Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The free oscillations of a buckled panel

Authors: W. D. Hayes and J. W. Miles
Journal: Quart. Appl. Math. 14 (1956), 19-26
MSC: Primary 73.2X
DOI: https://doi.org/10.1090/qam/78171
MathSciNet review: 78171
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Abstract: The non-linear equations of motion of a buckled, two-dimensional panel are formulated in dimensionless form. A Fourier expansion in the space variable is introduced and an approximate solution is obtained for the period of free oscillation on the assumption of only two degrees of freedom, one of which is eliminated by the buckling constraint. The periods of the simplest asymmetric and symmetric modes are plotted as a function of the energy level. It is found that for very small energy levels the period of the buckled panel lies between the periods of the (two) unbuckled degrees of freedom. As the energy is increased the period approaches infinity at some critical energy level and thereafter decreases monotonically.

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DOI: https://doi.org/10.1090/qam/78171
Article copyright: © Copyright 1956 American Mathematical Society

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