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Description
This study investigates the transverse vibration of tensioned membranes with spatially periodic surface-mass variations that represent embroidered fabrics. A two-dimensional membrane model is discretized using finite differences with fixed boundary conditions. The resulting generalized eigenvalue problem accounts for heterogeneous surface mass density and is evaluated for four representative designs inspired by the common weave bindings plain, satin and twill, and an asymmetric layout. Computed natural frequencies and mode shapes are compared with the analytical solution for a uniform square membrane. Symmetric patterns largely preserve classical modal symmetry and near-degenerate mode pairs, whereas the asymmetric layout breaks symmetry, lifts degeneracy, and produces larger frequency shifts accompanied by distorted mode shapes.