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

Abstract

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.

Biohybrid Actuators Based on Skeletal Muscle-Powered Microgrooved Ultrathin Films Consisting of Poly(styrene-block-butadiene-block-styrene)

“…In earlier work, we fabricated and characterized free-standing SBS thin films with thicknesses of hundreds of nanometers. , Their low elastic modulus and thickness let them conform extremely well to biological tissues (e.g., the skin). Notably, the flexural rigidity of a thin film, which describes its resistance to bending, is proportional to the cube of its thickness . Thus, the flexural rigidity of SBS thin films can be changed by changing its thickness.…”

“…Notably, the flexural rigidity of a thin film, which describes its resistance to bending, is proportional to the cube of its thickness. 19 Thus, the flexural rigidity of SBS thin films can be changed by changing its thickness.…”

Syringe-Injectable, Self-Expandable, and Ultraconformable Magnetic Ultrathin Films

“…The surface conformability of the sheet-type material depends on its flexural rigidity ( D ); a low flexural rigidity provides mechanically conformable adhesion to the rough surface of biological tissues . The flexural rigidity is calculated by the following equation: where E , t , and ν are Young’s modulus, thickness, and Poisson’s ratio of the sheet-type material, respectively . Since the flexural rigidity is in proportion to Young’s modulus and the cube of the thickness, the reduction of the thickness can drastically decrease the flexural rigidity and should be the most effective approach to enhance the conformability.…”

Связь Показателя Хёрста И Эффективности Самоорганизации Деформируемой Системы

“…Одним из самых интересных элементов деформационного рельефа являются гофрированные структуры (складки). Их морфология очень разнообразна, и они проявляются в различных условиях [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Гофрирование часто в качестве нежелательного эффекта сопровождает процессы обработки металлов давлением.…”

“…Подобные результаты независимо получены и описаны в работе [8]. На образование гофрированных структур и сморщивание при механическом нагружении указывается в работах [9,10]. О формировании гофрирования ( " сморщивания") при деформации пленок на подложках сообщается в ряде работ, например [11][12][13][14][15].…”