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Purpose -To predict the occurrence of the combination resonances in parametrically excited, simply supported laminated composite plates in contrast to the simple resonances by using first-order shear deformation lamination theory considering the effects of shear deformation and rotary inertia. Design/methodology/approach -Finite element technique is applied to obtain the equilibrium equation of a plate. Modal transformation is applied to transform the equilibrium equation into a suitable form for the application of the method of multiple scales (MMS). The MMS is applied to obtain the boundaries of the simple and combination resonances. Findings -The combination resonance zones contribute a considerable amount to the local instability region and the widths of combination resonance zones are comparable to those of the simple resonance zones for the loading of the small bandwidth at one end or for the concentrated edge loading. Practical implications -Aircrafts, spacecrafts and many other structures such as ships, bridges, vehicles and offshore structures use the plate type elements, which are susceptible to dynamic instability. Originality/value -It will assist the researchers of stability behavior of elastic systems.

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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 = ωm + ωn (Ω is the excitation frequency and ωm and ωn are the natural frequencies of the system), by using the method of multiple scales. It is shown that besides the principal instability region at Ω = 2ω 1 , where ω 1 is the fundamental frequency, other cases of Ω = ωm + ωn which 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.