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首页> 外文会议>Conference on Modern Problems of Structural Stability Jul 16-20, 2001 Udine >Some Unconventional Elastic Stability Problems
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Some Unconventional Elastic Stability Problems

机译：一些非常规的弹性稳定性问题

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In this paper new closed ― form solutions are obtained for instability of inhomogeneous columns. The problem is posed as the semi-inverse eigenvalue determination task ; namely the mode shape is formulated as the fourth order polynomial that satisfies all boundary conditions. Then the following question is posed: Find such variation of the flexural rigidity along the axial coordinate, that corresponds, in exact terms, to the postulated mode shape. Whereas usually the polynomial mode shapes are utilized in the approximate methods of Rayleigh, Rayleigh ― Ritz or Boobnov ― Galerkin, here the closed form solution is derived. Moreover, even for the columns with uniform cross-section, the closed-form solutions are obtained in terms of irrational expressions for the buckling load, here rational expressions are obtained. These semi-inverse problems can be used as benchmark solutions. In addition, when the technology will become available of producing the arbitrarily varying flexural rigidity, the derived solutions can be utilized for design purposes. One will be able to construct columns with pre-selected buckling loads. In the second part the effect of boundary conditions is investigated. It is intriguing that for the inhomogeneous column in question a linear relationship is established between the natural frequency squared and the applied load, exactly as it happens for the simply ― supported uniform column. These results show that even the classical problems may present rich opportunities for deriving unconventional solutions.
机译：本文针对非均质柱的不稳定性获得了新的闭式解。该问题被提出为特征值的半逆确定任务；即，众数形状被表示为满足所有边界条件的四阶多项式。然后提出以下问题：找到沿轴向坐标的抗弯刚度的这种变化，确切地说，这与假定的模态形状相对应。虽然通常在Rayleigh，Rayleigh-Ritz或Boobnov-Galerkin的近似方法中使用多项式模态，但是这里导出了封闭形式的解。此外，即使对于具有均匀横截面的圆柱，也可以根据屈曲载荷的无理表达式获得闭合形式的解，此处获得有理表达式。这些半反问题可以用作基准解决方案。此外，当该技术可用于产生任意变化的抗弯刚度时，派生的解决方案可用于设计目的。人们将能够构造具有预选屈曲载荷的柱。在第二部分中，研究了边界条件的影响。令人感兴趣的是，对于所讨论的非均质柱，在固有频率平方和所施加的载荷之间建立了线性关系，正好与简单的“支撑均匀柱”一样。这些结果表明，即使是经典问题也可能为推导非常规解决方案提供大量机会。

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