Combination Resonance Instability of Curved Panels with Cutout Subjected to Nonuniform Loading with Damping

Abstract

The dynamic instability of doubly curved panels with a centrally located circular cutout, subjected to nonuniform compressive in-plane harmonic edge loading is investigated. The present work deals with the problem of the occurrence of combination resonances in contrast to single (mode) resonances in parametrically excited doubly curved panels with a central circular cutout. The method of multiple scales is used to obtain analytical expressions for the single (mode) and combination resonance instability regions. It is shown that other cases of the combination resonance can be of major importance and yield a significantly enlarged instability region in comparison to the principal instability region. The effects of nonuniform edge loading, centrally located circular cutout, damping, the static, and dynamic load factors on dynamic instability behavior of simply supported doubly curved panels are studied. The results show that under localized edge loading, combination resonance zones are as important as single (mode) resonance zones. The effects of damping show that there is a finite critical value of the dynamic load factor for each instability region below which doubly curved panels cannot become dynamically unstable. A central circular cutout has the destabilizing effect on the dynamic stability behavior of doubly curved panels subjected to nonuniform edge loading. This example of simultaneous excitation of two modes, each oscillating steadily at its own natural frequency, may be of considerable interest in vibration testing of actual structures.