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The Mullins Effect in the Vibration of a Stretched Rubber Membrane

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

The effect of stress-softening on the small amplitude transverse vibrational frequency of a stretched rubber membrane is investigated. The fundamental frequency is determined for a general incompressible and isotropic stress-softening material. It is shown that for each fixed value of the stretch (1,), the fundamental frequency of the virgin material membrane is greater than the corresponding frequency of the same membrane preconditioned to a maximum previous stretch . Moreover, the stress-softened membrane frequency for the same stretch decreases further with the degree of softening damage incurred upon increasing the maximum previous stretch. A specific damage function is introduced and explicit results are illustrated for three material models.

Key Words: Mullins effect • stress-softening • pseudo-elasticity • membrane vibration

Mathematics and Mechanics of Solids, Vol. 8, No. 4, 435-445 (2003)
DOI: 10.1177/10812865030084005


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