Damping in Structures

Damping in Structures

1. Damping Models

   • Rayleigh (Proportional)
     • Used alone when only the general level of damping is known.
     • Low frequency dominated by mass proportional damping.
       • Arises from media surrounding the structure.
     • High frequency dominated by stiffness proportional damping.
       • Arises from internal damping within the structure.
   • Modal
     • Used alone if the damping has been measured.
     • Experimental tests can measure the damping in each mode.
   • Combined

2. Transient Response with Proportional & Modal Damping

   • Solution for Single DoF System
     • Transforming back to cartesian coordinates
       • Impulse Response Matrix

3. Modal Solution with Arbitrary Viscous Damping

   • 3 Independent Coefficient Matrices, M, C & K.
     • No single transformation that will make all three matrices diagonal.
     • Convert EoM from 2nd Order to 1st Order
       • Express EoM in terms of two coefficient matrices

4. Damped Eigenvalue Problem

   • For systems with zero damping, p is imaginary (zero real part) and, for heavily damped systems (greater than critical) p is a real number. 
   • Assume Harmonic Solution
   • p - Eigenvalue
   • s - Eigenvector

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