Review of Research in Japan on Nonlinear Oscillations of Elastic Structures

Probabilistic properties of nonlinear response of shallow spherical shells with clamped edges to random excitation are analytically investigated with the aid of simulation method in order to disclose the effects of the curvature on the acoustic fatigue lives. The deflection is expressed as a series expansion of the axisymmetric normal modes of vibration, and the nonlinear equations of vibration for the generalized coordinates are derived. The equations in the three modes approximation are numerically solved by NEW-MARK'S β method for random excitation forces. The probabilistic quantities of the response are calculated for various combinations of the pressure level and the curvature. The results have revealed the following properties. At high pressure levels the large amplitude vibration includes the snap-through buckling. The change of vibrational mode occurs during the snap-through. At very high pressure levels the probabilistic properties of the center deflection approach those of the flat panel. The fatigue lives of the shells can be shorter than those of the flat plate when the vibration includes the snap-through. The fatigue properties cannot be explained by the mean value and the standard deviation of the stress but explained by its probability density function (PDF), because the PDF is quite different from the Gaussian distribution. Then the static equilibrium load-deflection curves are calculated from the same discretized nonlinear equations and show good agreement with the previous results.

Takashi Kai

Papers

An Analytical Study of Nonlinear Response of Shallow Spherical Shells to Random Excitation