Abstract
In this paper, the jumping problems of a circular thin plate with initial deflection are studied by using ‘the method of two variables’[3],[4] proposed by Jiang Fu-ru and the method of the normal perturbation (in this paper (1.1), (1.2)). We obtain Nth-order uniformly valid asymptotic expansion of the solution of this problem ((1.66), (1.67)). When the initial deflection vanishes the solution of a circular thinplate with initial deflection is reduced to the solution of the problems of the nonlinear bending of a circular thin plate[6]. If the initial deflection is largish and the signs of the initial deflection with the intensity of the transverse load are opposite, when the intensity of the transverse load reaches a certain value, the circular thin plate with initial deflection should produce the jumping phenomenon[8].
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Communicated by Jiang Fu-ru
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Sheng-li, Q., Ai-shu, Z. On the jumping problems of a circular thin plate with initial deflection. Appl Math Mech 8, 447–458 (1987). https://doi.org/10.1007/BF02019631
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DOI: https://doi.org/10.1007/BF02019631