THE NON-LINEAR FREE VIBRATION OF FULLY CLAMPED RECTANGULAR PLATES: SECOND NON-LINEAR MODE FOR VARIOUS PLATE ASPECT RATIOS

Abstract The theoretical model based on Hamilton's principle and spectral analysis, previously used to obtain the first three non-linear modes of a clamped–clamped beam [1], and the first non-linear mode of a fully clamped rectangular plate [2], is used here in order to calculate the second non-linear mode of a fully clamped rectangular plate. The large vibration amplitude problem, reduced to a set of non-linear algebraic equations, is solved numerically. Results are given for the second mode of fully clamped rectangular plates, for various plate aspect ratios and vibration amplitudes. The non-linear mode shows a higher bending stress near to the clamps at large deflections, compared with that predicted by linear theory.

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