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首页> 外文会议>NATO Advanced Research Workshop on Surface Waves in Anisotropic and Laminated Bodies and Defects Detection; 20011030-1102; Moscow(RU) >THE INFLUENCE OF THE INITIAL STRESSES ON THE DYNAMIC INSTABILITY OF AN ANISOTROPIC CONE
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THE INFLUENCE OF THE INITIAL STRESSES ON THE DYNAMIC INSTABILITY OF AN ANISOTROPIC CONE

机译：初始应力对各向异性圆锥体动力不稳定性的影响

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摘要

The problem of surface instability of a right circular cone with an arbitrary opening made of a hexagonal single crystal is investigated. The surface of the cone is free from normal and tangential stresses, but in the layer near the surface initial constant tensile or compressive stresses act in the hoop direction and in the direction of the cone's generators. Surface instability is analyzed by the use of weak nonstationary disturbances which propagate along the surface of the cone in the form of the nonstationary surface wave of the "whispering gallery" type polarized perpendicular to the sagittal plane. The weak nonstationary surface wave is interpreted as the line of discontinuity (diverging circle) on which partial derivatives of the stress and strain tensor components with respect to coordinates and time have a discontinuity, but the components of these tensors are continuous. The line of discontinuity propagates with a constant normal velocity along the cone's surface in the direction of its generators and is obtained as a result of the exit onto the cone surface of a real conic wave surface of weak discontinuity (wave of the "whispering gallery" type). The analysis is carried out within the framework of the theory of discontinuities based on the kinematic, geometric and dynamic conditions of compatibility, using which the velocity of the surface wave propagation and its intensity have been found. It has been shown that the surface wave velocity is dependent only on the initial stress acting in the direction of the propagation of a surface disturbance, whereas the damping coefficients for the intensity of the surface waves is dependent not only on this stress but on the initial stress acting in the hoop direction as well. The relationship for the critical magnitude of the force compressive in the hoop direction has been obtained, and it has been shown that under the hoop compressive forces in excess of this magnitude the intensity of the surface wave of the "whispering gallery" type begins to increase without bounds during its propagation, i.e. the surface of the cone loses stability with respect to weak nonstationary disturbance.
机译：研究了具有由六角形单晶制成的任意开口的直角圆锥的表面不稳定性的问题。圆锥体的表面没有法向和切向应力，但是在表面附近的层中，初始恒定的拉伸应力或压缩应力沿环向和圆锥体生成器的方向起作用。通过使用弱的非平稳扰动来分析表面不稳定性，该扰动沿着圆锥体表面以垂直于矢状面极化的“低语廊”类型的非平稳表面波的形式传播。弱的非平稳表面波被解释为间断线（发散圆），在该线上应力和应变张量分量相对于坐标和时间的偏导数具有不连续性，但是这些张量的分量是连续的。不连续线以恒定法向速度沿锥体表面沿其生成器方向传播，并且是由于弱不连续的真正圆锥波表面（“低语廊”的波）进入圆锥表面而获得的类型）。该分析是在不连续性理论的框架内进行的，该理论基于相容性的运动学，几何学和动态条件，由此得出了表面波传播的速度及其强度。已经表明，表面波速度仅取决于作用在表面扰动传播方向上的初始应力，而表面波强度的阻尼系数不仅取决于该应力，还取决于初始应力。应力也沿环向作用。已经获得了在环向方向上压缩力的临界大小的关系，并且已经表明，在环向压缩力超过该大小时，“耳语通道”类型的表面波的强度开始增加。在其传播过程中没有边界，即，圆锥体的表面由于微弱的非平稳扰动而失去了稳定性。

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