Frequencies Of Torsional Oscillations Research Articles

Quasi-periodic oscillations during magnetar giant flares in the strangeon star model

ABSTRACT Soft gamma-ray repeaters (SGRs) are widely understood as slowly rotating isolated neutron stars. Their generally large spin-down rates, high magnetic fields, and strong outburst energies render them different from ordinary pulsars. In a few giant flares (GFs) and short bursts of SGRs, high-confidence quasi-periodic oscillations (QPOs) were observed. Although remaining an open question, many theoretical studies suggest that the torsional oscillations caused by starquakes could explain QPOs. Motivated by this scenario, we systematically investigate torsional oscillation frequencies based on the strangeon star (SS) model with various values of harmonic indices and overtones. To characterize the strong-repulsive interaction at short distances and the non-relativistic nature of strangeons, a phenomenological Lennard–Jones model is adopted. We show that, attributing to the large shear modulus of SSs, our results explain well the high-frequency QPOs (≳150 Hz) during the GFs. The low-frequency QPOs (≲150 Hz) can also be interpreted when the ocean–crust interface modes are included. We also discuss possible effects of the magnetic field on the torsional mode frequencies. Considering realistic models with general-relativistic corrections and magnetic fields, we further calculate torsional oscillation frequencies for quark stars. We show that it would be difficult for quark stars to explain all QPOs in GFs. Our work advances the understanding of the nature of QPOs and magnetar asteroseismology.

Self-similarity relations for torsional oscillations of neutron stars

ABSTRACT Self-similarity relations for torsional oscillation frequencies of neutron star crust are discussed. For any neutron star model, the frequencies of fundamental torsional oscillations (with no nodes of radial wavefunction, i.e. at n = 0, and at all possible angular wave numbers ℓ ≥ 2) is determined by a single constant. Frequencies of ordinary torsional oscillations (at any n > 0 with ℓ ≥ 2) are determined by two constants. These constants are easily calculated through radial integrals over the neutron star crust, giving the simplest method to determine full oscillation spectrum. All constants for a star of fixed mass can be accurately interpolated for stars of various masses (but the same equation of state). In addition, the torsional oscillations can be accurately studied in the flat space–time approximation within the crust. The results can be useful for investigating magneto-elastic oscillations of magnetars which are thought to be observed as quasi-periodic oscillations after flares of soft-gamma repeaters.

Effects of finite sizes of atomic nuclei on shear modulus and torsional oscillations in neutron stars

ABSTRACT The shear modulus of neutron star matter is one of the important properties used for determining torsional oscillations in neutron stars. We take into account the effects of finite sizes of spherical nuclei on the shear modulus and examine the frequencies of crustal torsional oscillations. The shear modulus decreases owing to the finite-size effect, which in turn decreases the frequencies of torsional oscillations. In particular, the finite-size effect becomes more crucial for oscillations with a larger azimuthal quantum number and for neutron star models with a weaker density dependence of nuclear symmetry energy. In practice, when one identifies quasi-periodic oscillations from a neutron star, where magnetic effects are negligible, with crustal torsional oscillations, the finite-size effect can be more significant at frequencies higher than ∼100 Hz.

РОЗРОБКА МЕТОДИКИ ВИЗНАЧЕННЯ ЗАПАСУ МІЦНОСТІ БОЙОВИХ ЛІТАКІВ НА ОСНОВІ АНАЛІЗУ ДИНАМІЧНИХ ХАРАКТЕРИСТИК З УРАХУВАННЯМ ЕКСПЛУАТАЦІЙНИХ ФАКТОРІВ

The article considers the issues of diagnostics of the technical condition of cantilevered aircraft structures based on the dynamic response analysis. This task provides for determining the real technical condition of the damaged structure and, as a result, the reserve factor. The main criterion is to use as little information as possible to obtain a precise objective assessment. It is suggested to use the structural dynamics being the most informative as diagnostic features. These are natural oscillation frequencies (torsional and flexural) and zero-twist axis position (according to the data from volitionally undamaged structures taken as reference). The methodology has been patented. As a technical solution, the methodology provides for frequency tests with dysfunction of flexural and torsional oscillation frequencies under which a minimum frequency of natural oscillations corresponding to the minimum residual strength shall be set for each type of aircraft, namely, for its part - wings, fins (cantilevered structures of the glider). The increased number of analysed natural oscillation frequencies increases the reliability of the residual strength estimation. Based on this, the developed and produced equipment and monitor equipment as a mobile version (which are also patented), can be effectively used when basing aircraft in the combat theatre. Based on the provisions of the NIAS similar monitoring system can be implemented in military units of the Air Force of the Armed Forces of Ukraine during the operation of aircraft according to the technical condition.

Diagnostics of Shaft Trains of Large Turbine Sets for Integrity Using Torsional Vibration Measurements

A promising solution to the problem of early detection for the growth of fatigue cracks in shaft trains of large turbine units at nuclear and thermal power stations based on the results of torsional vibration monitoring by the method of time intervals is considered. It has been demonstrated in the laboratory that this method enables us to detect the growth of fatigue cracks in the shafts of rotor systems from a decrease in the value on natural frequencies of torsional oscillations. However, attempts to use it in the industry were not so successful due to a slight influence of fatigue cracks on the values of the natural frequencies of torsional oscillations as compared with the effect of other factors. Nevertheless, the data obtained in the study of torsional oscillations of the shaft train in a turbine installation of an operating 300-MW power unit using a high-precision optoelectronic monitoring system enabled the establishment and consideration of the effect that the turbine operating conditions has on the natural frequencies of torsional oscillations for the first time. A modal finite-element analysis of the turbine installation shaft train’s most dangerous annular fatigue crack, which cannot be detected at an early stage of development using standard or special vibration-monitoring systems during steady state operation of the turbine installation, has been performed. The analysis yielded the dependence of the torsional natural frequencies on the cross-sectional area and location of the fatigue crack. Monitoring of fatigue crack development has been demonstrated to be performed by measuring the natural frequencies of torsional oscillations (or vibrations) during steady state operation of the turbine set considering the effect of its operating conditions.

New type of centrifugal instability in a thin rotating spherical layer

We numerically model the instability of viscous incompressible fluid flows caused by torsional oscillations of the inner sphere in a thin spherical layer with respect to the state of rest. We show that an increase in the frequency of torsional oscillations leads to a change in the mode of the instability, with a transition from secondary flows in the form of Taylor vortices to the structures, which were not previously observed. The revealed instability is found in the frequency range from 0.61 to 2.45 Hz or, if the wavelengths are taken relative to the layer thickness, from 0.67 to 1.33.

Resonant phenomena of elastic bodies that perform bending and torsion vibrations

The method of study of the influence of torsional oscillations of one-dimensional models of nonlinear elastic bodies, along which moves with a constant velocity continuous flow of inelastic homogeneous medium, into bending, is developed. It is believed that information on torsional oscillations is known from empirical studies. Based on the latter, the refined model of the dynamics of the process of the investigated object is constructed. The latter is a boundary value problem for nonlinear nonautonomous differential equations with partial derivatives. The imposed restrictions on power factors and the main parameters of torsional oscillations allow for the analytical study of the dynamics of the process to use the basic ideas of the asymptotic integration of equations with partial derivatives. With their help, we obtain a two-parameter set of solutions that describe the determinant parameters of bending vibrations of an elastic body. It is established that for the considered elastic body there can be resonance oscillations, which are caused not only by external factors, but also by internal – torsional oscillations. Regarding the law of the change in the basic parameters of the dynamics of the bending motion of an elastic body, its rotation around the vertical axis reduces the frequency of its own flexural oscillations of the body, and even small torsional oscillations cause an additional periodic action on the transverse. In connection with the above bending vibrations of the elastic body, which performs complex oscillations (torsion and bending), resonances are possible both at the frequency of the external periodic perturbation and at the frequencies of the torsional oscillations (internal resonances). The amplitude of the transition through the resonance: a) at the basic frequency of external perturbation takes less value for elastic bodies of greater flexural rigidity and for higher values of the relative motion of the medium; b) at the frequency of torsional oscillations for larger values of the angular velocity takes more importance; c) with “fast” transition through resonance at the frequency of external or internal perturbation is less than with “slow”. The obtained results can serve as the basis for the choice of operating parameters of elastic elements of machines that carry out complex oscillations.

Instability of the Flow in a Spherical Layer under Torsional Oscillations of the Inner Boundary

The instability of viscous incompressible fluid flows caused in a thin spherical layer by torsional oscillations of the inner sphere in a thin spherical layer with respect to the sate of rest is studied numerically. It has been established that an increase in the frequency of torsional oscillations leads to a change in the mode of the instability, with a transition from secondary flows in the form of Taylor vortices to structures not observed earlier. The revealed instability is observed in the frequency range from 0.61 to 2.45 Hz or, if the wavelengths are taken relative to the layer thickness, from 0.67 to 1.33.

Suppression of Weakly-Damped Torsional Oscillations in Autonomous Power Systems

Variants are considered for suppression of weakly-damped vibration effects caused by the first critical frequency of torsional oscillations of a gas-turbine unit in the autonomous electric power system of an oil and gas field. It is shown that torsional oscillations can be suppressed with the aid both of a reactive power source installed at the field power system, consisting of a controlled shunt reactor (CSR) and a static capacitor battery, and of an auxiliary active RLC filter, when using in both cases auxiliary control loops of torsional deviation as well as its first and second derivatives. A methodology has been developed for simultaneous coordination of the settings of any regulation system based on a numerical optimization, which permits selecting the characteristics of control loops of the source of reactive power and active RLC filter that are optimal from the point of view of suppressing torsional oscillations.

Неустойчивость течения в сферическом слое при вращательных колебаниях внутренней границы

AbstractThe instability of viscous incompressible fluid flows caused in a thin spherical layer by torsional oscillations of the inner sphere in a thin spherical layer with respect to the sate of rest is studied numerically. It has been established that an increase in the frequency of torsional oscillations leads to a change in the mode of the instability, with a transition from secondary flows in the form of Taylor vortices to structures not observed earlier. The revealed instability is observed in the frequency range from 0.61 to 2.45 Hz or, if the wavelengths are taken relative to the layer thickness, from 0.67 to 1.33.

Quantum force of tunneling macrospins with a mechanical resonator

We study force dynamics of macropsin of molecular magnets coupled to a torsional resonator. In the presence of an ac field and a static field with a gradient, the force is shown to display various types of quantum oscillations which depend upon the coupling strength and the frequency of torsional oscillations. Optimal conditions for observing them will be discussed within the framework of experimentally controllable parameters.

Probing nuclear bubble structure via neutron star asteroseismology

We consider torsional oscillations that are trapped in a layer of spherical-hole (bubble) nuclear structure, which is expected to occur in the deepest region of the inner crust of a neutron star. Because this layer intervenes between the phase of slab nuclei and the outer core of uniform nuclear matter, torsional oscillations in the bubble phase can be excited separately from usual crustal torsional oscillations. We find from eigenmode analyses for various models of the equation of state of uniform nuclear matter that the fundamental frequencies of such oscillations are almost independent of the incompressibility of symmetric nuclear matter, but strongly depend on the slope parameter of the nuclear symmetry energy $L$. Although the frequencies are also sensitive to the entrainment effect, i.e., what portion of nucleons outside bubbles contribute to the oscillations, by having such a portion fixed, we can successfully fit the calculated fundamental frequencies of torsional oscillations in the bubble phase inside a star of specific mass and radius as a function of $L$. By comparing the resultant fitting formula to the frequencies of quasi-periodic oscillations (QPOs) observed from the soft-gamma repeaters, we find that each of the observed low-frequency QPOs can be identified either as a torsional oscillation in the bubble phase or as a usual crustal oscillation, given generally accepted values of $L$ for all the stellar models considered here.

A new method to estimate effective elastic torsional compliance of single-stage Cycloidal drives

Standard single-stage tooth-to-pin-contact Cycloidal drives deliver various benefits such as high-ratio speed reduction, highly efficient torque delivery, compact physical structure etc. They lack torsional rigidity on their own because of inherent “lost-motion” and “backlash”, and hence inappropriate for precision-motion mechanical systems. However from dynamics point of view, this is beneficial for non-precision-motion systems, as it reduces the drive-train's shock factor. Currently there are no design standards for Cycloidal drives owing to their complicated component stiffness behaviour, increased tooth-load-sharing at overloads etc., which further obscures the analytical estimation of torsional rigidity of a given configuration. This paper presents a novel method comprising both analytical and numerical techniques for the effective determination of the elastic torsional compliance of single-stage Cycloidal drives based on static experimental results conducted on a commercially available gear-drive. We establish a unique key parameter −ηOP, ‘torque transfer efficiency’, of output-shaft-pins from mechanism-kinematics to be included in the system's dynamic model. Applying the techniques and outcomes presented here in a lumped mass/inertia dynamic model yielded agreeable natural frequency of torsional oscillations in comparison to experimental results obtained under the same loading conditions. This can lead to dynamically optimised designs and hence their standardisation.

Torsional oscillations of neutron stars in scalar-tensor theory of gravity

We study torsional oscillations of neutron stars in the scalar-tensor theory of gravity using the relativistic Cowling approximation. We compute unperturbed neutron star models adopting realistic equations of state for the neutron star's core and crust. For scalar-tensor theories that allow for spontaneous scalarization, the crust thickness can be significantly smaller than in general relativity. We derive the perturbation equation describing torsional oscillations in scalar-tensor theory, and we solve the corresponding eigenvalue problem to find the oscillation frequencies. The fundamental mode (overtone) frequencies become smaller (larger) than in general relativity for scalarized stellar models. Torsional oscillation frequencies may yield information on the crust microphysics if microphysics effects are not degenerate with strong-gravity effects, such as those due to scalarization. To address this issue, we consider two different models for the equation of state of the crust and we look at the effects of electron screening. The effect of scalarization on torsional oscillation frequencies turns out to be smaller than uncertainties in the microphysics for all spontaneous scalarization models allowed by binary pulsar observations. Our study shows that the observation of quasiperiodic oscillations following giant flares can be used to constrain the microphysics of neutron star crusts, whether spontaneous scalarization occurs or not.

Effects of torsional oscillation on tensile behavior of Sn–3.5 wt% Ag alloy with and without adding ZnO nanoparticles

Stress–strain characteristics of both Sn–3.5wt% Ag and Sn–3.5wt% Ag–0.3wt% ZnO alloys were investigated using tensile testing machine. Different superimposed torsional oscillation frequencies ranging from 0 to 1.3Hz at different deformation temperatures ranging from 303 to 363K were performed. X-ray diffraction (XRD), transition electron microscopy (TEM) and optical microscopy were used to investigate the microstructures of both alloys. The mechanical parameters such as Young׳s modulus Y, yield stress σy, fracture stress σf, work hardening coefficient χp and fracture strain εf were calculated. The fracture stress of both alloys decreases with increasing the superimposed frequency of torsional oscillations as well as deformation temperatures. The fracture strain behaves in a different manner i.e. it increases with increasing the deformation temperature in the alloy containing ZnO nanoparticles while decreases in the alloy free from ZnO nanoparticles. With respect to the effect of the frequency of the superimposed torsional deformation, the fracture strain increases in both alloys.

Constraints on the symmetry energy from neutron star observations

The modeling of many neutron star observables incorporates the microphysics of both the stellar crust and core, which is tied intimately to the properties of the nuclear matter equation of state (EoS). We explore the predictions of such models over the range of experimentally constrained nuclear matter parameters, focusing on the slope of the symmetry energy at nuclear saturation density L. We use a consistent model of the composition and EoS of neutron star crust and core matter to model the binding energy of pulsar B of the double pulsar system J0737-3039, the frequencies of torsional oscillations of the neutron star crust and the instability region for r-modes in the neutron star core damped by electron-electron viscosity at the crust-core interface. By confronting these models with observations, we illustrate the potential of astrophysical observables to offer constraints on poorly known nuclear matter parameters complementary to terrestrial experiments, and demonstrate that our models consistently predict L < 70 MeV.

Simultaneous Measurements of the Torsional Oscillator Anomaly and Thermal Conductivity in SolidHe4

In these torsional oscillator experiments, the samples of solid (4)He were characterized by measuring their thermal conductivity. Polycrystalline samples of helium of either high isotopic purity or natural concentration of (3)He were grown in an annular container by the blocked-capillary method and investigated before and after annealing. No correlation has been found between the magnitude of the low-temperature shift of the torsional oscillator frequency and the amount of crystalline defects as measured by the thermal conductivity. In samples with the natural (3)He concentration, a substantial excess thermal conductivity over the usual T(3) dependence was observed below 120 mK.

Torsional oscillations of longitudinally inhomogeneous coronal loops

We explore the effect of an inhomogeneous mass density field on frequencies and wave profiles of torsional Alfven oscillations in solar coronal loops. Dispersion relations for torsional oscillations are derived analytically in limits of weak and strong inhomogeneities. These analytical results are verified by numerical solutions, which are valid for a wide range of inhomogeneity strength. It is shown that the inhomogeneous mass density field leads to the reduction of a wave frequency of torsional oscillations, in comparison to that of estimated from mass density at the loop apex. This frequency reduction results from the decrease of an average Alfven speed as far as the inhomogeneous loop is denser at its footpoints. The derived dispersion relations and wave profiles are important for potential observations of torsional oscillations which result in periodic variations of spectral line widths. Torsional oscillations offer an additional powerful tool for a development of coronal seismology.

On the Bödewadt–Rosenblat flow

Fluid motion induced by the torsional oscillations (of angular velocity bΩcosω T) of an infinite disk in contact with an incompressible viscous rotating (with angular velocity aΩ) fluid of semi-infinite extent is analysed when the amplitude parameter α( = b/a) varies from zero to infinity. Composite solutions valid over the whole of the flow regime and specific expressions for the shearing stress components at the disk and for the axial flow in the far region are obtained for low and high frequencies of torsional oscillations. Using the method of matched asymptotic expansions, we find that the region of the mean flow increases with α and reaches a maximum before settling down to the Rosenblat profile. Series expressions (for α < 1) are deduced for physical quantities of interest when the fluid in the far field and the disk are rotating with different angular velocities (in the same or in the opposite sense), which agree well with the known numerical results.

Hydrodynamic properties on superfluid3He in high magnetic fields up to 12 tesla

Using a torsional oscillator, superfluid fraction and viscosity of superfluid3He were measured in the A1 and the a2 phase up to 12 Tesla below 1 mK in the pressure of 29 bar. This is the first measurement in the high magnetic field region in a well defined geometry and in a controlled texture. The a1 and the a2 transition were seen clearly in the torsional oscillator frequency and amplitude. Two GL parameters, β245 and β24, are independent of field up to 12 Tesla. β245 is 1.18 from the A2 phase measurements, which agree with those from heat capacity measurement. While β24 is 3.08 from the a1 phase, which is smaller than that from recent spin entropy wave measurement.