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Stress-Softening Effects in the Vibration of a Non-Gaussian Rubber Membrane

Department of Engineering Mechanics, University of Nebraska-Lincoln, PO Box 910215, Lexington, KY 40591-0215, USA

Alex Elías-Zúñiga

Departamento de Ingeniería Mecánica, Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Monterrey, E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, N.L., Mexico

The Mullins effect in the small amplitude transverse vibration of a stretched rubber membrane is investigated. The fundamental frequency, which decreases with increasing softening, is determined for a specific class of stress-softening materials. Analytical relations for the membrane vibration frequency are illustrated graphically for three phenomenological models and two kinds of non-Gaussian molecular network models for rubber elasticity. The results demonstrate the role of the material parameters and, although no experimental data for the vibration of a rubber membrane currently are known, the theoretical predictions are characteristic of the frequency-stretch response reported in vibration experiments on rubber cords.

Key Words: Mullins effect • non-Gaussian networks • rubber elasticity • membrane vibrations

Mathematics and Mechanics of Solids, Vol. 8, No. 5, 481-495 (2003)
DOI: 10.1177/10812865030085003


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