Vibrations of a Finite Row of Continuous Skin-Stringer Panels

Abstract

The determination of natural frequencies and normal modes is discussed for a row of skin-stringer panels which are continuous over supporting stringers, and which resembles more or less the fuselage construction for modern airplanes. The number of panels in the row is assumed finite. All the panels and the interior stringers are assumed identical. On the other hand, exterior stringers are allowed to be different from the interior ones. Formulation of the problem leads to a 4th-order symmetrical difference equation, common in problems of “repeated structures.” Relatively simple solution is obtained by assuming that each normal mode is periodic spatially. The implication of this assumption is discussed, and it is shown that the assumption is not restrictive for certain practical applications, in particular, in the study of panel response to jet noise. Two reduced cases are then discussed wherein the bending rigidity and torsional rigidity of the stringers are taken to be infinite, respectively, in each case. Analytical difficulties are greatly reduced in the special cases. It is found that, for the conventional airplane-panel construction, the natural frequencies may be computed with good accuracy by regarding the stringer-bending rigidity to be infinite. and closed-loop systems, and that the use of large amounts of normal-system operating data in condensed form combine to effect economies in time and accuracies in the transfer function (impulse functions or sinusoids are usually used). A brief recount of the theory is given with 3 suggestions for laboratory technique. Laboratory results are presented.