Damping

Damping is defined as energy dissipation property of materials and structures that are subjected to time-variable loading. Damping is associated with irreversible transition of mechanical energy into thermal energy. Energy radiation into a surrounding medium is called radiation or geometric damping (Benaroya 2004).

Damping classification

• material damping - energy dissipation by deformation in a medium.
• structural damping - damping in assembled structures at their contact surfaces and interfaces (such as frictional losses, losses at contact surfaces, etc.).
• radiation damping - energy radiation into the surrounding medium.
• geometric damping - same as radiation damping.
• active damping - damping with external energy and control.
• passive damping - damping without external energy and control.
• internal damping - damping inside defined system boundary.
• external damping - damping outside defined system boundary.

Computational models for damping

• modal damping ratios - applicable for linear elastic analysis of structures with classical damping that can be solved by classical modal analysis
• damping matrix - damping matrix must be used when classical modal analysis is not applicable. This is the case of structures with nonclassical damping (for both linear and nonlinear analyses) and nonlinear systems with the damping of classical form. To account for all energy dissipating mechanism, the damping matrix should be determined from the damping ratios of the structure and not from member sizes and material damping (Chopra 2002).
  • classical damping matrix - applicable for systems with similar damping mechanism distributed throughout the structure
    • Rayleigh damping
    • Cauchy damping
  • nonclassical damping matrix - applicable for systems that consist of two or more parts with different level of damping, such as a soil-structure system

References

• Haym Benaroya: Mechanical vibration: analysis, uncertainties, and control. 2004 p. 94
• Anil Chopra: Dynamics of Structures, 2nd Edition, 2002, ISBN-8120321391. p. 454, section 11.3 (damping matrix)