Abstract
This study investigates the displacement transmissibility of single-degree-of-freedom systems with a Coulomb friction contact between a mass and a fixed or oscillating wall. While forced vibration and base motion problems have been extensively investigated, little work has been conducted on the joined base-wall problem. Based on the work of Den Hartog (Trans Am Soc Mech Eng 53:107–115, 1930), analytical expressions of the displacement transmissibility are derived and validated numerically. The mass absolute motion was analysed in the joined base-wall motion case with a new technique, with results such as: (1) the development of a method for motion regime determination; (2) the existence of an inversion point in transmissibility curves, after which friction damping amplifies the mass response; (3) the gradual disappearing of the resonant peak when the ratio between friction and elastic forces is increased. Moreover, numerical analysis provides further insight into the frequency region where mass sticking occurs in the base motion problem.
Highlights
Developing a fundamental understanding of the role played by friction damping in structural dynamics is nowadays an important challenge for exploring suitable structural designs
The dynamic behaviour of a 1-DoF system under base motion is usually investigated with the displacement transmissibility, which is the ratio between the amplitudes of mass and base motions
A new approach has been developed for the evaluation of the main properties of a 1-DoF system with Coulomb friction under harmonic (i) base excitation with groundfixed wall; (ii) joined base-wall excitation
Summary
Developing a fundamental understanding of the role played by friction damping in structural dynamics is nowadays an important challenge for exploring suitable structural designs. The dynamic behaviour of a 1-DoF system under base motion is usually investigated with the displacement transmissibility, which is the ratio between the amplitudes of mass and base motions. In 1930, Den Hartog proposed in [1] a method for the analysis of forced vibration with Coulomb friction; the author suggested a local solution for the steady sliding motion, allowing the description of quantities such as the amplitude of the mass motion or the phase shift between input load and response, and a condition for locating the transition between stick-slip and continuous motion. Hong and Liu have shown that the same expressions as Den Hartog’s for the maximum displacement and its phase lag are recovered Their analytical results were validated with a numerical solution [10].
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