Parametric Study of Dynamic Wrinkling in a Thin Sheet on Elastic Foundation

• 作者: A. A. Al-Qaisia M. N. Hamdan S. Abdallah
• 来源期刊: 现代非线性理论与应用(英文)
• 学科: 数学
• 关键词: WRINKLING NONLINEAR ELASTIC FOUNDATION SHEET Metal Stability MMS
• 年，卷（期）: 2012,（3）
• 页码范围: 55-66
• 页数: 12页
• 分类号: O1

摘要

This work presents an approximate analytical study of the problem of dynamic wrinkling of a thin metal sheet under a specified time varying tension. The problem is investigated in the framework of the dynamic stability of a nonlinear plate model on elastic foundation which namely takes into account the nonlinear mechanics of mid-plane stretching and the dependence of the membrane force on this mechanics. The plate is assumed to be a wide rectangular slab, hinged at two opposite ends and free at the long ends, which can be deformed in a cylindrical shape so that the governing in-plane bending equation of motion takes the same form as that of a beam (e.g. lateral strip) element. An approximate analytical analysis of the beam wrinkling behavior under sinusoidal parametric excitation is carried out by using the assumed single mode wrinkling motion to reduce the beam field nonlinear partial differential equation to that of a single degree of freedom non-linear oscillator. A first order stability analysis of an approximate analytical solution obtained using the Multi-Time-Scales (MMS) method is used to derive a criterion defining critical driving frequency in terms of system parameters for the initiation of wrinkling motion in the thin metal sheet. Results obtained using this criterion is presented for selected values of system parameters.