a well-known non-linear longitudinal wave equ...

Solutions of a comprehensive dispersion relation for waves at the elastic interface of two viscous fluids

Abstract: Wave propagation in a system of two arbitrary fluids separated by a contaminated interface in the form of an insoluble monolayer is investigated. The effects of four parameters (density ratio, R ; kinematic viscosity ratio, V ; Marangoni number, P ; and squared wave-Reynolds number, σ ) on the solutions of a comprehensive dispersion relation for these waves are analyzed. In the first part of the manuscript, several special cases are considered wherein the comprehensive dispersion relation is modified to a simple polynomial equation and its numerical solutions are obtained for σ ∈ [ 0 , 1 ] . A bifurcation is observed at σ = σ b in two of the solutions in each case; and the system is shown to be overdamped for σ σ b , and underdamped for σ > σ b . The relative influences of { R , V , P } on σ b are also analyzed, and it is found that in general, σ b is a strong function of { R , V } , but a weak function of P . In the second part of the manuscript, numerical solutions of the comprehensive dispersion relation are obtained for waves in a decane-water system, in the limit of { P ≫ 1 , σ ≫ 1 } ; and these solutions are classified to correspond to a transverse wave or to a longitudinal wave. The presence of a maximum/minimum in the frequency of oscillation and in the damping rate is observed for the transverse/longitudinal waves. For both the transverse and longitudinal wave modes, the relative deviation of the numerical solution (obtained from the comprehensive dispersion relation) from the respective approximate solution (obtained from a simple dispersion relation) is calculated. The relative deviation, though small, cannot be neglected because it accounts for the effects of elasticity and of capillarity/gravity; and disregarding it in the analyses will fail to yield the inherent maximum/minimum in the frequency of oscillation and in the damping rate for the transverse/longitudinal waves.

On shock-induced heavy-fluid-layer evolution

Abstract: Investigation on the shock-induced finite-thickness fluid-layer evolution is very desirable but remains a challenge because it not only involves both the Richtmyer–Meshkov instability (RMI) and the Rayleigh–Taylor instability (RTI), but also strongly depends on the waves reverberated inside the layer. We experimentally and theoretically examined the evolution of a shocked gas layers with diverse layer thicknesses and amplitude combinations are created to explore the interfacial instabilities of the layer. When the initial fluid layer is thin, the two interfaces of the layer coalesce at a late time. The present study is the first to report that except for the RMI induced by a shock wave on the two interfaces, the rarefaction waves (RW) inside the fluid layer induce the additional RTI and decompression effect on the first interface, and the compression waves (CW) inside the fluid layer cause the additional Rayleigh–Taylor stabilisation (RTS) and compression effect on the second interface. A general one-dimensional theory is established to describe the motions of the two interfaces. Linear and nonlinear models are successfully established by considering the interface-coupling effect on the RMI and the additional interfacial instabilities induced by these waves inside the heavy fluid layer. The established models predict well the perturbation growths on the two interfaces at all regimes.

Numerically investigation on blast-induced wave propagation in catastrophic large-scale bedding rockslide

Abstract: Large-scale landslides as a common geological hazard can be easily triggered by natural factors, while it is extremely difficult to be activated by anthropolical blasting operations. The paper presents a comprehensive analysis of characteristics of stress wave propagation in a blasting-triggered large-scale rockslide, termed Wangshan–Zhuakousi Landslide, to investigate the effect of blasting wave on multi-layer interface condition. A detailed analysis of the propagation of P wave in the filling joints was conducted to verify the reliability of the analytical model and the deterioration characteristics of the weak interlayer. The results indicate that the reflection tensile wave can be formed when P wave propagates from the basalt across the tuff interlayer. The theoretical equation for damage assessment of soft rock interlayers is proposed, which can be adopted in calculating the additional stress of soft rock mass in blasting operation. It is found that the material density is the most influential factor in attenuation rate. Besides, the longitudinal wave velocity of materials and the period of incident waves perform the identical effect on the attenuation rate. It is demonstrated that the cumulative failure of tuff layer plays a crucial role in triggering successive sliding. According to the modelling, the tuff interlayer appears to be in a compressed state before the complete damage under P-wave propagation. The locally tensile behaviour can be observed after the complete damage of the tuff. The underlying tuff interlayer forms a discontinuous cumulative damage zone, which significantly triggered major ruptures and destabilized the original bedding rock slope. This paper could prove new insight towards the enforcement of risk assessments and mitigation countermeasures for blasting-induced landslide.

Stability analysis and soliton solutions for the longitudinal wave equation in magneto electro-elastic circular rod

Abstract: This paper presented exact solutions and stability analysis to the nonlinear longitudinal wave equation (NLLWE) in a magneto electro-elastic (MEE) circular rod. The new generalized exponential rational function method (GERFM) has been applied for finding the exact solutions of NLLWE in MEE circular rod. It has the capacity to generate many types of solutions in different form. Therefore, it is effective in extracting new types of solutions in other nonlinear partial differential equations (NLPDEs) that commonly model applications in engineering, mathematical physics. Furthermore, some 2D, 3D graphs are obtained to understand the physical phenomena of this longitudinal wave equation and the stability of governing equation is investigated.