Stress-softening effects in the vibration of a non-Gaussian rubber membrane

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.