Study of Nonlinear Oscillations of Elastic Membrane
Abstract
Nonlinear oscillations of a circular elastic membrane with a simply supported boundary are investigated. They are caused by a source of acoustic waves, so that the membrane serves as an acoustic receiver. Vertical deflections of the membrane and the acoustic pressure are to be found and, if possible, the direction to the source. The boundary value problem is solved by a nonlinear version of the method of eigenfunction expansions. Vertical deflections and the acoustic pressure are found in the form of an expansion into the series of eigenfunctions of the Laplace operator in a disc. Numerical simulations were conducted to establish the sensitivity of a nonlinear membrane. The nonlinear effect of frequency multiplication was established. Position of the vertical plane containing the source was found.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 26, 2006
- Accession Number
- ADA459494
Entities
People
- Andras Balogh
- Vladmir Varlamov