Longitudinal Oscillations Research Articles

Speed Oscillations of a Vehicle Rolling on a Wavy Road

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.

Сучасні проблеми низькочастотної динаміки рідинних ракетних двигунних установок

One of the key problems in liquid-propellant rocket engine (LPRE) design is to provide the stability of LPRE working processes, in particular low-frequency stability. In LPRE experimental tryout, every so often there occur situations where the development of divergent oscillations set up in some of the LPRE loops or units results in contingencies: exceeding the engine ultimate strength, pump stall, chamber ignition, etc. Such contingencies may lead to grave consequences, including engine and bench equipment failure. Because of this, mathematical simulation is one of the main tools that allow one to predict he dynamic performance of an LPRE both in its steady operation and in transients and its startup operation features at the design and tryout stage. This paper overviews and analyzes scientific publications for the past 15 years concerned with the study of the dynamics and low-frequency stability of advanced LPREs and units thereof along different lines. This analysis made it possible to identify problems in low-frequency stability prediction and assurance for liquid-propellant rocket propulsion systems (LPRPSs) under design, to cover new research results (experimental and theoretical) on the origination and development of all-engine low-frequency oscillations and low-frequency oscillations in LPRPS systems and units and to identify new approaches to the mathematical simulation and study of low-frequency processes in LPRPSs and promising lines of investigation. The man lineы of the analysis are as follows: the low-frequency dynamics of cavitating inducer-equipped centrifugal pumps and LPRE gas paths, LPRE thrust control problems, the interaction of launch vehicle airframe longitudinal oscillations with low-frequency processes in the sustainer LPRPS, dynamic processes during an LPRE startup/shutdown, and low-frequency in-chamber oscillations.

Research of solution of the problem about longitudinal oscillation of heterogeneous rod in presence of linear law of relaxation and after-effect

We obtain the solution of the problem about longitudinal impact of heterogeneous rod in presence of linear law of relaxation and after-effect in case when one end of rod is connected to some mass, and the other undergoes the impact by some load, we conduct the research of this solution.

Large-amplitude longitudinal oscillations in solar prominences simulated with different resolutions

Context. Large-amplitude longitudinal oscillations (LALOs) in solar prominences have been widely studied in recent decades. However, their damping and amplification mechanisms are not well understood. Aims. In this study, we investigate the attenuation and amplification of LALOs using high-resolution numerical simulations with progressively increasing spatial resolutions. Methods. We performed time-dependent numerical simulations of LALOs using the 2D magnetic configuration that contains a dipped region. After the prominence mass loading in the magnetic dips, we triggered LALOs by perturbing the prominence mass along the magnetic field. We performed the experiments with four values of spatial resolution. Results. In the simulations with the highest resolution, the period shows good agreement with the pendulum model. The convergence experiment revealed that the damping time saturates at the bottom prominence region with increasing resolution, indicating the existence of a physical reason for the damping of oscillations. At the prominence top, the oscillations are amplified during the first minutes and are then slowly attenuated. The characteristic time suggests more significant amplification in the experiments with the highest spatial resolution. The analysis revealed that the energy exchange between the bottom and top prominence regions is responsible for the attenuation and amplification of LALOs. Conclusions. High-resolution experiments are crucial when studying the periods and the damping mechanism of LALOs. The period agrees with the pendulum model only when using a sufficiently high spatial resolution. The results suggest that numerical diffusion in simulations with insufficient spatial resolution can hide important physical mechanisms, such as amplification of oscillations.

Control of a reversible electric machine included in the vehicle suspension

The relevance of the work is due to the constantly growing requirements for the ride comfort of automobiles. The purpose of the study is a rational choice and combination of principles for constructing an algorithm for controlling an electric machine, replacing a hydraulic damper in the design of a vehicle’s suspension system. The study of the behavior of suspension, depending on the applied control algorithms, was carried out by the method of mathematical modeling. In this work, the control of the suspension of one wheel was considered. The angular and longitudinal oscillations of the body were not the subject of this study. In this regard, the applied design scheme is two-mass. The positive and negative aspects of various principles for calculating the target force generated by an electric machine are considered, and an algorithm for calculating the magnetic flux and armature current of an electric machine necessary for the implementation of the target force under various conditions is developed. It is shown that the calculation of the target force should be based on a combination of several principles, since this allows significant expanding of the suspension operating conditions range.

LOADING ON THE CARRYING STRUCTURE OF A FLAT WAGON IN TRANSPORTATION OF MILITARY EQUIPMENT

The article presents the results of determining the loads on the carrying structure of a flat wagon transported military equipment. The authors suggest that stable fixation of military equipment can be provided with special rings mounted on the flat wagon structure. The results of the strength calculation confirmed the efficiency of this solution. The study deals with the mathematical modelling of the dynamic loads on the carrying structure of a flat wagon with a military tank. The research was made for the plane coordinates. The following oscillations were taken into account: longitudinal plane oscillations, jumping oscillations and galloping oscillations. The differential equations were solved by the Runge–Kutta method in MathCad software suite. The maximum accelerations on the carrying structure of a flat wagon in the longitudinal plane were about 34 m/s2, and in the vertical plane were about 5.0 m/s2. Thus, these accelerations values were within the admissible ones.The study also presents the results of the computer modelling of the dynamic loads on the flat wagon. The calculations were made in SolidWorks Simulation (CosmosWorks) software suite with the finite element method. The study presents the distribution fields of the accelerations relative to the carrying structure of a flat wagon and the numerical values of these accelerations.The models of the dynamic loads on the carrying structure of a flat wagon were verified with an F-test. It has been found that the hypothesis on adequacy is not rejected.The study also included determination of the natural frequencies of the carrying structure of a flat wagon. It was found that the values of the natural frequencies were within the permissible values.
 This research will contribute to better operation efficiency of the rolling stock with consideration of some military-strategic issues, and will be of help for anyone concerned with development and research into innovative rolling stock structures

The interaction between a crack and an inclusion in a cylindrical body under the longitudinal shear oscillations

The interaction between a crack and an inclusion in a cylindrical body under the longitudinal shear oscillations

Identification of Magnetorheological Layer Properties by Using Refined Plate Theory

In this paper, the dynamic characteristics of sandwich plates with external rigid layers and an upper layer with magnetorheological properties (MR) are investigated. An analysis of the effect of the magnetic field on frequency and loss factor is presented. Vibration can be controlled by a magnetic-rheological viscoelastomer (MRVE), when used in sandwich plates. During vibration, MRVE exhibits an inhomogeneous complex module, which is controlled by an applied magnetic field and depends on the oscillation frequency. Using the dynamic equilibrium conditions, physical and kinematic relationships, and the partial differential equations for the conjugate transverse and longitudinal oscillations of a sandwich plate, are derived. This paper presents a new method for stress analysis that provides accurate stress distributions for multilayer plates subject to cylindrical bending. It uses an adaptive method that does not make strict assumptions about the plate model. Based on the depicted theoretical model, the deformations of each layer of the plate are accounted for, including both transverse shear deformations and transverse normal deformations where the thickness is concerned, and nonlinear displacement changes. The magnetorheological (MR) identification of an inner layer is carried out using refined plate theory and sandwich bending tests. Using combined methods, the possibility of determining the MRVE parameters robustly, is examined.

TWO CUTTING TURNING OF BODIES OF REVOLUTION

The technology of two-cut rough and rough turning of rotation bodies in relation to lathes is considered. Dynamics of part working surfaces formation by longitudinal oscillations of cutters with phase delay of finishing cutter from rough one is shown. Dynamics of finishing cutter in function of damping coefficient is considered. The mathematical model of two-cut turning process is given.

Resonance magnetoelectric effect in a composite ferromagnet–dielectric–piezoelectric Langevin-type resonator

The direct and converse magnetoelectric (ME) effects in a Langevin-type resonator are observed and investigated for the first time. The resonator comprised a disk made of lead–zirconate titanate ceramic, located between two sapphire cylinders, with layers of amorphous ferromagnet glued to its side surfaces. ME effects were observed at frequencies of bending (∼70 kHz) and longitudinal (∼200 kHz) oscillations of the resonator upon its excitation by ac magnetic and electric fields. The field conversion efficiency for the direct ME effect was α E ≈ 31 V (Oe−1 cm−1). The magnetization modulation efficiency for the converse ME effect reached α B ≈ 0.72 G cm−1 V−1. The nonlinear ME effects such as frequency doubling, frequency mixing, and resonance frequency shift are observed at high field amplitudes. The magnitude of both the direct and converse ME effects in the resonator is controlled by an external dc magnetic field. The Langevin-type ME resonators can be used in highly sensitive magnetic field sensors, controlled resonators and transformers, and other components of electronics and microsystem technology.

Kinetic theory of monochromatic waves bunching in a low-voltage beam discharge in rare gases

The kinetic theory of phase focusing, that is bunching in a low-voltage beam discharge in rare gases (LVBD) during the propagation of longitudinal electrostatic oscillations at the Knudsen numbers of the order of unity have developed. The anomalous relaxation of the almost monoenergetic electron beam in momentum and energy is described for the case when this process cannot be explained by electron–atom collisions. The paper has shown the important role of electrons that have the beam energy and isotropic directional distribution, which is formed as a result of elastic collisions between the beam electrons and atoms. The dependence of the anomalous relaxation length on parameters of the LVBD in rare gases is studied.The developed theory makes it possible to quantitatively interpret experimental data on the LVBD under conditions when the electron mean free path is of the order of the interelectrode gap. According to these data, regardless of the density of the charged particles in the LVBD plasma in rare gases, five Langmuir plasma wavelengths fit along the length of the anomalous relaxation of the electron beam. The study of the electron beam dynamics laws in a plasma is important for the development of plasma-electrical devices, where the beam discharge is applied, namely: widely used all-movable stabilizers, sources of intense electromagnetic radiation, controlled elements of electronic circuits, plasma chemical reactors, etc.

Large Magnetoresistance and Nontrivial Berry Phase in Nb3Sb Crystals with A15 StructureSupported by the National Key R&D Program of China (Grant No. 2016YFA0300402), the National Natural Science Foundation of China (Grant Nos. 12074335, and 11974095), and the Fundamental Research Funds for the Central Universities.

Compounds with the A15 structure have attracted extensive attention due to their superconductivity and nontrivial topological band structures. We have successfully grown Nb3Sb single crystals with the A15 structure and systematically measured the longitudinal resistivity, Hall resistivity and quantum oscillations in magnetization. Similar to other topological trivial/nontrivial semimetals, Nb3Sb exhibits large magnetoresistance (MR) at low temperatures (717%, 2 K and 9 T), unsaturating quadratic field dependence of MR and up-turn behavior in ρxx (T) curves under magnetic field, which is considered to result from a perfect hole-electron compensation, as evidenced by the Hall resistivity measurements. The nonzero Berry phase obtained from the de-Hass van Alphen (dHvA) oscillations demonstrates that Nb3Sb is topologically nontrivial. These results indicate that Nb3Sb superconductor is also a semimetal with large MR and nontrivial Berry phase. This indicates that Nb3Sb may be another platform to search for the Majorana zero-energy mode.

Analysis of initiation of instability zones of drilling string and intensification of drilling process at well boring by rotating an d rotating-bit methods

Instable operation of a drilling string can be caused by design flaws, unreasonably selected drilling modes, as well as specific features of the drilling by bit, fixed on a long flexible rod with initial irregularities. It was established that a drilling string under the influence of constant torque and longitudinal feed load is deformed along a screw line. It was shown that the source of the dynamic state initiation of a rotating drilling string is an alternative friction between rock and the instrument, as well as variation of potential energy of the drilling string at its twisting and untwisting. At the string twisting the potential anergy is accumulating, at the untwisting it is released. In this case the drilling sting length begins to increase and the work of feed force is imposed to this shifting resulting in the instrument beat over the rock. The torsion oscillating process causes longitudinal periodic shifting of the string end, which lead to joint longitudinal and bending oscillations of the whole drilling column. Systems of differential equations obtained describing the joint bending-longitudinal oscillations of a drilling string, caused by torsion vibrations, initiating at the contact of a drilling instrument with rock. Approximate solutions of the systems presented, which take place with the basic natural frequency of the torsion oscillations of a two-mass system instrument - string - rotator drive. In this case the amplitudes of the drilling string bending oscillations are associated with characteristics variation of the friction between the instrument and the rock as well as with the angular frequency of the drilling string rotation. Zones of dynamic instability at rotation of the deformed drilling string due to acting force factors, as well as initial irregularities and centrifugal forces revealed. It was shown that they are initiated at critical speeds of the drilling string rotation, which coincides with any natural frequency of the bending oscillations of the stave. To intensify the drilling process, recommendation elaborated for equipping the rotary drilling rig with an additional pneumatic hammer. A calculated diagram of a drilling string, equipped by an additional pneumatic hammer considered. Parameters of the hammer in terms of frequency and amplitude are matched with the translational speed of well drilling. The total longitudinal and transverse shifts can be obtained by superposition of self-exciting and induces shifts.

Parallel‐to‐orthogonal polarisation‐state converter for dual‐mode Nd:YVO 4 microchip laser

Polarisation-state conversion from parallel linear polarisation to orthogonal linear polarisation was successfully demonstrated using a birefringence crystal for the two longitudinal oscillation modes of a dual-mode Nd:YVO4 microchip laser. The laser emitted two longitudinal oscillation modes simultaneously in the vertical linear polarisation state with a frequency difference of 101 GHz. In the experiment, it was shown that by using a 17-mm-long LiNbO3 birefringence crystal, it was possible to almost perfectly convert the polarisation state of the two oscillation modes by providing a π-rad difference in phase retardations between the two oscillation modes. The residual elliptic component was eliminated using a pair of waveplates.

Longitudinal oscillations of relaxating rod with free endpoints

Longitudinal oscillations of relaxating rod with free endpoints.

Experimental Investigation of Self-Excited Combustion Instabilities in a LOX/LNG Rocket Combustor

Two types of combustion instabilities were observed in a multi-injector research combustor with liquid oxygen and liquefied natural gas (LOX/LNG) propellants operating at conditions similar to an upper stage rocket engine. The first was identified as an excited tangential acoustic mode of the combustion chamber and can be explained by coupling with the LOX injectors, similar to the mechanism previously observed in tests with propellants. The other type is characterized by longitudinal acoustic oscillations with peak-to-peak amplitudes of at least 40% of the mean chamber pressure. Analysis of the test data suggests that sudden upstream displacement of a lifted flame may be the trigger mechanism for the second type of instabilities.

Research on the influence of the discharge breakdown process on the crater formation during EDM

PurposeThis paper aims to study the breakdown, oscillation and vanishing of the discharge channel and its influence on crater formation with simulation and experimental methods. The experiment results verified the effect of the oscillating characteristics of the discharge channel on the shape of the crater.Design/methodology/approachA mathematical model that considers the magnetohydrodynamics (MHD) and the discharge channel oscillation was established. The micro process of discharging based on magnetic-fluid coupling during electrical discharge machining (EDM) was simulated. The breakdown, oscillation and vanishing stage of the discharge channel were analyzed, and the crater after machining was obtained. Finally, a single-pulse discharge experiment during EDM was conducted to verify the simulation model.FindingsDuring the breakdown of the discharge channel, the electrons move towards the center of the discharge channel. The electrons at the end diverge due to the action of water resistance, making the discharge channel appear wide at both ends and narrow in the middle, showing the pinch effect. Due to the mutual attraction of electrons and positive ions in the channel, the transverse oscillation of the discharge channel is shown on the micro level. Therefore, the position of the discharge point on the workpiece changes. The longitudinal oscillation in the discharge channel causes the molten pool on the workpiece to be ejected due to the changing pressure. The experimental results show that the shape of the crater is similar to that in the simulation, which verifies the correctness of the simulation results and also proves that the crater generated by the single pulse discharge is essentially the result of the interaction between transverse wave and longitudinal wave.Originality/valueIn this paper, the simulation of the discharge breakdown process in EDM was carried out, and a new mathematical model that considers the MHD and the discharge channel oscillation was established. Based on the MHD module, the discharge breakdown, oscillation and vanishing stages were simulated, and the velocity field and pressure field in the discharge area were obtained.

Numerical and Experimental Investigation of Longitudinal Oscillations in Hall Thrusters

One of the main oscillatory modes found ubiquitously in Hall thrusters is the so-called breathing mode. This is recognized as a relatively low-frequency (10–30 kHz), longitudinal oscillation of the discharge current and plasma parameters. In this paper, we present a synergic experimental and numerical investigation of the breathing mode in a 5 kW-class Hall thruster. To this aim, we propose the use of an informed 1D fully-fluid model to provide augmented data with respect to available experimental measurements. The experimental data consists of two datasets, i.e., the discharge current signal and the local near-plume plasma properties measured at high-frequency with a fast-diving triple Langmuir probe. The model is calibrated on the discharge current signal and its accuracy is assessed by comparing predictions against the available measurements of the near-plume plasma properties. It is shown that the model can be calibrated using the discharge current signal, which is easy to measure, and that, once calibrated, it can predict with reasonable accuracy the spatio-temporal distributions of the plasma properties, which would be difficult to measure or estimate otherwise. Finally, we describe how the augmented data obtained through the combination of experiments and calibrated model can provide insight into the breathing mode oscillations and the evolution of plasma properties.

Influence of laser wavelength on surface enhanced Raman spectroscopy using Mn based nano-particles produced by laser ablation synthesis in 4,4′ Bipyridine solution (LASiS)

In this work surface Raman spectroscopy of Mn based nano-particles produced by laser ablation technique in 4,4′ Bipyridine (Bipy: C10H8N2) aqueous environment is studied using three Raman spectroscopes with different laser wavelengths of 532, 632.8 and 785 nm. Transmission electron microscopy (TEM), X-ray diffraction (XRD), UV–visible spectroscopy (UV-Vis), dynamic light scattering (DLS) and Fourier transformations infra-red spectroscopy (FTIR) produced the characteristics of the obtained samples. Results of TEM and DLS showed that spherical Mn based nano-particles with a diameter of 40 nm and nano-rods with different lengths were produced. A value of − 23.61 mV for zeta potential and a mobility of − 1.84 × 10−8 m2s−1V−1 showed the instability of the produced nano-particles in the solution which can be stabilized by ultrasonic treatment of the solution. The absorption spectra showed two peaks at 400 and 422 nanometer wavelengths that may be assigned as transverse and longitudinal plasmonic oscillations of the nano-rod particles, respectively. The most intense peak in the XRD pattern of nano-particles in Bipy solution was assigned as MnO2(131) and no Mn peak was observed. Raman and FTIR analyses should not result in similar data for molecules with center of symmetry. This is confirmed in the results of this work for Bipy as such molecule. High enhancement of the Raman peaks of Bipy was achieved using all three different laser wavelengths. The influence of laser wavelength on different main Raman shifts of Bipy is discussed and related to the correlation between the laser wavelength and size of the nano-particles. In particular, and consistent with this and previous results some combined Raman shifts are also observed using 632.8 nm laser wavelength.

A Machine Learning Approach for Wear Monitoring of End Mill by Self-Powering Wireless Sensor Nodes.

There are many tool condition monitoring solutions that use a variety of sensors. This paper presents a self-powering wireless sensor node for shank-type rotating tools and a method for real-time end mill wear monitoring. The novelty of the developed and patented sensor node is that the longitudinal oscillations, which directly affect the intensity of the energy harvesting, are significantly intensified due to the helical grooves cut onto the conical surface of the tool holder horn. A wireless transmission of electrical impulses from the capacitor is proposed, where the collected electrical energy is charged and discharged when a defined potential is reached. The frequency of the discharge pulses is directly proportional to the wear level of the tool and, at the same time, to the surface roughness of the workpiece. By employing these measures, we investigate the support vector machine (SVM) approach for wear level prediction.