Abstract
The exact mode shapes of linear vibrations of a shallow shell rectangular in the horizontal projection with two freely supported opposite edges are obtained. These shapes are used to construct a discretemodel of vibrations of a shallow shell in geometrically nonlinear deformation. The harmonic balance method is used to study the free and forced nonlinear vibrations under internal resonance. The Lyapunov stability of the obtained periodic vibrations is analyzed.
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Original Russian Text © K.V. Avramov, I.D. Breslavskii, 2013, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2013, No. 2, pp. 86–95.
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Avramov, K.V., Breslavskii, I.D. Vibrations of shallow shells rectangular in the horizontal projection with two freely supported opposite edges. Mech. Solids 48, 186–193 (2013). https://doi.org/10.3103/S0025654413020106
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DOI: https://doi.org/10.3103/S0025654413020106