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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Stability of a gradient elastic beam compressed by non-conservative forces
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Stability of a gradient elastic beam compressed by non-conservative forces

机译：非保守力压缩的梯度弹性梁的稳定性

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摘要

The critical loads for five non-conservative problems are defined under the context of gradient elasticity theory of a beam. The first problem deals with the stability of a gradient elastic beam compressed by a follower force (Beck’s problem) and the second deals with the stability of a gradient elastic beam compressed by a force with a fixed line of action (Rent’s problem). The governing dynamic equation with the boundary conditions is formulated on the bases of simple linear elasticity theory with the beam mass concentrated on the moving end. Also the case with uniform distribution of the mass along the beam will be considered. Further the effect of an additional conservative force acting on the moving end of the beam will also be discussed. Numerical applications indicate that although the surface energy term does not have a substantial effect, the intrinsic length due to gradient elasticity is of major importance. In fact, it increases of the critical load.
机译：在梁的梯度弹性理论的背景下，定义了五个非保守问题的临界载荷。第一个问题涉及由跟随力压缩的梯度弹性梁的稳定性（贝克问题），第二个问题涉及由作用力固定的力压缩的梯度弹性梁的稳定性（伦特问题）。在简单线性弹性理论的基础上，将束质量集中在运动端，建立了具有边界条件的控制动力学方程。也将考虑沿光束质量均匀分布的情况。此外，还将讨论附加的保守力作用在梁的移动端上的效果。数值应用表明，尽管表面能项没有实质性影响，但由于梯度弹性而引起的固有长度至关重要。实际上，它增加了临界负荷。

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