Circular Frequency Research Articles

Direct numerical simulation and biglobal stability investigations of the gaseous motion in solid rocket motors

AbstractIn this article, a biglobal stability approach is used in conjunction with direct numerical simulation (DNS) to identify the instability mode coupling that may be responsible for triggering large thrust oscillations in segmented solid rocket motors (SRMs). These motors are idealized as long porous cylinders in which a Taylor–Culick type of motion may be engendered. In addition to the analytically available steady-state solution, a computed mean flow is obtained that is capable of securing all of the boundary conditions in this problem, most notably, the no-slip requirement at the chamber headwall. Two sets of unsteady simulations are performed, static and dynamic, in which the injection velocity at the chamber sidewall is either held fixed or permitted to vary with time. In these runs, both DNS and biglobal stability solutions converge in predicting the same modal dependence on the size of the domain. We find that increasing the chamber length gives rise to less stable eigenmodes. We also realize that introducing an eigenmode whose frequency is sufficiently spaced from the acoustic modes leads to a conventional linear evolution of disturbances that can be accurately predicted by the biglobal stability framework. While undergoing spatial amplification in the streamwise direction, these disturbances will tend to decay as time elapses so long as their temporal growth rate remains negative. By seeding the computations with the real part of a specific eigenfunction, the DNS outcome reproduces not only the imaginary part of the disturbance, but also the circular frequency and temporal growth rate associated with its eigenmode. For radial fluctuations in which the vorticoacoustic wave contribution is negligible in relation to the hydrodynamic stability part, excellent agreement between DNS and biglobal stability predictions is ubiquitously achieved. For axial fluctuations, however, the DNS velocity will match the corresponding stability eigenfunction only when properly augmented by the vorticoacoustic solution for axially travelling waves associated with the Taylor–Culick profile. This analytical approximation of the vorticoacoustic mode is found to be quite accurate, especially when modified using a viscous dissipation function that captures the decaying envelope of the inviscid acoustic wave amplitude. In contrast, pursuant to both static and dynamic test cases, we find that when the frequency of the introduced eigenmode falls close to (or crosses over) an acoustic mode, a nonlinear mechanism is triggered that leads to the emergence of a secondary eigenmode. Unlike the original eigenmode, the latter materializes naturally in the computed flow without being artificially seeded. This natural occurrence may be ascribed to a nonlinear modal interplay in the form of internal, eigenmode-to-eigenmode coupling instead of an external, eigenmode pairing with acoustic modes. As a result of these interactions, large amplitude oscillations are induced.

Cycloidal pendulum with a rolling cylinder

Free vibrations of a heavy homogeneous cylinder rolling in a cylindrical cavity whose directing curve is a brachistochrone are considered. The equation of motion of the cylinder is derived and the circular frequency of free vibrations of the cylinder center of mass is determined. An analogy between the cycloidal pendulum with a rolling cylinder and the classical cycloidal pendulum in the form of a material point is obtained.

N-cadherin specifies first asymmetry in developing neurons

The precise polarization and orientation of developing neurons is essential for the correct wiring of the brain. In pyramidal excitatory neurons, polarization begins with the sprouting of opposite neurites, which later define directed migration and axo-dendritic domains. We here show that endogenous N-cadherin concentrates at one pole of the newborn neuron, from where the first neurite subsequently emerges. Ectopic N-cadherin is sufficient to favour the place of appearance of the first neurite. The Golgi and centrosome move towards this newly formed morphological pole in a second step, which is regulated by PI3K and the actin/microtubule cytoskeleton. Moreover, loss of function experiments in vivo showed that developing neurons with a non-functional N-cadherin misorient their cell axis. These results show that polarization of N-cadherin in the immediate post-mitotic stage is an early and crucial mechanism in neuronal polarity.

Dynamic of Billboard Thin Plate

The authors of the paper designed the project of the structure of billboard with size 8x18 m. The design includes reinforced concrete foundations, steel vertical column, two advertising boards. The grand view of boards arranged in “V” with 30 ¡ angle. For the possibility of emplacement advertising films ladders and walkways as well as supporting structure for mounting lights must be built. Nowadays in place of sticking promotional material a special film is used attached around the perimeter of grid system covered by the thin steel plate. The geometric non-linear theory of large deflections must be used for a description of behaviour of such a plate. Thin steel sheet changes its own circular frequency depending on the load level. In case of the wind load, it is necessary to analyze the possibility of resonant phenomena, as well.

One sign ion mobile approximation

The electrical response of an electrolytic cell to an external excitation is discussed in the simple case where only one group of positive and negative ions is present. The particular case where the diffusion coefficients of the negative ions, D(m), is very small with respect to that of the positive ions, D(p), is considered. In this framework, it is discussed under what conditions the one mobile approximation, in which the negative ions are assumed fixed, works well. The analysis is performed by assuming that the external excitation is sinusoidal with circular frequency ω, as that used in the impedance spectroscopy technique. In this framework, we show that there exists a circular frequency, ω*, such that for ω > ω*, the one mobile ion approximation works well. We also show that for D(m) ≪ D(p), ω* is independent of D(m).

Dynamic Properties of Small Chamber Air Gages

In the paper, the investigations on the dynamic properties of air gauges are presented. As an important parameter, the time response underwent the analysis. The measurement of the amplitudes of back-pressure pk dependent on the input signal circular frequency ω for the group of air gauges with various parameters has been performed, too. The obtained results underwent comparative analysis with the results of investigation of the step response. The examinations of the step response of typical back-pressure air gage with small measuring chamber and with a piezoresistive pressure transducer led to the conclusion that its behavior is very close to the first-order dynamical system. The examined air gauges could be successfully exploited in the industrial measurement of values changing in time (dynamical measurement).

A Balance Ability Evaluation Method Based on Multidimension Passive Motion Excitement from 6-PSS Robot

Focusing on personal balance ability evaluation, a method was developed to improve the dependency to many uncertainties, and to enhance veracity and objectivity, where impulse disturbance for human gravity center was produced by a six degree-of-freedom motion platform of 6-PSS under feet, and corresponding wave of gravity center was measured by a force plate real time. Dynamic process of overcoming this disturbance was abstracted as classic second-order linear model, where the product of damp coefficient and undammed circular frequency was estimated through recorded data based on system identification theory. By using this value, settling time was calculated and used as the balance evaluating index. Through the evaluating results of 103 students or graduate students, the feasibility of this method was validated, and reference ranges of healthy persons’ settling time were concluded for clinical balance evaluation.

Spatial Coherency Function of Seismic Ground Motion Based on UPSAR Records

The U.S. Geological Survey Parkfield Dense Seismograph Array (UPSAR) successfully recorded strong motions during 2003 San Simeon earthquake (M 6.5) and 2004 Parkfield earthquake (M 6.0). Because the array covers a very small area (0.45km2), these data offer some interesting insights into spatial variations of seismic ground motions that suits for engineering scale. In this research, we study the spatial coherency function of seismic ground motion in the horizontal and vertical directions by digital signal processing. The results show that when the circular frequency is smaller than , the degressive trend of the coherency function becomes significant with the separation distance elongation, while the data deviation of the coherency function becomes larger with the frequency rise, which shows no obvious rules. In addition, based on the strong-motion data, a suitable spatial coherency model of ground motion is selected through comparing existing model functions, and the appropriate recommendations for improvement is put forward. Finally, according to different frequency range, the fitting parameters of the spatial coherency function of ground motion are obtained through numerical simulation. The spatial coherency function proposed in this paper is practical in simulation of ground motion field.

Estimation of parameters of a laser Doppler velocimeter and their Cramer–Rao lower bounds

Considering the influence of acceleration and the Gaussian envelope for a laser Doppler velocimeter (LDV), parameter estimation of a Doppler signal with a Gaussian envelope was investigated based on introducing acceleration. According to the theory of mathematics statistics, the Cramer-Rao lower bounds (CRLBs) of Doppler circular frequency and its first order rate were analyzed, formulas of CRLBs were given, and the power spectrum estimation with adjustment was discussed. The results of theory and the simulation show that the CRLBs are related to the data length, the signal-to-noise ratio (SNR), and the width of the Gaussian envelope, and they can be decreased by increasing the data length or improving the SNR; the larger the acceleration is and the narrower the Gaussian envelope is, the larger the CRLBs of Doppler circular frequency and its first order rate are; the gap between the variances of the measuring results and the CRLBs narrows when the SNR of the signal is improved, and is almost eliminated when the SNR is higher than 6 dB. It is concluded that the model presented is much more suitable for a LDV than that acquired by Rife and Boorstyn [IEEE Trans. Inform. Theory 20, 591 (1974)].

An evolutionary stochastic ground-motion model defined by a seismological scenario and local site conditions

This paper is concerned with modeling earthquake-induced ground accelerations and the simulation of the dynamic response of linear structures through the principles of stochastic dynamics. A fully evolutionary approach, with nonstationarity both in amplitude and in frequency content, is proposed in order to define the seismic action, based on seismological information in the form of a small number of input parameters commonly available in deterministic or probabilistic seismic design situations. The signal is obtained by filtering a Gaussian white-noise. The finite duration and time-varying amplitude properties are obtained by using a suitable envelope function. By utilizing a subset of the records from the PEER-NGA strong-motion database, and time-series analysis tools extended to nonstationary processes, the key transfer-function properties, in terms of circular frequency, damping ratio and spectral intensity factor, are identified. A regression analysis is conducted for practical and flexible application of this model, in order to empirically relate the identified time-varying parameters of the filter to the characteristics defining earthquake scenarios such as magnitude, rupture distance and soil type. A validation study and a parametric investigation using elastic response spectra is also included. Results show that the final seismic model can reproduce, with satisfactory accuracy, the characteristics of acceleration records in a region, over a broad range of response periods.

Parametric vibration of submerged floating tunnel tether under random excitation

For the study of the parametric vibration response of submerged floating tunnel tether under random excitation, a nonlinear random parametric vibration equation of coupled tether and tube of submerged floating tunnel is set up. Subsequently, vibration response of tether in the tether-tube system is analyzed by Monte Carlo method. It may be concluded that when the tube is subjected to zero-mean Gaussian white noise random excitation, the displacement and velocity root mean square responses of tether reach the peak if the circular frequency of tube doubles that of tether; the displacement and velocity root mean square responses of tether increase as the random excitation root mean square increases; owing to the damping force of water, the displacement and velocity root mean square responses of tether decrease rapidly compared with tether in air; increasing the damping of the tether or tube reduces the displacement and velocity root mean square responses of tether; the large-amplitude vibration of tether may be avoided by locating dampers on the tether or tube.

Dynamic basic displacement functions for free vibration analysis of tapered beams

Introducing new functions, namely Basic Displacement Functions (BDFs), free transverse vibration of non-prismatic beams is studied from a mechanical point of view. Following structural/mechanical principles, new dynamic shape functions could be developed in terms of BDFs. The new shape functions appear to be dependent on the circular frequency, configuration of the element and its physical properties such as mass density and modulus of elasticity. Differential transform method, a relatively new efficient semi analytical-numerical tool for solving differential equations, is employed to obtain BDFs via solving the governing differential equation for transverse motion of non-prismatic beams. The method poses no restrictions on either type of cross-section or variation of cross-sectional dimensions along the beam element. Using the present element, free vibration analysis is carried out for five numerical examples including beams with (a) linear mass and inertia, (b) linear mass and fourth order inertia, (c) second order mass and fourth order inertia, (d) tapered beam with non-classical boundary conditions and (e) exponentially varying area and inertia. It is observed that the results are in good agreement with the previously published ones in the literature. Finally convergence of the method is investigated.

Investigation of Profile Cutting on Glass Plates Using a Pulsed UV Laser System

A solid-state ultraviolet laser with a circular processing path was used for profile cutting on soda-lime glass plates. Simulation results show that decreasing scanning speed and path spacing and increasing circular processing path frequency yields a smooth cutting edge for the same processing length. Profile glass-plate cutting shows the machined surface with more obvious roughness and numerous microcracks near areas of laser focus than in areas of laser defocusing. This phenomenon is attributed to high laser-energy density and strongly affecting surface roughness.

Parameter Study on Pogo Stability of Liquid Rockets

Nomenclature As = cross-sectional area of suction line, m 2 Ath = nozzle throat area, m 2 Cf = thrust coefficient, dimensionless g = standard gravitational acceleration, m=s hs = height of propellant in suction line, m ht = height of propellant in tank, m Is = inertance of propellant in suction line, s =m K = effective stiffness of accumulator which is defined as KaKp= Ka Kp , 1=m Ka = stiffness of the accumulator, 1=m 2 Kp = stiffness of pump cavitation, 1=m 2 k = the ratio between effective stiffness and stiffness of accumulator defined as K =Ka, dimensionless L = length, m Ms = modal mass of structure mode, kg i, j, n = index, dimensionless m 1 = pump gain, dimensionless N = number of thrust chambers, dimensionless p = oscillatory pressure, Pa Rc = linearalized combustion resistance for propulsion flow perturbation, s=m w = weight displacement of flow, N = mass flow gain factor of a pump, s = the propulsion modal damping coefficient, dimensionless = dimensionless mass flow gain factor of a pump defined as , dimensionless = couple strength between the structure mode and the propulsion system, dimensionless = frequency ratio between the propulsion mode and the structure mode, dimensionless = the structure damping ratio, dimensionless = density of the propellant, kg=m ’ = structural mode gain, dimensionless = circular natural frequency of the structure mode, 1=s ! = circular natural frequency of the propulsion mode, 1=s Subscripts

Investigating the stabilizing effect of stochastic excitation on a chaotic dynamical system

The response of an interactive Mathieu–Duffing system in R 4, subjected to a harmonic excitation is investigated. For a deterministic circular frequency, chaotic behavior is observed. Subsequently it is shown that when the excitation becomes stochastic, chaos is subsided and trajectories tend to a diffused attracting set. The stabilizing effect of stochastic excitation is verified by finding the largest Lyapunov exponent for the two cases.

A posteriori error estimators of finite-element approximations for problems of forced harmonic vibrations of piezoelectrics

A variational problem of determination of the amplitude of the velocity vector of elastic displacements and the electric potential of a piezoelectric with instantaneous memory that executes steady-state vibrations under the influence of harmonic loads of given circular frequency is formulated. We establish conditions of well-posedness of this class of problems and find a priori estimates of convergence of approximations of the finite-element method to their solution. A posteriori error estimators of approximations of the finite-element method, which enable us to determine the distribution of energy norms of errors by solving local problems of the residual of approximation at each finite element of triangulation, are constructed. An algorithm for calculating estimators of this type is described in detail for two-dimensional problems for both triangular and tetragonal finite elements, which may be extended to the three-dimensional case. The efficiency and reliability of the estimator of piecewise bilinear approximations of the finite-element method is illustrated by numerical solutions of a model problem.

THE ANALYSIS OF A BEAM UNDER MOVING LOADS

Abstract: It is assumed that a beam made of material has a physical nonlinear behavior. This beam is analyzed under the moving concentrated and distributed continuous loads. The vibration equations of motion are derived from the Hamilton's Principle and Euler–Lagrange Equation. In this study, the amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam has been calculated. At the state of concentrated moving load, the obtained analytic solution has been exemplified. The results of this study indicate that when the material of the beam is considered physically nonlinear, there is no critical velocity and the resonance phenomenon doesn’t happen.

Numerical wave tank for the application in ocean engineering

采用FLUENT 软件中的用户自定义函数功能和动网格功能进行造波和消波, 采用VOF 方法捕捉自由液面, 开发了一个数值波浪水池, 该水池可以生成规则波浪、按照波谱生成不规则波浪以及生成既定的不规则波波列. 文中开展了网格和时间步长试验, 力图找到经济精确的网格划分方案和高效的时间步长方案. 文中按照Jonswap 谱进行了不规则波浪的数值模拟, 采用了等分能量法分解波谱的频率区间来得到组成波的 圆频率, 模拟结果显示计算波谱与目标波谱一致, 波浪的统计特征得到了很好的体现, 模拟不规则波波谱的 缺点是耗时过长. 由于真实海况下对海洋浮式结构物造成损坏的往往不是整个波浪时间序列, 而是少数的几个大波或者波列中的波群. 因此采用CFD方法准确模拟出既定的波列将会对了解极端海况下海洋结构物的损 坏事故提供极大帮助. 采用本文提出的方法成功模拟出了既定的极大波, 这个方法的关键在于确定造波板的 运动规律. 类似按照波谱造波, 文中将造波板处的波浪时历进行了分解, 得到了若干个小振幅波, 通过傅里 叶级数法推导出了每个小振幅波的特征参数. 同样采用水力传递函数确定每个小振幅波对应的推板振幅, 之后将这些组成波对应的推板运动规律进行叠加得到了模拟不规则波波列时需要的推板运动规律.

Coherent controlling surface plasmon transport properties in Ag nanowire by classic optical field

Coherent controlling surface plasmon transport in metal nanowire coupled to quantum dot is investigated theoretically by real-space method. In the calculations, the dispersion relation of metal nanowire is supposed to be linear and the quantum dot is a cascaded three-level system. The calculations reveal that whether the surface plasmon is transmitted or reflected by turning off or on the classic field can be controlled. The surface plasmon transmission and reflection spectra can be controlled by adjusting the intensity and the circular frequency of classic optical field even the energy of surface plasmon and quantum dot is not matched. The dissipations affecting on the transport properties are also discussed.

Magnetic Field Induction and Time Intervals of the Electron Transitions Approached in a Classical and Quantum-Mechanical Way

The motion of electron wave packets of a metal is examined classically in the presence of the magnetic field with the aim to calculate the time intervals between two states lying on the same Fermi surface. A lower limiting value of the transition time equal to about 10–18 sec is estimated as an average for the case when the states are lying on the Fermi surface having a spherical shape. Simultaneously, an upper limit for the electron circular frequency in a metal has been also derived. A formal reference of the classical transition time to the time interval entering the energy-time uncertainty relations known in quantum mechanics is obtained.