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R. Heuer:
"Free Large Vibrations of Buckled Laminated Plates";
Talk: IUTAM Symposium on Dynamics of Advanced Materials and Smart Structures, Yonezawa, Japan (invited); 2002-05-20 - 2002-05-24.

Large amplitude natural flexural vibrations about a buckled reference configuration are studied. In particular thermally buckled plates made of multiple transversely isotropic layers are considered. Equations of motion according to the dynamic version of the von Karman theory are the starting point. The edges are assumed to be hard hinged supported and the in-plane displacements are constrained. The influence of shear on the plate vibrations is taken into account while the influence of rotatory inertia is neglected, an assumption which is appropriate for thin plates made of transversely isotropic materials, or for sandwich structures. The influence of a thermal prestress, corresponding to a spatial distribution of cross-sectional mean temperatures, is considered. This thermal loading exemplarily represents the effect of sources of selfstress on the natural vibration periods, and extends the analysis to the problem of free vibrations into the postcritical range. In case of straight boundary segments of skew or even more generally shaped polygonal plates, a multi-mode approach and the Galerkin procedure are subsequently applied to approximately solve the boundary value problem. The result of the projection is a set of nonlinearly coupled ordinary differential equations in time for the generalized coordinates with both cubic and quadratic nonlinearities. In a single-term approximation, the corresponding solution is in terms of Jacobian elliptic functions which is independent of the special polygonal planform of the plate. For an evaluation of the real-time spectrum of the nonlinear natural fundamental frequency from this unifying similarity solution, only the Dirichlet-Helmholtz-eigenvalue of the corresponding plate must be known. The analytical solution of the single-term approximation is compared to the numerical solution of the coupled system.