Finite element formulation for non-smooth oscillations of an elastic beam with a friction device

Calculated are forced oscillations of a clamped elastic beam with a friction device at its free end. Considering partial states, namely sticking and sliding, and applying FEM leads to a discrete non-smooth dynamic problem. Stationary oscillations are of interest, depending on the number of finite elements and on different types of friction laws. Due to the linearity of partial states of motion, the numerical integration is reduced to the calculation of switching times which separate the sequence of partial states. Appropriate chosen internal damping diminishes the numerical effort considerably.