A criterion for optimal damping design

The design of elements for maximum damping of vibrations in a linear elastic system is described. Single and multiple damping elements of purely viscous, visco-elastic, rigid-plastic, or Coulomb type are treated.A general theorem is developed which equates the optimal impedance (dynamic stiffness) of the damping element to the impedance (elastic plus inertial stiffness) of the linear system at the point at which the element is applied. This theorem provides a criterion which may be used directly to design the elements: Formulae are derived from there to specify the elements and to evaluate their effectiveness and thus indirectly indicate where to locate them.Applications include damping of sway vibrations of tall buildings, and of vibrations in floor systems, vehicles and machines. Noise producing vibrations may be included. In each case, the optimal impedance characteristics of the damping element may be expressed in terms of the impedance characteristics of linear system, e.g. the elastic stiffness of the structure or the mass of the machine, and the frequency of the loading force.