NONLINEAR VIBRATIONS OF DOUBLY-CURVED CROSS-PLY SHALLOW SHELLS

We consider nonlinear forced vibrations of a doublycurved cross-ply laminated shallow shell with simply supported boundary conditions. We investigate its response to a primary resonance of its fundamental mode (i.e., fi « ^11). The nonlinear partial-differential equations governing the motion of the shell are based on the von Karman-type geometric nonlinear theory and the first-order sheardeformation theory. An approximation based on the Galerkin method is used to reduce the partialdifferential equations of motion to an infinite system of nonlinearly coupled second-order ordinarydifferential equations. These equations are solved by using the method of multiple scales. We found that symmetric modes do not have an effect on the results for the case of primary resonance of the fundamental mode of vibration. It is shown that using a single-mode approximation can lead to quantitatively and in some cases qualitatively erroneous results. A multi-mode approximation that includes as many modes as needed for convergence is used.

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