This paper is concerned with the wrinkling and free vibration analysis of catenary supported membranes. In the development, the use is made of a two-variable-parameter (2VP) model for the thin-film membrane, and tensioned bar model for the catenary support. The entire membrane structure is assembled through reinforcement of a shear-free constraint between the membrane and the supporting catenary, which leads to a global dynamic equation governing the free vibration of the catenary-supported membrane. The natural frequencies and modes shapes of the membrane are then computed. The proposed modeling and solution technique is illustrated in a numerical example.

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