RANDOM VIBRATIONS OF NONLINEAR ELASTIC STRUCTURES,

Abstract

The theory of the Markoff process and the associated FokkerPlanck equation is used to investigate the large vibrations of beams and plates with arbitrary boundary conditions subjected to white noise excitation. An expression for the joint probability density function of the first N coefficients of series expansions of the middle surface displacements is obtained. Detailed calculations presented for simply supported beams and plates show that the probability density function of the modal amplitudes are non-Gaussian and statistically dependent. Numerical computations for the plate indicate a significant reduction of the mean squared displacement for values of the parameters well inside the range of practical considerations. Furthermore, for smaller aspect ratios the per cent reguction is greater. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 01, 1964
Accession Number
AD0602488

Entities

People

  • Richard E. Herbert

Organizations

  • University of Florida

Tags

DTIC Thesaurus Topics

  • Amplitude
  • Aspect Ratio
  • Boundaries
  • Coefficients
  • Computations
  • Displacement
  • Equations
  • Excitation
  • Mathematical Analysis
  • Mathematics
  • Noise
  • Probability
  • Probability Density Functions
  • Random Vibration
  • Vibration
  • White Noise

Fields of Study

  • Physics

Readers

  • Statistical inference.
  • Structural Dynamics.