A time-dependent form of the von Karman equations is studied. The problem of a simply supported rectangular plate subjected to a constant edge thrust is considered. A formal asymptotic representation of the solution is obtained by a two time method. One time scale describes the initial behavior and the second, of ″slow″ time theta , is required to describe the long-time large-amplitude response. The response of the plate is approximated by the leading term in the asymptotic expansion. This consists of a fast-time high-frequency secondary motion superposed on primary motion that depends only on theta . For the undamped plate, the primary motion is periodic and may be either a polarized oscillation about one of the two static buckled states or a swaying oscillation between the two static buckled states. When damping is present, the plate always approaches one of the static buckled states as t approaches infinity .
ASJC Scopus subject areas
- Applied Mathematics