An axially moving viscoelastic plate immersed in the liquid, having the variable speed, was considered.According to the classical thin plate theory and the d'Alembert’s principle, the governing equation of the transverse vibration of the system was derived.The liquid was assumed as ideal fluid and thus was inviscid, irrotational, and incompressible.The dynamic pressure of fluid on the plate could be described by added plate mass.Then, using the method of multiple scales, we analyzed the partial differential equations and boundary conditions of the system.Based on the solvability conditions and the Routh-Hurwitz criterion, the instability regions for sum-type and difference-type combination resonances of the system were determined.Finally, the effects of different parameters on the instability regions of the two kinds of combination resonance were discussed.
Key words
Axially moving plate with variable speed /
liquid /
parametric resonance /
multiple scale method /
viscoelasticity
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