Search Results (12)

Magneto-electro-elastic materials, a novel class of smart materials, exhibit remarkable energy conversion properties, making them highly suitable for applications in nanotechnology. This study focuses on various aspects of the fractional nonlinear longitudinal wave equation (FNLWE) that models wave propagation in a magneto-electro-elastic circular rod. Using the direct algebraic method, several new soliton solutions were derived under specific parameter constraints. In addition, Galilean transformation was employed to explore the system’s sensitivity and quasi-periodic dynamics. The study incorporates 2D, 3D, and time-series visualizations as effective tools for analyzing quasi-periodic behavior. The results contribute to a deeper understanding of the nonlinear dynamical features of such systems and demonstrate the robustness of the applied methodologies. This research not only extends existing knowledge of nonlinear wave equations but also introduces a substantial number of new solutions with broad applicability. Full article

Due to irregular hydrodynamic–aerodynamic coupling, the modeling and simulation of near-surface flight are extremely complex. For the present study, a practical dynamic model and a complete motion simulation method for the solution of such problems were established for engineering applications. A discrete non-linear time-varying dynamics model was employed in order to ensure the universality of the method; thereafter, force models—including gravity, aerodynamic, hydrodynamic, control, and thrust models—were established. It should be noted that a non-linear approach was adopted for the hydrodynamic model, which reflects the influences of waves in real-world situations; in addition, a Proportional–Integral–Derivative (PID) control law was added to realize closed-loop simulation of the motion. Considering a take-off flight as a study case, longitudinal three Degrees of Freedom (DoF) motion was simulated. The velocity, angle of attack, height, and angular velocity were selected as the state vectors in the state–space equations. The results show that, with the equilibrium state as the initial setting for the motion, reasonable time–history curves of the whole take-off phase can be obtained using the proposed approach. Furthermore, it is universally applicable for aircraft operating under hydrodynamic–aerodynamic coupling scenarios, including amphibious aircraft, seaplanes, Wing-in-Ground-Effect (WIGE) aircraft, and Hybrid Aerial–Underwater Vehicles (HAUVs). Full article

The branch of physics known as magnetohydrodynamics (MHD) emerged in the middle of the 20th century. MHD models, being substantially nonlinear, are quite challenging for theoretical study and allow nontrivial consideration only in particular limited cases. Thus, due to the exceptional growth of calculation power, research on MHD is now primarily concentrated on numerical modeling. The achievements are considerable; however, there is a possibility of overlooking some phenomena or missing an optimal approach to modeling and calculating that could be identified with theoretical guidance. The paper presents a theoretical study of a particular class of boundary and initial conditions. The flow of a viscous, electrically conductive fluid on a rotating plate in the presence of a magnetic field is considered. The fluid and the bounding plate rotate together with a constant angular velocity around an axis that is not perpendicular to the plane. The flow is induced by sudden longitudinal vibrations of the plate, injection (suction) of the medium through the plate, and an applied magnetic field directed normal to the plate. The full equation of magnetic induction is used, taking into account both the induction effect and energy dissipation due to the flow of electric currents. An analytical solution of three-dimensional magnetohydrodynamics equations in a half-space bounded by a plate is presented. The solution is given in the form of a superposition of plane waves propagating with certain wave numbers along the y-coordinate axis. For certain regions of system parameters, the vibration of the bounding plate does not cause waves in the media. Full article

Assessing the safety of amphibious aircraft hinges significantly on two key factors: wave-added resistance and motion stability during takeoff and landing on water surfaces. To tackle this, we employed the Reynolds-averaged Navier–Stokes (RANS) equations solved via the finite volume method. We utilized the volume fraction method to accurately capture the free surface and employed the overset grid technique to manage the relative motion between the aircraft and the liquid surface. Our approach involves establishing a numerical simulation scheme to investigate the water-planing motion of amphibious aircraft across varying wave heights, wavelengths, speeds, and center-of-gravity positions. The computational findings demonstrate a close match between calculated forces and aircraft motion compared to experimental values. Notably, we observed pronounced nonlinearity in wave-added resistance. Under high sea conditions, operating in a short-wavelength environment or with a rearward center-of-gravity position proves advantageous for reducing wave-added resistance. Conversely, poor longitudinal stability is evident during planing in long waves. Full article

This study investigates the Slepyan–Palmov (SP) model, which describes plane longitudinal waves propagating within a medium comprising a carrier medium and nonlinear oscillators. The primary objective is to analyze the integrability properties of this model. The research entails two key aspects. Firstly, the study explores the group invariant solution by utilizing reductions in symmetry subalgebras based on the optimal system. Secondly, the conservation laws are studied using the homotopy operator, which offers advantages over the conventional multiplier approach, especially when arbitrary functions are absent from both the equation and characteristics. This method proves advantageous in handling complex multipliers and yields significant outcomes. Full article

Based on the layered and porous characteristics of functionally graded materials and the finite deformation assumption of solids, the fractal nonlinear propagation equation of longitudinal waves in a functionally graded rod is derived. A large number of exact displacement gradient traveling wave solutions of the fractal equation are obtained by using an equivalent simplified extended (G′/G) expansion method. Three sets of existing and different displacement gradient solutions are obtained by analyzing these exact solutions, and then three corresponding fractal dimension strain waves are derived. The results of numerical simulation of the evolution of these three strain waves with fractal dimension show that when the strain wave propagates in the rod, the smaller the fractal dimension or, the larger the radius of the rod, the higher the tensile strength of the material. Full article

To investigate the vibration behavior of ship-borne tethered UAVs under taut–slack conditions, the Hamilton principle is used to establish the three-dimensional dynamic equations of the ship-borne tethered UAVs while taking into account geometric nonlinearity and simplifying them into the corresponding stress wave equations. By employing the characteristic line technique to solve the stress wave equation of ship-borne tethered UAVs, it is possible to numerically determine the effects of various factors on the vibration behavior of these drones. Dimensional analysis is then used to build the experimental model, ensuring that the numerical outcomes are accurate. The findings show that the impact of equilibrium curvature connects longitudinal and transverse waves and that the geometric dispersion of stress wave propagation in the tethered cable is caused by equilibrium curvature. The standing wave takes the lead and causes subharmonic and frequency doubling components in the top tension response when the end excitation frequency is near the tethered UAVs’ natural frequency. Additionally, the cable’s center as well as its end will display the highest dynamic tension value. Full article

In this study, the dispersal caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod is taken into consideration using the nonlinear longitudinal wave equation (LWE), a mathematical physics problem. Using the generalized exp-function method, we investigate the families of solitary wave solutions of one-dimensional nonlinear LWE. Using the computer program Wolfram Mathematica 10, these new exact and solitary wave solutions of the LWE are derived as trigonometric function, periodic solitary wave, rational function, hyperbolic function, bright and dark solitons solutions, sinh, cosh, and sech² function solutions of the LWE. These solutions represent the electrostatic potential and pressure for LWE as well as the graphical representation of electrostatic potential and pressure. Full article

Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads. This paper investigates the resulting travel speed oscillations of a quarter car model rolling in contact on a sinusoidal and stochastic road surface. The nonlinear equations of motion of the vehicle road system leads to ill-conditioned differential-algebraic equations. They are solved introducing polar coordinates into the sinusoidal road model. Numerical simulations show the Sommerfeld effect, in which the vehicle becomes stuck before the resonance speed, exhibiting limit cycles of oscillating acceleration and speed, which bifurcate from one-periodic limit cycle to one that is double periodic. Analytical approximations are derived by means of nonlinear Fourier expansions. Extensions to more realistic road models by means of noise perturbation show limit flows as bundles of nonperiodic trajectories with periodic side limits. Vehicles with higher degrees of freedom become stuck before the first speed resonance, as well as in between further resonance speeds with strong vertical vibrations and longitudinal speed oscillations. They need more power supply in order to overcome the resonance peak. For small damping, the speeds after resonance are unstable. They migrate to lower or supercritical speeds of operation. Stability in mean is investigated. Full article

More and more applications require semiconductor lasers distinguished not only by large modulation bandwidths or high output powers, but also by small spectral linewidths. The theoretical understanding of the root causes limiting the linewidth is therefore of great practical relevance. In this paper, we derive a general expression for the calculation of the spectral linewidth step by step in a self-contained manner. We build on the linewidth theory developed in the 1980s and 1990s but look from a modern perspective, in the sense that we choose as our starting points the time-dependent coupled-wave equations for the forward and backward propagating fields and an expansion of the fields in terms of the stationary longitudinal modes of the open cavity. As a result, we obtain rather general expressions for the longitudinal excess factor of spontaneous emission (K-factor) and the effective $\alpha$-factor including the effects of nonlinear gain (gain compression) and refractive index (Kerr effect), gain dispersion, and longitudinal spatial hole burning in multi-section cavity structures. The effect of linewidth narrowing due to feedback from an external cavity often described by the so-called chirp reduction factor is also automatically included. We propose a new analytical formula for the dependence of the spontaneous emission on the carrier density avoiding the use of the population inversion factor. The presented theoretical framework is applied to a numerical study of a two-section distributed Bragg reflector laser. Full article

This article investigates longitudinal deformation waves in physically nonlinear coaxial elastic shells containing a viscous incompressible fluid between them. The presence of a viscous incompressible fluid between the shells, as well as the influence of the inertia of the fluid motion on the amplitude and velocity of the wave, are taken into account. The mathematical model phenomenon is constructed by means of the method of two-scale asymptotic expansion. Structural damping in the shells and surrounding elastic media did not allow discovery of the exact solution of the problem of the deformation waves propagation. This leads to the need for numerical methods. A numerical study of the model constructed in the course of this work is carried out by using a difference scheme for the equation similar to the Crank–Nicholson scheme for the heat equation. In the absence of the structural damping and surrounding media influences, and under the similar initial conditions for both shells, the velocity and amplitude of the wave do not change. The result of the numerical experiment coincides with the exact solution, which is found in the case of the absence of the structural damping and surrounding media influences; therefore, the difference scheme is adequate to the generalized modified Korteweg–de Vries equations system. There is energy is transferred in the presence of the fluid, between the shells. The presence of inertia of the fluid motion leads to a decrease in the velocity of the deformation wave. Full article

The reasons for the difficulty in simulating accurately strong 3-D shock wave/turbulent boundary layer interactions (SBLIs) and high-alpha flows with classical turbulence models are investigated. These flows are characterized by the appearance of strong crossflow separation. In view of recent additional evidence, a previously published flow analysis, which attributes the poor performance of classical turbulence models to the observed laminarization of the separation domain, is reexamined. According to this analysis, the longitudinal vortices into which the separated boundary layer rolls up in this type of separated flow, transfer external inviscid air into the part of the separation adjacent to the wall, decreasing its turbulence. It is demonstrated that linear models based on the Boussinesq equation provide solutions of moderate accuracy, while non-linear ones and others that consider the particular structure of the flow are more efficient. Published and new Reynolds Averaged Navier–Stokes (RANS) simulations are reviewed, as well as results from a recent Large Eddy Simulation (LES) study, which indicate that in calculations characterized by sufficient accuracy the turbulent kinetic energy of the reverse flow inside the separation vortices is very low, i.e., the flow is almost laminar there. Full article