Parametric instability of a Leipholz beam due to distributed frictional axial load

In this paper, the parametric instability of a beam subjected to a moving distributed contact load that also oscillates in the transverse direction of the beam is studied. Due to the presence of friction between the beam and the moving contact surface, the beam is excited by a pulsating, distributed, follower-type axial load, which results in the problem of a Leipholz column subjected to parametric excitation. The study of this prototypical one-dimensional model is intended to provide further understanding of the instability of systems that have similar loading conditions such as automotive disc brake pads rubbed by the oscillatory rotor or beam-like structures. Effects of several parameters such as boundary conditions, coefficient of friction, intermediate supports, and waviness of the contact load on the instability are examined. Results show that the combination resonance of both the sum and difference types exists for the boundary conditions considered in this study. It is also found that the shearing motion of the friction material plays an important role in determining the stability of the Leipholz beam model. Analogous behavior of instability between the present model and the disc brake pad system is also discussed.