Dynamics of skin-stringer panels using modified wave methods

Abstract

The response of a damped, periodic, simply supported skin-stringer structure is studied by two variants of the decaying wave method. The proposed method is based on a combination of a wave propagation method with transfer matrices. One variant of the decaying wave method is based on an exact solution transfer matrix; the other is based on a finite element formulation. It is shown that both variants give response curves that compare very well with previous results for the undamped structure, which illustrates both the accuracy and the numerical stability of the decaying wave method variants. Numerical results, including deflections at various points at various frequencies as well as mode shapes, are presented, and comparisons are offered. The numerical results demonstrate the accuracy and reliability of both variants of the decaying wave method, and this is because advantages of three methods are combined in each variant. admittedly difficult to model, but much of the fuselage's dynamic behavior can be captured by a much simpler struc- ture: a flat, periodic, single row, simply supported skin- stringer structure of finite length. This one row structure, seen in Fig. 1, is designed to emulate somewhat a long circumferen- tial strip of the fuselage structure between two supporting circumferential beams, whose effects are somewhat simulated by a simple support boundary condition. The assumptions of a flat and periodic structure, while designed to make the calculation easier, are not completely unreasonable. Thus, the simpler structure should contain much of the same dynamic behavior as sections of fuselage skin would. The single row simply supported skin-stringer structure has been analyzed by many different researchers using several different methods. Lin1 found the dynamic behavior of this structure analytically, using the bending and torsional charac- teristics of the stringers. His analysis gives some important results, such as the existence and location of frequency filter bands in the infinite structure, but it does not provide a simple way to get complete response curves for the finite or infinite structure. Further, were the boundary conditions at the top or bottom of the structure to change, this type of analysis be- comes extremely difficult. Thus, it became necessary to look at this problem using a numerical method. The first choice of numerical method for many engineers is the finite element method, and finite element codes are com- monplace throughout industry. With regard to skin-stringer structures, Mei2 obtained the finite element matrices for a thin-walled open cross-sectional stringer, and he takes into account coupled bending and torsional vibrations that com- monly occur in this type of beam. Bogner et al. 3 derived a panel element using Hermite cubic polynomials for displace- ment patterns, which ensure continuity of displacement and slope at the element edges. The combination of these element types has led to finite element analysis of skin-stringer struc-