The free oscillations of a buckled panel

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.