Pendulum vibration absorbers with spatially-varying tangential friction: modelling and design

Passive vibration absorbers are widely used in structural control. They usually consist in a single-degree-of-freedom appendage of the main structure, tuned to a selected structural target mode by means of frequency and damping optimization. A classical configuration is the pendulum type, whose mass is bilaterally constrained along a curved trajectory and is typically connected to the structure through viscous dashpots. Although the principle is well known, the search for improved arrangements is still under way. In recent years this investigation has inspired a new type of bidirectional pendulum absorber (BPA), consisting of a mass moving along an optimal three-dimensional (3D) concave-up surface. For the BPA, the surface principal curvatures are conceived to ensure a bidirectional tuning to both principal modes of the structure, while damping is provided either by horizontal viscous dashpots or by vertical friction dampers between the BPA and the structure. In this paper, a BPA variant is proposed, in which damping is produced by the variable tangential friction force developing between the pendulum mass and the 3D surface, because of a spatially-varying friction coefficient. In fact, a friction coefficient pattern is proposed that varies along the pendulum surface proportionally to the modulus of the surface gradient. With this assumption, the absorber dissipative model proves nonlinear homogeneous at low response amplitudes. The resulting homogeneous BPA (HBPA) has a fundamental advantage over conventional friction-type absorbers, in that its equivalent damping ratio is independent of the amplitude of oscillations, i.e. its optimal performance is independent of the excitation level. At the same time, the HBPA is more compact and simpler than viscously damped BPAs, not requiring the installation of dampers. This paper presents the analytical modelling framework of the HBPA and a method for its optimal design. Numerical simulations under wind and earthquake loads are reported to compare the HBPA with classical viscously damped BPAs. Finally, the HBPA proves a promising alternative to existing pendulum absorbers, and the homogeneous tangential friction proves an effective way to realize amplitude-independent damping in structural systems.