Free vibration 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 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 fourth-order symmetrical difference equation, common in problems of “repeated structures”. A relatively simple solution is obtained by assuming that each normal mode is spatially periodic. The implication 0f this assumption is discussed, and it is shown that the assumption is not restrictive for certain practical applications, in particular, in the study 0f panel response to jet noise. Two reduced cases are then discussed wherein the bending rigidity and the torsional rigidity of the stringers, respectively, are taken to be infinite. Analytical difficulties are greatly reduced in the special cases. It is found that for conventional airplane-panel construction the natural frequencies may be computed with good accuracy by regarding the stringer-bending rigidity to be infinite.