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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.