Dynamic instability of stiffened plates subjected to non-uniform harmonic in-plane edge loading

The dynamic instability characteristics of stiffened plates subjected to in-plane partial and concentrated edge loadings are studied using finite element analysis. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The method of Hill's infinite determinants is applied to determine the dynamic instability regions. Numerical results are presented to study the effects of various parameters, such as static load factor, aspect ratio, boundary conditions, stiffening scheme and load parameters on the principal instability regions of stiffened plates using Bolotin's method. The results show that location, size and number of stiffeners have a significant effect on the location of the boundaries of the principal instability region.     

Dynamic instability of composite plates subjected to non-uniform in-plane loads

In this paper, the dynamic instability of a shear deformable composite plate subjected to periodic non-uniform in-plane loading is studied for four sets of boundary conditions. The static component and the dynamic component of the applied periodic in-plane loading are assumed to vary according to either parabolic or linear distributions. Initially, the plate membrane problem is solved using the Ritz method to evaluate the plate in-plane stress distributions within the prebuckling range due to the applied non-uniform in-plane edge loading. Subsequently using the evaluated stress distribution within the plate, the equations governing the plate instability boundaries are formulated via Hamilton's variational principle. Employing Galerkin's method, these partial differential equations are reduced into a set of ordinary differential equations (Mathieu type of equations) describing the plate dynamic instability behaviour. Following Bolotin's method, the instability regions are determined from the boundaries of instability, which represents the periodic solution of the differential equations with period T and 2T to the Mathieu equations. The instability regions are determined for uniform, linear and parabolic dynamic in-plane loads using first-order and second-order approximations. Numerical results are also presented to bring out the effects of span to thickness ratio, shear deformation, aspect ratio, boundary conditions and static load factor on the instability regions.     

Parametric resonance of truncated conical shells rotating at periodically varying angular speed

Parametric resonance of a truncated conical shell rotating at periodically varying angular speed is studied in this paper. Based upon the Love?s thin shell theory and generalized differential quadrature (GDQ) method, the equations of motion of a rotating conical shell are derived. The time-dependent rotating speed is assumed to be a small and sinusoidal perturbation superimposed upon a constant speed. Considering the periodically rotating speed, the conical shell system is a parametric excited system of the Mathieu–Hill type. The improved Hill?s method is utilized for parametric instability analysis. Both the primary and combination instability regions for various natural modes and boundary conditions are obtained numerically. The effects of relative amplitude and constant part of periodically rotating speed and cone angle on the instability regions are discussed in detail. It is shown that for the natural mode with lower circumferential wavenumber, only the primary instability regions exist. With the increasing circumferential wavenumber, the instability widths are reduced significantly and the combination instability region might appear. The results for different boundary conditions are substantially similar. Increasing the constant rotating speed (or cone angle) all lead to the movements of instability regions and the appearance of combination instability region. The former will cause the instability width increasing, while the latter will reduce the instability width. The variation of length-to-radius ratio only causes the movements of instability regions.     

Dynamic instability of collective myosin Ⅱ motors

Some kinds of muscles can oscillate spontaneously,which is related to the dynamic instability of the collective motors.Based on the two-state ratchet model and with consideration of the motor stiffness,the dynamics of collective myosin Ⅱmotors are studied.It is shown that when the motor stiffness is small,the velocity of the collective motors decreases monotonically with load increasing.When the motor stiffness becomes large,dynamic instability appears in the forcevelocity relationship of the collective-motor transport.For a large enough motor stiffness,the zero-velocity point lies in the unstable range of the force-velocity curve,and the motor system becomes unstable before the motion is stopped,so spontaneous oscillations can be generated if the system is elastically coupled to its environment via a spring.The oscillation frequency is related to the motor stiffness,motor binding rate,spring stiffness,and the width of the ATP excitation interval.For a medium motor stiffness,the zero-velocity point lies outside the unstable range of the force-velocity curve,and the motion will be stopped before the instability occurs.     

Electric dispersion of fluid under the oscillatory instability of its free surface

A semiphenomenological analysis is performed of possible modes of electric dispersion of drops and menisci at the end of the capillary used to deliver the liquid into the discharge system under an oscillatory instability of the charged liquid surface. The instability is assumed to be induced by a time-dependent external force acting on the liquid surface, a finite rate of charge redistribution over the surface under virtual deformations, and tangential discontinuity of the velocity field across the interface.     

Shear instability of gamma-Fe in bulk and in ultrathin films

Using ab initio local-spin-density calculations we demonstrate that along the Bain path describing the transformation of face-centered-cubic (fcc) gamma-Fe into body-centered-cubic (bcc) alpha-Fe, tetragonal Fe is unstable against monoclinic shear deformations producing a nearly bcc structure. In the limit of a monolayer adsorbed on a fcc substrate, the epitaxial constraint suppresses the shear instability, but in ultrathin films with three to six monolayers a striped pattern of near-bcc domains develops, confirming recent observations by scanning tunneling microscopy. A strong correlation between the shear instability and the magnetic state is reported.     

The dynamic Peierls instability

The ‘effective field’ model of the Peierls transition in one-dimensional metals is shown to have a dynamic instability in the presence of a large electric field. The behavior is analogous to laser action, and has a critical temperature above that of the static instability.     

Modal voltages and micro-signal analysis of conical shells of revolution

Conical shells and components are widely used as nozzles, injectors, rocket fairings, turbine blades, etc. Dynamic and vibration characteristics of conical shells have been investigated over the years. In this paper, micro-electromechanics and distributed sensing phenomena of a generic double-curvature shell and a conical shell are discussed, and governing sensing signal-displacement equations are derived. Spatially distributed modal voltages and micro-signal generations of conical shells laminated with distributed piezoelectric sensor layers are investigated based on the Donnel-Mushtari-Valsov theory. Distributed modal voltages and their various signal components of two conical shells reveal that the dominating signal component among the four contributing micro-signal components is the circumferential membrane component. This dominance is even more significant for lower shell modes and/or deep shells. In general, high strain regions result in high signal magnitudes. Accordingly, the spatially distributed signal patterns—the modal voltages—clearly represent the modal dynamic and micro-strain characteristics of conical shells.     

On thermomagnetic instability during ionospheric modification by powerful radio waves

The possibility of excitation of thermomagnetic instability in the ionospheric F-region with an external DC electric field on exposure to waves from powerful ground-based radio transmissions is discussed. The threshold and growth rate of the instability are determined. It is shown that such instability can appear in local regions with a rather high level of plasma waves and in the high-latitude ionosphere, especially for high ionospheric-plasma drift velocities.Scientific-Research Institute of Radiophysics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 5, pp. 674–679, May, 1994.     

Effect of ionic temperature on the modulational instability of ion acoustic waves in the presence of a magnetic field

The modulational instability of ion acoustic waves is studied in the presence of a dc magnetic field, taking the ion temperature into account. It is well known that the instability sets in for wave numbers exceeding 1.47 k_D when there is no magnetic field and the ion temperature is negligible. The instability behaviour, however, changes drastically when either the magnetic field is switched on or the ion temperature becomes important or both. In general three different regions emerge wherein the waves becomes modulationally unstable. The relative sizes of these regions change as the magnetic field, the angle of propagation and the ion temperature are varied.     

DYNAMIC STABILITY OF CURVED PANELS WITH CUTOUTS

The parametric instability behaviour of curved panels with cutouts subjected to in-plane static and periodic compressive edge loadings are studied using finite element analysis. The first order shear deformation theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to Sanders' first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The effects of static and dynamic load factors, geometry, boundary conditions and the cutout parameters on the principal instability regions of curved panels with cutouts are studied in detail using Bolotin's method. Quantitative results are presented to show the effects of shell geometry and load parameters on the stability boundaries. Results for plates are also presented as special cases and are compared with those available in the literature.     

Nonlinear Rayleigh-Taylor instability in magnetic fluids between two parallel plates

A nonlinear stage of the two-dimensional Rayleigh-Taylor instability for two magnetic fluids of finite thickness is studied by including the effect of surface tension between the two fluids. The system is subjected to a tangential magnetic field. The method of multiple scale perturbations is used in order to obtain uniformly valid expansions near the cutoff wavenumber separating stable and unstable deformations. Two nonlinear Schrödinger equations are obtained, one of which leads to the determination of the cutoff wavenumber. The other Schrödinger equation is used to analyze the stability of the system. It is found that if a finite-amplitude disturbance is stable, then a small modulation to the wave is also stable. It is also found that the tangential magnetic field plays a dual role in the stability criterion. Finally, the magnetic permeability constants of the fluid affect the stability conditions.     

Attractive instability of oppositely charged membranes induced by charge density fluctuations

We predict the conditions under which two oppositely charged membranes show a dynamic, attractive instability. Two layers with unequal charges of opposite sign can repel or be stable when in close proximity. However, dynamic charge density fluctuations can induce an attractive instability and thus facilitate fusion. We predict the dominant instability modes and time scales and show how these are controlled by the relative charge and membrane viscosities. These dynamic instabilities may be the precursors of membrane fusion in systems where artificial vesicles are engulfed by biological cells of opposite charge.     

黏性流体中超细长弹性杆的动力学不稳定性

基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.     

Influence of the tangential velocity on the compressible Kelvin−Helmholtz instability with nonequilibrium effects

Kelvin−Helmholtz (KH) instability is a fundamental fluid instability that widely exists in nature and engineering. To better understand the dynamic process of the KH instability, the influence of the tangential velocity on the compressible KH instability is investigated by using the discrete Boltzmann method based on the nonequilibrium statistical physics. Both hydrodynamic and thermodynamic nonequilibrium (TNE) effects are probed and analyzed. It is found that, on the whole, the global density gradients, the TNE strength and area firstly increase and decrease afterwards. Both the global density gradient and heat flux intensity in the vertical direction are almost constant in the initial stage before a vortex forms. Moreover, with the increase of the tangential velocity, the KH instability evolves faster, hence the global density gradients, the TNE strength and area increase in the initial stage and achieve their peak earlier, and their maxima are higher for a larger tangential velocity. Physically, there are several competitive mechanisms in the evolution of the KH instability. (i) The physical gradients increase and the TNE effects are strengthened as the interface is elongated. The local physical gradients decrease and the local TNE intensity is weakened on account of the dissipation and/or diffusion. (ii) The global heat flux intensity is promoted when the physical gradients increase. As the contact area expands, the heat exchange is enhanced and the global heat flux intensity increases. (iii) The global TNE intensity reduces with the decreasing of physical gradients and increase with the increasing of TNE area. (iv) The nonequilibrium area increases as the fluid interface is elongated and is widened because of the dissipation and/or diffusion.     

超常介质中部分相干光束传输的调制不稳定性研究

超常介质与常规光学介质的一个最重要的区别是前者具有色散磁导率,其折射率呈现出可正可负,这样调制不稳定性出现新特点。借助于Wigner变换,从一般的非线性薛定谔方程出发,得到了部分相干光满足Wigner-Moyal的方程,获得了色散关系和增益谱,揭示了部分相干度不仅可抑制调制不稳定性,而且还可以缩小发生不稳定性的频率范围。     

Coupler-loss and coupling-coefficient-dependent bistability and instability in a fiber ring resonator

In this paper, we demonstrate the dynamic simulation of light traveling in a fiber ring resonator with a single coupler. Optical nonlinear phenomena including bistability, the Ikeda instability, bifurcation and chaos are studied. The Ikeda instability in ring resonator arises from the ring-cavity lifetime being much longer than the Kerr-effect response time of the fiber. The transmission curves of the bistability and the instability as function of the insertion losses (γ) and the coupling coefficients (κ) of the coupler are derived.     

超短激光脉冲调制上转换放大

在超短激光脉冲倍频过程中，由于调制不稳定性而产生多色圆锥辐射. 在多色圆锥辐射的任 意方向上同步注入一束宽带种子光，可以得到相应频率的调制上转换放大. 放大的光脉冲的 中心波长在500 nm时单脉冲能量最大可至150 μJ并且具有60 nm的频谱宽度. 通过改变种子 光的入射角度而实现上转换放大中心波长的连续调谐，范围约为290 nm. 关键词： 调制上转换放大 调制不稳定性 多色圆锥辐射