Abstract
The problem of the parametric excitation of a thins tensioned sheet with a cracklike opening is discussed Data obtained from an experimental investigation are presented and they indicated that both principal and secondary regions of instability are developed. Plts of the stability boundaries are presented in terms of excitation frequency, mean tensile load and alternating load.
The principal region is observed to be significantly larger than the secondary region and the amplitudes of the oscillations associated with the principal region are also much larger than those of the secondary region. Oscillation amplitudes of the order of twelve times the thickness are reported and amplitude vs. excitation-frequency data are shown to exhibit an overhang behavior in the direciton of increasing frequency. This indicates the presence of a nonlinear stiff effect which is attributed to middle-surface stretching due to bending.
Although damping and membrane effects were found to prevent the development of unbounded oscillations, it is noted that the large deflections associated with the principal region of instability could be expected to have a deterious effect on both crack nucleation and crack propagation.
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Carlson, R.L. An experimental study of the parametric excitation of a tensioned sheet with a cracklike opening. Experimental Mechanics 14, 452–458 (1974). https://doi.org/10.1007/BF02324026
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DOI: https://doi.org/10.1007/BF02324026