Summary
Geometrical nonlinearity has a major influence on the flexural response of beams and plates in free and forced vibrations. Recently it was found for free vibrations of simply supported polygonal plates that a modal decomposition (a Ritz-Galerkin procedure using the linear eigenfunctions) gives a unifying result for the nonlinear eigenfrequencies that holds independently of the special planform and for all modes when time is properly non-dimensionalized. The present paper gives a proper extension to forced vibrations that are described in a multimode approximation by a set of coupled inhomogeneous Duffing-type equations. The restoring forces can be derived from a potential function, and for random vibrations the FPK-equation can be set up and solved in closed form for the stationary transition probability density with the further assumption of linear modal damping. Numerical studies illustrate the beauty of the analytical solution.
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Heuer, R., Irschik, H., Ziegler, F. (1992). Large Amplitude Random Vibration of Polygonal Plates. In: Bellomo, N., Casciati, F. (eds) Nonlinear Stochastic Mechanics. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84789-9_25
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DOI: https://doi.org/10.1007/978-3-642-84789-9_25
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