Parametric Combination Resonance Characteristics of Doubly Curved Panels Subjected To Non-uniform Harmonic Edge Loading

This paper is concerned with the problem of occurrence of combination resonances in parametrically excited doubly curved panels. The dynamic instability of doubly curved panels, subjected to non-uniform in-plane harmonic loading is investigated. Sander's first_order shear deformation theory is used to model the doubly curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory can be reduced to Love's and Donnell's theories by means of tracers. Analytical expressions for the instability regions are obtained at Ω = ω_m+ ω_n(Ω is the excitation frequency and ω_mand ω_nare the natural frequencies of the system), by using the method of multiple scales. It is shown that besides the principal instability region at Ω =2ω₁, where ω₁is the fundamental frequency, other cases of Ω = ω_m+ ω_nwhich are related to other modes, can be of major importance and yield a significantly enlarged instability region. The results show that under localized edge loading, combination resonance zones are as important as simple resonance zones. The effects of edge loading, curvature, shallowness ratio, edge length to thickness ratio, aspect ratio, boundary conditions and the static load factor on dynamic instability regions are considered.