TRANSITIONS AND STABILITY IN THE NONLINEAR BUCKLING OF ELASTIC PLATES.

Benard J. Matkowsky*, Leonard J. Putnick

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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 .

Original languageEnglish (US)
Pages (from-to)17-147
Number of pages131
JournalQuarterly of Applied Mathematics
Volume32
Issue number2
DOIs
StatePublished - 1974

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint

Dive into the research topics of 'TRANSITIONS AND STABILITY IN THE NONLINEAR BUCKLING OF ELASTIC PLATES.'. Together they form a unique fingerprint.

Cite this