Abstract
This technical note presents the exact solutions for the vibration frequencies of rectangular membranes placed in a vertical plane. The membranes are fixed on the top edge and side edges. The bottom edge may be either free and carrying a uniformly distributed mass, or fixed. It is found that the width of the membrane b and lateral tension ratio c appears in the exact solution in a combined form [Formula: see text]. This important similarity parameter implies that a larger width has the same frequencies as lowered lateral tension, therefore, this parameter greatly reduces the number of tables. For the vibrating vertical membranes, we find that when ξ increases generally, the frequencies decrease. For small ξ (small width or large lateral tension ratio), the horizontal modes are all n = 1, or a half-sine wave in the horizontal direction. For large ξ, the horizontal modes increase with each increased frequency. The fundamental frequencies always correspond to n = 1.
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