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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 26, 2006
Accession Number
ADA459494

Entities

People

  • Andras Balogh
  • Vladmir Varlamov

Tags

Communities of Interest

  • Air Platforms
  • Sensors
  • Space

DTIC Thesaurus Topics

  • Acoustic Waves
  • Algorithms
  • Applied Mathematics
  • Bessel Functions
  • Boundary Value Problems
  • Computations
  • Differential Equations
  • Eigenvectors
  • Elastic Waves
  • Electrical Solitons
  • Energy Transfer
  • Equations
  • Geometry
  • Integral Equations
  • Mathematical Analysis
  • Simulations
  • Waves

Readers

  • Linear Algebra
  • Molecular and Cellular Biochemistry
  • Plasma Physics / Magnetohydrodynamics