Eigenfrequencies Of Modes Research Articles

Fluid pulsation modes from strange stars in a higher-dimensional spacetime

In this work, we make the first step to derive non-radial pulsation equations in extra dimensions and investigate how the $f$- and $p_1$-mode frequencies of strange quark stars, within the Cowling approximation, change with the number of dimensions. In this regard, the study is performed by solving numerically the non-radial pulsation equations, adjusted for a $d$-dimensional space-time $(d\geq4)$. We connect the interior to a Schwarzschild-Tangherlini exterior metric and analyze the $f$- and $p_1$- mode frequencies. We found that the frequencies could become higher than those found in four-dimensional space-time. The $f$-mode frequency is essentially constant and only for large gravitational radius values grows monotonically and fast with the gravitational radius. In a gravitational radius range, where $f$-mode frequencies are constant, they increase for space-time dimensions $4\leq d\leq6$ and decrease for $d\geq7$. Regarding $p_1$-mode frequencies they are always larger for higher dimensions and decay monotonically with the increase of the gravitational radius. In extra dimensions, as it happens for four-dimensional space-time, we found $p_1$-mode frequencies are always larger than the $f$-modes ones. In the Newtonian gravity, for a homogeneous star in $d$ dimensions, we observe that the $f$-mode eigenfrequencies are constant and given by the relation $\omega^2=l\, M\, G_d/R^{d-1}$; where $l$ represents the spherical harmonic index, $M\,G_d$ being the total star mass and $R$ the stellar radius.

Results from the Alfvén Eigenmode Active Diagnostic during the 2019-2020 JET deuterium campaign

This paper presents results of extensive analysis of mode excitation observed during the operation of the Alfvén Eigenmode Active Diagnostic (AEAD) in the JET tokamak during the 2019-2020 deuterium campaign. Six of eight toroidally spaced antennas, each with independent power and phasing, were successful in actively exciting stable MHD modes in 479 plasmas. In total, magnetic resonances were detected with up to fourteen fast magnetic probes. In this work, we present the calculations of resonant frequencies f 0, damping rates γ < 0, and toroidal mode numbers n, spanning the parameter ranges f 0≈ 30–250 kHz, −γ ≈ 0–13 kHz, and . In general, good agreement is seen between the resonant and the calculated toroidal Alfvén Eigenmode frequencies, and between the toroidal mode numbers applied by the AEAD and estimated of the excited resonances. We note several trends in the database: the probability of resonance detection decreases with plasma current and external heating power; the normalized damping rate increases with edge safety factor but decreases with external heating. These results provide key information to prepare future experimental campaigns and to better understand the physics of excitation and damping of Alfvén Eigenmodes in the presence of alpha particles during the upcoming DT campaign, thereby extrapolating with confidence to future tokamaks.

High-speed digitization of the amplitude and frequency in open-loop sideband frequency-modulation Kelvin probe force microscopy

A more inclusive and detailed measurement of various physical interactions is enabled by the advance of high-speed data digitization. For surface potential characterization, this was demonstrated recently in terms of open-loop amplitude modulation Kelvin probe force microscopy (OL AM-KPFM). Its counterpart, namely open-loop frequency modulation Kelvin probe force microscopy (OL FM-KPFM), is examined here across different materials and under various bias voltages in the form of OL sideband FM-KPFM. In this implementation the changes in the amplitude and resonance frequency of the cantilever were continuously tracked as a conductive AFM probe was modulated by a 2 kHz AC bias voltage around the first eigenmode frequency of the cantilever. The contact potential difference (CPD) between the AFM probe and sample was determined from the time series analysis of the high-speed 4 MHz digitized amplitude and frequency signals of the OL sideband FM-KPFM mode. This interpretation is demonstrated to be superior to the analysis of the parabolic bias dependent response, which is more commonly used to extract the CPD in OL KPFM modes. The measured OL sideband FM-KPFM amplitude and frequency responses are directly related to the electrostatic force and force-gradient between the AFM probe and sample, respectively. As a result, clear distinction was observed for the determined CPD in each of these cases across materials of different surface potentials, with far superior spatial resolution when the force-gradient detection was used. In addition, the CPD values obtained from OL sideband FM-KPFM amplitude and frequency measurements perfectly matched those determined from their closed-loop AM-KPFM and FM-KPFM counterparts, respectively.

Manipulating the frequency response of small high-frequency atomic force microscope cantilevers

We study small (less than 10 µm-long) high-frequency (greater than 1 MHz) cantilevers specially designed for visualization of biomolecular processes in high-speed atomic force microscopes. The frequency responses of the first three flexural eigenmodes are investigated for the modified geometries. It is found that the Q-factors can be significantly altered in the desired way by reengineering the cantilever geometry without affecting its main operational parameters, such as the spring constant and the resonance frequency of the first flexural eigenmode in an air environment. In addition, higher-order flexural resonances can be moved away from the fundamental resonance with these geometrical modifications. The Q-factors in liquid, on the other hand, do not show a significant difference due to high viscous damping of the medium. Regular cantilevers modified by a focused ion beam are used to demonstrate the validity of the finite element simulation model.

Simulation of Drop Oscillation Using the Lattice Boltzmann Method

We simulate the oscillation of the viscous drop in the viscous liquid. We combine methods of chromodynamics model and Shan-Chen pseudo-potential for the immiscible fluids. We measure the frequency of the first nontrivial eigenmode using the initial ellipsoid form of the drop. Drop oscillates about the equilibrium spherical form of radius $$R$$ . Computed frequency as a function of the radius $$R$$ follows to the well known Rayleigh formula. We discuss the simulation setup in the framework of the Lattice Boltzmann method.

Method of calculating dynamic designs of space launch vehicles for designing systems of stabilization of their motion

Dynamic designs of tandem space launch vehicles are calculated according to the standard OST 92-4548-85. The eigenmodes and eigenfrequencies of the elastic structure are calculated using the MSC Nastran or a similar program. We propose an addition to the existing methods of calculating dynamic designs of liquid-propellant rockets with account for their elasticity applying a method oriented towards operational generation of input data for developing systems of stabilizing their motion. We developed a procedure containing calculation of eigenmodes and eigenfrequencies of missile body elastic modes and the coefficients of impact of the elastic modes and surplus degrees of freedom. To demonstrate the methods efficiency, in taking down the results for tandem launch vehicles in the analytical form the OST formulas are re-derived. In validating the proposed method of calculating design schemes we obtained results practically coincident with the already applied formulas for the range of tasks under examination. The versatility of the proposed method is illustrated by calculation of coefficients absent from the OST because the factors influencing rocket dynamics are not taken into account in the standard. The proposed method is distinguished by its generality, which allows describing various types of launch vehicles while taking into account all significant factors that influence the dynamics of their motion.

Non-Hermitian topological metamaterials with odd elasticity

We establish non-Hermitian topological mechanics in one dimensional (1D) and two dimensional (2D) lattices consisting of mass points connected by meta-beams that lead to odd elasticity. Extended from the "non-Hermitian skin effect" in 1D systems, we demonstrate this effect in 2D lattices in which bulk elastic waves exponentially localize in both lattice directions. We clarify a proper definition of Berry phase in non-Hermitian systems, with which we characterize the lattice topology and show the emergence of topological modes on lattice boundaries. The eigenfrequencies of topological modes are complex due to the breaking of $\mathcal{PT}$-symmetry and the excitations could exponentially grow in time in the damped regime. Besides the bulk modes, additional localized modes arise in the bulk band and they are easily affected by perturbations. These distinguishing features may manifest themselves in various active materials and biological systems.

True 3D-AFM sensor for nanometrology

A new three dimensional (3D) atomic force microscopic (AFM) probe, referred to as the 3D-Nanoprobe, is introduced. The 3D-Nanoprobe is realized by introducing flexure hinge structures to the cantilever of a conventional critical dimension AFM (CD-AFM) probe. It has quasi-isotropic stiffness in 3D directions and is thus more powerful for detecting 3D tip-sample interaction forces in AFM measurements. In addition, the stiffness of the 3D-Nanoprobe is balanced to the bending stiffness of slender CD-AFM tips, offering improved 3D sensitivity. In this paper, a design example of a 3D-Nanoprobe based on a CD-AFM probe with a tip nominal diameter of 70 nm is presented. The design parameters are optimized via analytic modelling and the finite element analysis (FEA) method. The simulation results indicate that the designed 3D-Nanoprobe has much better performance than that of the original CD-AFM probe, for instance, its stiffness’ anisotropy ratio (including the tip contribution) has been improved from 8:8:1 (x, y, z) to 0.9:0.9:1 (x, y, z). The probing sensitivity is improved by a factor of more than 106, 128 and 1.6 in x-, y- and z-direction, respectively. Moreover, the designed 3D-Nanoprobe has the first bending mode eigenfrequency of 84.4 kHz and the first torsional mode eigenfrequency of 346 kHz. The 3D-Nanoprobe has been manufactured by applying a focused ion beam (FIB) tool. Finally, to detect the full 3D interaction forces by the 3D-Nanoprobe, a new AFM-head prototype which consists of two independently adjustable dual optical levers have been developed.

Researches Regarding the Mechanical Properties of a NewHybrid Vegetal Resin

The paper presents the mechanical behaviour and properties of a new hybrid vegetal based resin. For this, through static loading tests, the main mechanical characteristics were determined: static Young modulus, breaking strength, breaking elongation and transversal Poisson ratio. Samples of the proposed materials were subjected also to free vibration tests, by clamping them at one end and leaving them free at the other. The observation and results from these were used for deduction of the first vibration mode eigenfrequency, the dynamic Young modulus, the loss and damping factors. Some representative SEM images with an electronic microscope were collected and the samples surface roughness was determined. By using the Thermogravimetric analysis (TGA), the mass loss up to 800� C was investigated. Compared to the other resins that have dammar in composition, the proposed dammar based resin from this research has a 15.32 times higher static Young modulus than the oil palm trunk and 8.885 times higher than the oil palm trunk (OPT) with 20% dammar resin.

Development of an Interference Filter-Stabilized External-Cavity Diode Laser for Space Applications

The National Time Service Center of China is developing a compact, highly stable, 698 nm external-cavity diode laser (ECDL) for dedicated use in a space strontium optical clock. This article presents the optical design, structural design, and preliminary performance of this ECDL. The ECDL uses a narrow-bandwidth interference filter for spectral selection and a cat’s-eye reflector for light feedback. To ensure long-term stable laser operation suitable for space applications, the connections among all the components are rigid and the design avoids any spring-loaded adjustment. The frequency of the first lateral rocking eigenmode is 2316 Hz. The ECDL operates near 698.45 nm, and it has a current-controlled tuning range over 40 GHz and a PZT-controlled tuning range of 3 GHz. The linewidth measured by the heterodyne beating between the ECDL and an ultra-stable laser with 1 Hz linewidth is about 180 kHz. At present, the ECDL has been applied to the principle prototype of the space ultra-stable laser system.

Pull-in response and eigen frequency analysis of graphene oxide-based NEMS switch

In this work, finite element analysis of shunt capacitive switch having Gold/Graphene oxide (GO) bridge structure is reported. The pull-in voltage analysis of two structures, intact and circularly perforated Gold/GO-based shunt capacitive switch is performed. The pull-in voltage of 5.6 V and 4.75 V are obtained for intact and circularly perforated structure respectively for 2 µm long, 0.3 µm wide and 4.9 nm thick GO suspended beam. The pull-in voltage gets reduced by making circular holes (perforations) in the suspended beam. Also, the extraction of basic modes of vibration of the switch is done using eigen frequency analysis. The eigen frequency analysis for both the structure is performed. The eigen mode obtained in eigen frequency analysis gives information about the desired functioning of NEM switch. The obtained eigen frequencies for primary eigen modes are 3.8 MHz and 3.21 MHz for intact and circularly perforated NEM switch structure. The perforations in the beam reduce the flexural rigidity of the beam hence the frequency of eigen mode is less.

A Micro Piezoelectric Motor With Multiple Excitation Modes and Methods

To widen the performance of piezoelectric motors, this paper demonstrates a micro piezoelectric motor having multiple driving ways. The stator includes a hollow polygon bar and two groups of PZT plates. PZT plates are symmetrically bonded onto a brass base, and used to actuate the vibration modes of the stator. The symmetrical design enables the motor to operate in two types of vibration modes. The working modes are the second/third-order in-plane bending modes, and can be excited by different ways. Elliptical motion of stator surface points is generated by superposition of two bending modes with the same order. To investigate the feasibility of multi-mode and multi-motivation mechanisms, vibration behaviors of stator driving particles are simulated using ANSYS software. The structural parameters of the stator are strictly designed to harmonize the eigenfrequencies of the vibration modes. The calculated results reveal that the motor performance can be adjusted by selecting different operating modes and excitation ways. The motor performances under various excitation ways and driving modes are also investigated experimentally to validate the proposed design. The dimension of the fabricated prototype motor is 8.3 mm$\times 7.2$ mm$\times 15.0$ mm. The maximum torques are respectively 8.3 cN$\cdot \text{m}$ and 13.3 cN$\cdot \text{m}$ under single-phase and two-phase excitation voltages, when the motor operates in the second-order bending modes. The corresponding no-load speeds are respectively 40 rpm and 47 rpm. The maximum torque and speed under the third-order bending modes are much smaller than that under the second-order bending modes.

Analysis of Mode Interaction in Ultra-low Frequency Oscillation Based on Trajectory Eigenvalue

Complex phenomena such as prolongedly undamped ultra-low frequency oscillation (ULFO) and eigenmode re-excitation are observed in the simulations of hydroelectric power systems. Emphases are put on nonlinearities and mode interactions, which cannot be analyzed by traditional eigen-analysis methods. In order to investigate the mechanism of the evolvement of the nonlinear dynamic process in ULFO, this paper proposes a method to analyze the mode interactions quantificationally. First, a disturbed trajectory is decoupled into a set of time-varying components. Second, transfer matrices of eigenmodes are extracted along the trajectory. Third, consecutive sequences of eigenvalues and trajectories of components are formed by a proposed technique. Based on the decoupled components and transfer matrices, the mechanisms of mode interactions and inheritance relationships between eigenmodes are analyzed. The causes and developments of the above complex phenomena are revealed by the proposed method in a test two-machine system. Meanwhile, the accuracy of the eigenmode matching technique is verified in the New England system.

О влиянии внутреннего давления на колебания цилиндрического газового пузырька

Natural and forced oscillations of a gas bubble are studied. The bubble has the shape of a round cylinder in the state of equilibrium. It is bounded in the axial direction by two parallel solid surfaces and is surrounded by an incompressible liquid of a finite volume with a free outer surface. The entire system is under an alternating pressure field. The velocity of the contact line of three media (gas-liquid-solid substrate) is proportional to the deviation of the contact angle from the equilibrium value. The frequency of eigenmodes of a gas bubble can increase with an increase in the Hocking parameter, in contrast to the frequencies of an incompressible liquid drop, which only decrease. It is shown that radial oscillations of a cylindrical bubble are possible only in a finite volume of liquid. The effect of crossing the modes of natural oscillations is considered for the dissipative case. The amplitude-frequency characteristics are constructed for different values of the internal gas pressure. Resonance phenomena are found. It is shown that the external influence excites, first of all, volumetric oscillations of the bubble. Variations in shape are caused by the movement of the contact line. Expressions are found for the vibration amplitude in the case of a fixed contact line and a fixed contact angle.

Fourier Analyses of High-Order Continuous and Discontinuous Galerkin Methods

We present a Fourier analysis of wave propagation problems subject to a class of continuous and discontinuous discretizations using high-degree Lagrange polynomials. This allows us to obtain explicit analytical formulas for the dispersion relation and group velocity and, for the first time to our knowledge, characterize analytically the emergence of gaps in the dispersion relation at specific wavenumbers, when they exist, and compute their specific locations. Wave packets with energy at these wavenumbers will fail to propagate correctly, leading to significant numerical dispersion. We also show that the Fourier analysis generates mathematical artifacts, and we explain how to remove them through a branch selection procedure conducted by analysis of eigenvectors and associated reconstructed solutions. The higher frequency eigenmodes, named erratic in this study, are also investigated analytically and numerically.

Pc4‐5 Poloidal ULF Wave Observed in the Dawnside Plasmaspheric Plume

AbstractA localized Pc4‐5 ultralow‐frequency (ULF) wave event associated with a plasmaspheric plume was observed by THEMIS‐E on the dawnside near L = 6, which was identified as a second harmonic poloidal wave. The plume was identified as a sudden density enhancement during an outbound pass. The charged particle populations in the plume have a variety of periodic modulation characteristics at different energies. First, there is an antiphase relationship between magnetic field Br and particle flux across a wide energy range both for ions and electrons (~50 keV to 1 MeV). Second, there is a 180° phase shift in the modulated ion flux within an energy range of ~2–6 keV, with negative slope dispersions of ion pitch angle distributions at ~2–6 keV and ~50–75 keV, which are characteristic of drift‐bounce resonances. Third, the lower‐energy (&lt;32 eV) ion flux is modulated at double the wave frequency, which are the result of E × B effect. Considering the generation mechanism of this poloidal mode wave within the plume, we find that it is likely generated by drift‐bounce resonance from an unstable population of ions, due to an inward radial phase space density gradient. We suggest that the localization of waves to the plume is because the high plasma density reduces the local poloidal mode eigenfrequency, enabling a match to the drift‐bounce frequencies of these ions, and resonant energy transfer from these particles to the eigenfunction at this location. This generates the Pc4‐5 second harmonic poloidal waves at a much lower L region than would otherwise be expected.

Improving high precision cam mover’s stiffness

Pre-alignment is a key challenge of the Compact Linear Collider (CLIC) study. The requirement for CLIC main beam quadrupole (MBQ) alignment is positioning to within 1 μm from target in 5 degrees of freedom (DOF) with ± 3mm travel. After motion, the position should be kept passively while the system's fundamental frequency is above 100Hz. Cam movers are considered for the task. Traditionally they are used for the alignment of heavier magnets with lower accuracy and stiffness requirement. This paper presents a new CLIC prototype cam mover with design emphasis on the fundamental frequency. A finite element method (FEM) model predicts the mode shapes and eigenfrequencies of the system and can be used for further improving the design. Experimental modal analysis (EMA) of the prototype shows that the prototype's fundamental frequency is at 44Hz. It also validates the FEM model.

Nonlinear Parametric Vibration of a Fluid-Conveying Pipe Flexibly Restrained at the Ends

In this paper, the nonlinear parametric vibration of fluid-conveying pipes flexibly restrained at both ends and subjected to the pulsation flow excitation is investigated. The nonlinear equation of motion is derived using Hamilton’s principle by considering the Kevin–Voigt viscoelastic damping, the geometric nonlinearity and the translational and rotational springs supported at the ends. The mode functions and eigen-frequencies are determined by the assumed mode method according to the elastic boundary conditions. The Galerkin method is implemented to obtain the natural frequencies and mode shapes of the pipe conveying fluid with different flow velocities. The effects of flexibly restrained conditions on stability of the pipe are analyzed. The nonlinear responses of the pipe under pulsating flow excitation are solved by the direct numerical method. The vibration behaviors are discussed in details, such as time history, frequency spectrum, phase-plane portrait, Poincare map and motion trajectory. The results show that the responses of sub-harmonic resonance and combination resonance can also be reflected in the rigidly supported pipes. The 1/5, 1/8 and 1/13 sub-harmonic resonances can occur at certain excitation frequencies of the nonlinear parametric vibration system. The steady-state response amplitudes increase by a large margin and significantly affect the stability of the pipe. The effects of different spring stiffness coefficients on the parametric resonance responses are presented. For larger translational springs and rotational stiffness coefficients, the resonance frequencies shift to higher regions and the resonance amplitudes may reduce by a certain extent in accordance with the rigid-body motion. This study can provide helpful guidance on the analysis and design of piping systems subject to vibrations.

Secondary source and error sensing strategies for the active control of sound transmission through a small opening

The openings of an enclosure allow natural ventilation and light ingress but also act as a point of entry for noise of the whole structure. In this paper, the active control of the sound transmitted through a small opening in a wall formed by two infinitely-large baffles is investigated up to 4 kHz. Based on an analytical model developed with the modal expansion method, the effects of different secondary source and error sensor strategies are compared numerically for different types of primary sound fields. The upper frequency limit of effective control is found to be determined by the eigen-frequency of the acoustic modes of the opening. Experimental results with an opening of 6 cm by 6 cm on a 31.8 cm thick wall agree well with the numerical results. The upper frequency limit of effective control is found to be 2750 Hz for a single-channel system and 3900 Hz for a 4-channel system with more than 10 dB noise reduction. It is concluded that implementing active control in small openings with an appropriate secondary source and error sensing strategy can extend the frequency range of control significantly, so that the active control systems can be applied to more noise control scenarios which have both noise reduction and ventilation requirements in the middle to high frequency range.

Shear Alfvén wave continuum spectrum with bifurcated helical core equilibria

The radial structure of the continuum spectrum of shear Alfvén and Alfvén-acoustic waves in the beta-induced Alfvén eigenmode (BAE) frequency range is modeled for tokamak plasmas in the presence of 3D effects obtained from the bifurcated MHD equilibrium reconstruction. Plasma compressibility and geodesic curvature effects responsible for the low-frequency continuum spectrum calculations are invoked. In the equilibrium calculations we find that the helically distorted MHD equilibria may exist even for the axisymmetric devices if q = 1 rational surfaces are present. The continuum calculations with the bifurcated equilibria lead to a frequency splitting between the highest frequency branch and the lowest frequency branch continua at the frequency accumulation point. Radially localised shifting of modes happens via coupling of the adjacent n − 1 continuum around an accumulation point. Our modelling (including 3D effects) correctly reproduces the phenomenon of continuum frequency splitting and provides a possible solution for the differences of few kHz in frequency splitting, which remained unexplained with the 2D kinetic calculations (Curran et al 2012 Plasma Phys. Control. Fusion 54 055001). The pressure scaling confirms the increase of helical excursion of the magnetic axis in equilibrium reconstruction and hence the range of continuum frequency splitting. In our calculations, the existence of low-frequency continua is in agreement with the experimentally observed low-frequency modes.