Post-critical analysis of highly deformable Joined Wings: The concept of snap-divergence as a characterization of the instability

Theoretical modeling of the aeroelastic static instability with the possibility of tracing post-critical branches (via arc length technique) in the framework of Joined Wings has never been presented before. A complete formulation of the numerical iterative method of solution of the aeroelastic equations is presented.The true critical condition is compared with the divergence speed evaluated by solving an eigenvalue problem about a steady state equilibrium, showing how this last approach may be unreliable and even nonconservative.This work also explores the theoretical implications of using mechanical loads to mimic the real loading conditions.A physical interpretation based on the aeroelastic effects, overconstrained nature of the system, and the bending/torsion coupling, is provided to interpret the conditions that lead to the snap-divergence.     

Vibration and instability analysis of tubular nano- and micro-beams conveying fluid using nonlocal elastic theory

A nonlocal Euler–Bernoulli elastic beam model is developed for the vibration and instability of tubular micro- and nano-beams conveying fluid using the theory of nonlocal elasticity. Based on the Newtonian method, the equation of motion is derived, in which the effect of small length scale is incorporated. With this nonlocal beam model, the natural frequencies and critical flow velocities for the case of simply supported system and for the case of cantilevered system are obtained. The effect of small length scale (i.e., the nonlocal parameter) on the properties of vibrations is discussed. It is demonstrated that the natural frequencies are generally decreased with increasing values of nonlocal parameter, both for the supported and cantilevered systems. More significantly, the effect of small length scale on the critical flow velocities is visible for fluid-conveying beams with nano-scale length; however, this effect may be neglected for micro-beams conveying fluid.     

Periodic flow boiling in a non-uniformly heated microchannel heat sink

Hydrodynamic and thermal characteristics of flow boiling in a non-uniformly heated microchannel were studied. Experiments were performed with a single microchannel and a series of microheaters to study the microscale boiling of water under axially non-uniform heat input conditions. A simultaneous real time visualization of the flow pattern was performed with the measurement of experimental parameters. Tests were performed over a mass flux of 309.8 kg/m² s, and heat flux of 200–600 kW/m². Test results showed different fluctuations of heated wall temperature, pressure drop, and mass flux with variations of the heat input along the flow direction. The unique periodic flow boiling in a single microchannel was observed at all heat flux conditions except for the increasing heat input distribution case which is the nearly uniform effective heat input distribution condition. The instability is correlated with flow pattern transition. For the nearly uniform effective heating condition, no fluctuation of the wall temperature, pressure drop, or mass flux was observed. We can relieve the instability by increasing total heat input along the flow direction and predict the instability using the transition criteria and flow pattern map.     

On elastocapillarity: A review

Elastocapillary phenomena involving elastic deformation of solid structures coupled with capillary effects of liquid droplets/films can be observed in a diversity of fields,e.g.,biology and microelectromechanical systems(MEMS).Understanding the physical mechanisms underlying these phenomena is of great interest for the design of new materials and devices by utilizing the effects of surface tension at micro and nano scales.In this paper,some recent developments in the investigations on elastocapillary phenomena are briefly reviewed.Especially,we consider the deformation,adhesion,self-assembly,buckling and wrinkling of materials and devices induced by surface tensions or capillary forces.The main attention is paid to the experimental results of these phenomena and the theoretical analysis methods based on continuum mechanics.Additionally,the applications of these studies in the fields of MEMS,micro/nanometrology,and biomimetic design of advanced materials and devices are discussed.     

Geodesic mode instability driven by the electron current in tokamak plasmas

Effect of the parallel electron current on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current modeled by shifted Maxwell distribution may overcome the phase velocity threshold and ion Landau damping thus resulting in the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity Rqω. The instability occurs due to its cross term of the current with the ion diamagnetic drift. Possible applications to tokamak experiments are discussed.     

Instability of unburnt gas for a scalar nonconvex combustion model

The ignition solutions for the scalar nonconvex Chapman-Jouguet (CJ) combustion model are studied as the ignited perturbation vanishes. We let the perturbation vanish in the result of the interactions of the combustion waves and noncombustion waves, thereby obtaining that the unburnt gas is unstable when the binding energy is larger than a critical value. Furthermore, in the vanishing process, the transitions between deflagration and detonation waves are observed.     

Dynamics of terraces on a silicon surface due to the combined action of strain and electric current

A (0 0 1) surface of silicon consists of terraces of two variants, which have an identical atomic structure, except for a 90° rotation. We formulate a model to evolve the terraces under the combined action of electric current and applied strain. The electric current motivates adatoms to diffuse by a wind force, while the applied strain motivates adatoms to diffuse by changing the concentration of adatoms in equilibrium with each step. To promote one variant of terraces over the other, the wind force acts on the anisotropy in diffusivity, and the applied strain acts on the anisotropy in surface stress. Our model reproduces experimental observations of stationary states, in which the relative width of the two variants becomes independent of time. Our model also predicts a new instability, in which a small change in experimental variables (e.g., the applied strain and the electric current) may cause a large change in the relative width of the two variants.     

映秀—卧龙公路沿线汶川地震地质灾害研究

映秀—卧龙公路是汶川地震灾区距震中最近、震害最为严重的一条公路,本文对沿线地震地质灾害进行了详细的调查研究。依据震害特征,将沿线震害划分为斜坡中上部强风化岩体及土层失稳、结构面切割岩体崩滑失稳、滑坡、泥石流等4类,并分析了沿线震害发育规律。调查表明：龙门山后山断裂两侧地震地质灾害呈现显著的差异性,主要是由深大断裂的消震隔震效应,地貌放大效应,地质结构等三方面因素决定的。通过134条实测剖面分析,研究了地震失稳斜坡坡度和失稳部位。地震诱发失稳斜坡坡度在33°～84°之间,主要分布在41°～65°之间,可以认为地震诱发斜坡失稳灾害主要发生在40°以上的斜坡。斜坡失稳部位主要分布在斜坡中上部以及地貌突出部位,主要失稳部位在04坡高以上。从研究斜坡动力失稳的角度,将沿线斜坡划分为基岩-土层及强风化层斜坡地质结构、不利外倾结构面基岩斜坡地质结构、块状构造基岩斜坡地质结构、块碎石土层斜坡地质结构等几种地质结构模型,分析论述了各种地质结构相应的地震地质灾害类型及特点。
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Swelling instability of surface-attached gels as a model of soft tissue growth under geometric constraints

The purpose of this work is to provide a theoretical analysis of the mechanical behavior of the growth of soft materials under geometrical constraints. In particular, we focus on the swelling of a gel layer clamped to a substrate, which is still the subject of many experimental tests. Because the constrained swelling process induces compressive stresses, all these experiments exhibit surface instabilities, which ultimately lead to cusp formation. Our model is based on fixing a neo-Hookean constitutive energy together with the incompressibility requirement for a volumetric, homogeneous mass addition. Our approach is developed mostly, but not uniquely, in the plane strain configuration. We show how the standard equilibrium equations from continuum mechanics have a similarity with the two-dimensional Stokes flows, and we use a nonlinear stream function for the exact treatment of the incompressibility constraint. A free energy approach allows the extension both to arbitrary hyperelastic strain energies and to additional interactions, such as surface energies. We find that, at constant volumetric growth, the threshold for a wavy instability is completely governed by the amount of growth. Nevertheless, the determination of the wavelength at threshold, which scales with the initial thickness of the gel layer, requires the coupling with a surface effect. Our findings, which are valid in proximity of the threshold, are compared to experimental results. The proposed treatment can be extended to weakly nonlinearities within the aim of the theory of bifurcations.     

自治差分方程的稳定性

本文首先给出了文献[2]中关于一次近似系统不稳定性定理的一个反例,然后给出了关于自治差分方程利用其一次近似系统的不稳定性来判别原系统不稳定性的判别定理。