Please use this identifier to cite or link to this item: https://doi.org/10.1142/S1758825111001160
Title: Exact solutions for vibrating rectangular membranes placed in a vertical plane
Authors: Wang, C.Y.
Wang, C.M. 
Keywords: exact solutions
frequencies
membranes
Vibration
Issue Date: Sep-2011
Source: Wang, C.Y., Wang, C.M. (2011-09). Exact solutions for vibrating rectangular membranes placed in a vertical plane. International Journal of Applied Mechanics 3 (3) : 625-631. ScholarBank@NUS Repository. https://doi.org/10.1142/S1758825111001160
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 $\xi = b/\sqrt{c}$. 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. © 2011 Imperial College Press.
Source Title: International Journal of Applied Mechanics
URI: http://scholarbank.nus.edu.sg/handle/10635/59050
ISSN: 17588251
DOI: 10.1142/S1758825111001160
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