Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths (Advances in Applied Mathematics and Mechanics, 2021)
The nonlinear transverse vibrations of ordered and disordered two-dimensional(2D) two-span composite laminated plates are studied. Based on the vonKarman's large deformation theory, the equations of motion of each-span compositelaminated plate are formulated using Hamilton's principle, and the partial differentialequations are discretized into nonlinear ordinary ones through the Galerkin's method.The primary resonance and 1/3 sub-harmonic resonance are investigated by using themethod of multiple scales. The amplitude-frequency relations of the steady-state responsesand their stability analyses in each kind of resonance are carried out. Theeffects of the disorder ratio and ply angle on the two different resonances are analyzed.From the numerical results, it can be concluded that disorder in the length ofthe two-span 2D composite laminated plate will cause the nonlinear vibration localizationphenomenon, and with the increase of the disorder ratio, the vibration localizationphenomenon will become more obvious. Moreover, the amplitude-frequency curvesfor both primary resonance and 1/3 sub-harmonic resonance obtained by the presentanalytical method are compared with those by the numerical integration, and satisfactoryprecision can be obtained for engineering applications and the results certify thecorrectness of the present approximately analytical solutions.