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R. Heuer, H. Irschik, F. Ziegler:
"Forced Large Flexural Vibrations of Plates";
in: "Festschrift anläßlich des 80. Geburtstags von Prof. K. Magnus", TU-München, München, 1992, 233 - 246.

Geometric nonlinearity has a major influence on the flexural response of beams and plates in free and forced vibrations. Recently it was found for simply supported beams and polygonal plates that a modal decomposition (a Ritz-Galerkin procedure using the linear eigenfunctions) gives a unifying result which holds independently of the special planform and for all modes when time is properly non-dimensionalized. Natural vibrations in a multi-mode approximation are described by homogeneous Duffing-type coupled equations. Hence, for forced vibrations nonlinearly coupled modal equations can be set-up and their stationary solutions are discussed by means of the method of multiple scales. Numerical studies of primary, superharmonic and subharmonic resonances of the lowest mode illustrate the beauty of the analytical domain-independent formulation.