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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.

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.

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.

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.

It will assist the researchers of stability behavior of elastic systems.