Random vibration of a beam with a stick-slip end condition

An analysis is presented of the response of a randomly excited beam with an axial stick-slip end condition. The emphasis of the present effort is on the case in which slipping is a relatively rare event so that, while it does not contribute significantly to the system damping, it does have a marked influence on the non-linear behaviour. A simple approximate analysis is developed to estimate the rate at which slipping will occur in a randomly excited beam. This facilitates the construction of guidelines for designing a clamping fixture for a given beam so that slipping occurs infrequently. Comparisons of approximate estimates of the slipping rate with those obtained by numerical simulations show that the approximate method leads to conservative estimates.