A model for the stick-slip motion of slender structures subjected to axial loads and coulombian frictional constraints

A number of slender beam-like structures subjected to axial load and frictional constraints (for example, undercarriage legs, digging buckets, blades of turbines, brushes and wiper systems) exhibits a complex dynamic behavior. The main components of these systems are often constrained to slide on a surface with friction. Here we present a dynamical model where a flexible beam is spring-hinged at one end, while the opposite end can slide with coulombian friction on a rigid surface moving with prescribed velocity. The beam is subjected to a concentrated compressive load at the top end. The equations of motion are solved analytically as a combination of free-modes shapes and elastically deformed axis’ line shapes. Once refined, the proposed model could constitute a design tool useful in many of the above-described applicative contexts. One of the first results is that the frequency of the alternation between the stick and the slip phase may be sensibly different from the natural frequencies of the system.