r7.10.01 Analysis of random responses

Summary:

The introduction of a « stochastic approach to seismic calculation » to solve a vibratory mechanics problem under random excitation requires specific post-processing.

The command POST_DYNA_ALEA [U4.76.02] makes it possible, based on the power spectral density of a response-spectrum, to evaluate its standard deviation, its apparent frequency, and the distribution of its peaks. In a first approach, it also makes it possible to calculate the Vanmarcke function useful in the case of seismic analysis.

NOTE:

This command also makes it possible to perform statistical estimates for any type of interspectrum of response to random excitation that is not necessarily seismic (for example: effect of waves or turbulent flow) .

Table of Contents

• 1. Introduction
• 2. Spectrum - Interspectrum - Interspectral Matrix
  • 2.1. Signal processing - Conventions retained
  • 2.2. Power concept - Power Spectral Density
  • 2.3. Implementation in Code_Aster
• 3. Reminders on statistical laws [bib4]
  • 3.1. Definitions
  • 3.2. Hypotheses in random dynamics
  • 3.3. Power spectral density
  • 3.4. Spectral moments
• 4. Exceeding threshold measures and reliability
  • 4.1. Spectral moments and characteristic parameters
  • 4.2. Distributions of positive peaks
  • 4.3. Seismic response: Vanmarcke’s law
  • 4.4. Peak factor implemented in Code_Aster
• 5. notes
• 6. Bibliography
• 7. Description of document versions