The Nonlinear Vibrations of Membranes under Random Influences,

Abstract

Nonlinear transverse vibrations of a plane rectangular membrane are examined for random steady state effects. The pertureational effect is assumed to be delta correlational in time ('white noise'). The fundamental equations are compared with the Foeppel-Karman theory. Transverse displacement is represented in the form of a double trignometric series, each member of which is expressed by the product of a generalized coordinate for the shape of the natural frequencies of the corresponding linear problem. Nonlinear equations in terms of generalized coordinates are obtained by Bubnov-Galerkin method. The solution to these equations was arrived at by using the Fokker-planck-Kolmogorov equations. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 03, 1972
Accession Number
AD0742801

Entities

People

  • V. A. Ivovich

Organizations

  • National Air and Space Intelligence Center

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Equations
  • Frequency
  • Galerkin Method
  • Kolmogorov Equations
  • Membranes
  • Resonant Frequency
  • Steady State
  • Transverse
  • Vibration
  • White Noise

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.
  • Structural Dynamics.