Keywords: vibrations, nonlinear dynamics, postbuckling, thermal variations, fluid, plate.

Geometrically nonlinear vibrations (also referred to as large-amplitude vibrations) arise when the vibration amplitude is of the order of the plate thickness. For perfectly flat plates with fixed edges, a strong hardening type nonlinearity is obtained [1]. However, geometric imperfections may cause the plate to deviate for the ideal configuration taking a small initial curvature, which may cause an initial softening type nonlinearity, turning to hardening type for larger amplitudes [1].

The literature presents a large number of studies dealing with different boundary conditions, different solution methods and complicating effects. Girish and Ramachandra [2] investigated the postbuckling and the postbuckled linear (small-amplitude) vibrations of rectangular plates with initial geometric imperfections. Ribeiro [3] studied nonlinear vibrations of rectangular plates under thermal loads. Ribeiro and Jansen [4] and Librescu and Lin [5] extended the study to shells.

Thermal variations with respect to the assembly temperature of fixed plates may introduce very large thermal stresses in plates since they are flat and they cannot expand due to the boundary conditions. Plates with fixed edges may buckle due to small thermal variations, assuming a configuration with initial curvature.

In the present study, nonlinear forced vibrations and postbuckling of isotropic rectangular plates subjected to thermal variations and in presence of fluid-structure interaction are studied. Geometric imperfections are taken into account since they play a fundamental role. The plate is modelled by using the Von Kármán hypothesis and the equations of motion are obtained by using an energy approach. A pseudo-arclength continuation method is used in order to obtain numerical results. Laboratory experiments have been performed to support the numerical results.

Results show that thermal variations can cause buckling of the plate, which may result in an initial buckled configuration (not flat) also in case of plates without any initial imperfection. The classical hardening-type nonlinearity, which is characteristic of flat plates, is transformed by significant imperfections and thermal variations into softening-type nonlinearity, turning to the hardening-type only for larger vibration amplitudes. It has been also observed that liquid in contact with the plate on one or both sides changes completely the nonlinear dynamics. Therefore, fluid-structure interaction and nonlinearity of the system must be both carefully considered.

1

M. Amabili, "Nonlinear Vibrations and Stability of Shells and Plates", Cambridge University Press, New York, USA, 2008.

2

J. Girish, L.S. Ramachandra, "Thermal postbuckled vibrations of symmetrically laminated composite plates with initial geometric imperfections", Journal of Sound and Vibration, 282, 1137-1153, 2005. doi:10.1016/j.jsv.2004.04.005

3

P. Ribeiro, "Thermally induced transitions to chaos in plate vibrations", Journal of Sound and Vibration, 299, 314-330, 2007. doi:10.1016/j.jsv.2006.08.003

4

P. Ribeiro, E. Jansen, "Non-linear vibrations of laminated cylindrical shallow shells under thermomechanical loading", Journal of Sound and Vibration (accepted). doi:10.1016/j.jsv.2008.01.017

5

L. Librescu, W. Lin, "Non-linear response of laminated plates and shells to thermomechanical loading: implications of violation of interlaminar shear traction continuity requirement", International Journal of Solids and Structures, 36, 4111-4147, 1999. doi:10.1016/S0020-7683(98)00185-1

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