The Mullins Effect in the Vibration of a Stretched Rubber Membrane

Abstract

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 λ ε (1,Λ), the fundamental frequency of the virgin material membrane is greater than the corresponding frequency of the same membrane preconditioned to a maximum previous stretch Λ. 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.