Stability of a rectangular plate under nonconservative and conservative forces

Abstract A study is made of the flutter and divergence instabilities of a rectangular plate with two independent loading parameters. The plate is subjected to the combined action of a tangential follower force and a unidirectional axial force along one edge. Two opposite sides of the plate are simply supported, one side being clamped and the other being a free edge where the in-plane forces act. Depending on the relative magnitudes of the follower and axial forces, the plate may lose its stability by flutter or divergence. The flutter problem is solved by maximizing the flutter load over the frequency and thereby obtaining the maximum point of an eigencurve. The stability boundaries are given for plates with different aspect ratios. The two-dimensional nature of the problem reveals some interesting results not observed in the one-dimensional counterpart of the problem, which is a cantilevered column under vertical and follower forces. The effect of an elastic foundation on the stability boundaries are determined. The influence of Poisson’s ratio on the flutter load and frequency is investigated. It is shown that no general rule can be formulated as to the effect of Poisson’s ratio on the flutter load, and that this effect will vary according to the aspect ratio and axial load.

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