Versions Compared


  • This line was added.
  • This line was removed.
  • Formatting was changed.


  • δ is the stiffness-proportional damping coefficient.


Relationships between the modal equations and orthogonality conditions allow this equation to be rewritten as:


  • ω n is the natural frequency ( ω n = 2 π f n ).


Here, it can be seen that the critical-damping ratio varies with natural frequency. The values of η and δ are usually selected, according to engineering judgement, such that the critical-damping ratio is given at two known frequencies. For example, 5% damping ( ξ = 0.05 ) at the first natural frequency of the structure ( ω i = ω 1 ), and at ω j = 188.5 (30 Hz). According to the equation above, the critical-damping ratio will be smaller between these two frequencies, and larger outside.


  • Wilson, E. L. (2004). Static and Dynamic Analysis of Structures (4th ed.). Berkeley, CA: Computers and Structures, Inc.
    Available for purchase on the CSI Products >

    Books page