Exact solutions to the oscillations of composite aircraft wings withwarping constraint and elastic coupling

Abstract

Exact solutions within the framework of standard aeroelastic bending and twisting assumptions are found to the free oscillations of composite aircraft wings with warping constraint and elastic coupling. The problem is treated as a regular boundary-value problem consisting of two fourth-order partial-differential equations coupled by the presence of elastic coupling. This system, which is linear, is therefore equivalent to an eighth-order ordinary-differential equation. Classical linear methods are used to extract fundamental solutions that are superimposed appropriately to obtain an exact functional form for the mode shapes. These mode shapes are then required to satisfy the necessary boundary conditions, a process that leads to the formulation of the required eigenvalue problem. The eigenvalues are extracted numerically by using appropriate ordering of the eight roots of the operator equation. The bending-torsion frequencies obtained as a result of this analysis are compared favorably with existing results. New insights made possible by these results, which are preliminary, appear to be that 1) the first coupled frequency decreases with increasing coupling, and 2) the phenomenon of modal transformations found by earlier investigators is explainable in terms of some conservative intermodal energy transfer.