Built-up systems consisting of rectangular cable networks covered by or embedded in a membrane matrix are considered; small oscillations about an initially flat, pretensioned state are studied. By employing Dirac delta functions to aid in representation of preload and weight distribution acting on the system, the system response is shown to be given by a generalized version of the equation for a vibrating membrane. A solution of the field equation is effected using Galerkin’s method and approximating functions are suggested for a wide class of boundary shapes. As an illustration of the method a rectangular boundary shape is considered and results are obtained for typical values of preload, cable distribution, etc. Results are compared with previous analyses of similar systems, and advantages of the present approach are discussed.

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