Damping and Vibration of Beams With Various Types of Frictional Support Conditions

The damping characteristics of a flexible beam with various types of frictional supports is considered. For each configuration studied, the only source of damping is dry friction at one support. The study considers supports with constant normal forces and supports for which the normal force varies with beam displacement. The case of transverse slipping is contrasted with that of in-plane slipping. The beam is analyzed using a single spacial mode and first-order harmonic balance is used to study the qualitative features of the damping and vibratory properties. It is seen that the nature of the damping depends on whether the frictional interface is transverse to or in plane with the beam. It is also seen that the equivalent viscous damping of the system can be inversely proportional to, invariant with respect to, directly proportional to, or directly proportional to the square of the displacement amplitude.