# Exact solutions for vibrating rectangular membranes placed in a vertical plane

Wang, C. Y. and Wang, C. M. (2011) Exact solutions for vibrating rectangular membranes placed in a vertical plane. International Journal of Applied Mechanics, 3 3: 625-631. doi:10.1142/S1758825111001160

Author Wang, C. Y.Wang, C. M. Exact solutions for vibrating rectangular membranes placed in a vertical plane International Journal of Applied Mechanics   Check publisher's open access policy 1758-8251 2011-01-01 Article (original research) 10.1142/S1758825111001160 Not yet assessed 3 3 625 631 7 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 $\xi = b/\sqrt{c}$. 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 &xi, the horizontal modes increase with each increased frequency. The fundamental frequencies always correspond to n = 1. exact solutionsfrequenciesmembranesVibration C1 Provisional Code Non-UQ

 Document type: Journal Article Article (original research) School of Mechanical & Mining Engineering Publications

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