RESEARCH PAPERS: Papers on Noise Control and Acoustics

Variational Formulations for the Finite Element Analysis of Noise Radiation from High-Speed Machinery

[+] Author and Article Information
B. S. Thompson

Department of Mechanical Engineering, Wayne State University, Detroit, Mich. 48202

J. Eng. Ind 103(4), 385-391 (Nov 01, 1981) (7 pages) doi:10.1115/1.3184502 History: Received July 29, 1981; Online July 30, 2009


Variational theorems are presented for analyzing the vibrational response of flexible linkage mechanisms and the surrounding acoustic medium in which they are immersed. These theorems are established by generalizing Hamilton’s principle through using Lagrange multipliers to incorporate field equations and boundary conditions within the functional. The same philosophy is adopted to handle the conditions at the fluid-structural interface. When independent arbitrary variations of the system parameters are permitted, these acousto-elastodynamic theorems yield as characteristic equations the equation of motion for each member of the linkage, the acoustical wave equation, the compatibility conditions at the interface between the fluid and solid continua, and also the boundary conditions. These variational statements provide the foundations for several different classes of finite element analysis.

Copyright © 1981 by ASME
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