r5.05.04 Modeling of damping in linear dynamics

Summary:

Linear dynamic analyses of structures subject to imposed forces or movements require the addition of mechanical damping characteristics to the stiffness and mass characteristics of the model.

Several classical models are available, applicable to all types of finite elements available:

• the viscous damping model,

• the hysteretic damping model (also called « structural damping »)

for the harmonic analysis of viscoelastic materials.

For analyses using dynamic response methods by modal recombination, with a modal basis of real eigenmodes, it is possible to introduce modal damping coefficients.

• 1. Notion of mechanical damping
  • 1.1. Depreciation models
  • 1.2. General definitions to characterize depreciation [bib1]
• 2. Viscous damping model
  • 2.1. Physical definition of viscous damping
  • 2.2. Harmonic oscillator with viscous damping
• 3. Hysteretic damping model
  • 3.1. Physical definition of hysteretic damping
  • 3.2. Harmonic oscillator with hysteretic damping
  • 3.3. Focus on linear viscoelasticity
• 4. Other amortization models
• 5. Structure analysis with damping
  • 5.1. Overall amortization of the structure
  • 5.2. Localized amortization
• 6. Using the depreciation matrix
  • 6.1. Use of the viscous damping matrix
  • 6.2. Use of the complex stiffness matrix
  • 6.3. Complex modal analysis
• 7. Bibliography