{"title":"Exact Solution of a Class of Non-Circular Vibrating Membranes","authors":"C.Y. Wang","doi":"10.1115/1.4054256","DOIUrl":null,"url":null,"abstract":"\n Saint-Venant's method to solve the Poisson equation is applied to the Helmholtz equation which governs membrane vibration. A family of non-circular membrane shapes with N-fold rotational symmetry is presented. Membrane shapes, properties and fundamental frequencies are tabulated. The solutions are exact and can serve as accuracy standards for approximate methods.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"22 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Vibration and Acoustics-Transactions of the Asme","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4054256","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0
Abstract
Saint-Venant's method to solve the Poisson equation is applied to the Helmholtz equation which governs membrane vibration. A family of non-circular membrane shapes with N-fold rotational symmetry is presented. Membrane shapes, properties and fundamental frequencies are tabulated. The solutions are exact and can serve as accuracy standards for approximate methods.
期刊介绍：
The Journal of Vibration and Acoustics is sponsored jointly by the Design Engineering and the Noise Control and Acoustics Divisions of ASME. The Journal is the premier international venue for publication of original research concerning mechanical vibration and sound. Our mission is to serve researchers and practitioners who seek cutting-edge theories and computational and experimental methods that advance these fields. Our published studies reveal how mechanical vibration and sound impact the design and performance of engineered devices and structures and how to control their negative influences.
Vibration of continuous and discrete dynamical systems; Linear and nonlinear vibrations; Random vibrations; Wave propagation; Modal analysis; Mechanical signature analysis; Structural dynamics and control; Vibration energy harvesting; Vibration suppression; Vibration isolation; Passive and active damping; Machinery dynamics; Rotor dynamics; Acoustic emission; Noise control; Machinery noise; Structural acoustics; Fluid-structure interaction; Aeroelasticity; Flow-induced vibration and noise.
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