Influence of Large Amplitudes on Free Flexural Vibrations of Rectangular Elastic Plates

Abstract

Abstract In a recent paper (1) a set of plate equations was derived, which governs motions with small elongations and shears, but moderately large rotations, valid for an isotropic material obeying Hooke’s law. The resulting theory, which may be considered the dynamic analog of the von Karman plate theory, is applied presently to the study of free vibrations of a rectangular, elastic plate with hinged, immovable edges. The nonlinear equations are solved approximately by employing a perturbation procedure and also the principle of conservation of energy directly. The influence of large amplitudes on the period of free vibration and on the maximum normal stress is established. The free vibrations of a beam are studied as a special case and the resulting period compared with a previous investigation.