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Nonlinear Vibration of an Initially Stressed Plate Based on a Modified Plate Theory by Chun-Sheng Chen; Jiun-Ren Hwang; Ji-Liang Doong is a Engineering article available to read on EtoBox.

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Nonlinear partial dierential equations for the vibrating motion of a plate based on a modi®ed higher order plate theory with seven kinematic variables are derived. The present seven-variable modi®ed higher order plate theory sat-is®es the stress-free boundary conditions. Using these derived governing equations, the large amplitude vibrations of a simply supported thick plate subjected to initial stresses are studied. The Galerkin method is used to transform the governing nonlinear partial dierential equations to ordinary nonlinear dierential equations and the Runge±Kutta method is used to obtain the ratio of linear to nonlinear frequencies. Frequency ratios obtained by the present theory are compared with the Mindlin plate theory results and Lo's 11-variable higher order plate theory results. It can be concluded that present modi®ed plate theory predicts frequency ratios very accurately. Also, the bene®t of signi®cant simpli®cation can be observed as compared with the Lo's higher order plate theory. The eects of initial stress and other factors on frequency ratio are investigated.

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Author

Chun-Sheng Chen; Jiun-Ren Hwang; Ji-Liang Doong

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0020-7683)

Published

2001

Language

EN

Field

Engineering (Physical Sciences)