Two-dimensional stick-slip motion of an oscillator subjected to dry friction is investigated in this paper. The equations of motion of the non-smooth system are discretized in the time domain by means of the implicit Bozzak-Newmark scheme. The system state equations in a time step are written in the incremental displacements to model the frictional constraints in accordance with Coulomb's law. With the help of a coordinate transformation and introduction of paired non-negative and complementary variables, the non-smooth vibration problem is reduced to a mathematical programming problem for which a numerical solution can be obtained. Numerical results for a single body oscillator under a harmonic excitation are obtained using the proposed method and compared with those in the literature; excellent agreement is achieved. The proposed method is then applied to a general two-dimensional oscillator with stiffness and viscous coupling in addition to the frictional coupling. Experiments are conducted for free vibration of a single body vibration system subjected to two-dimensional dry friction. Good agreement between the measurements and numerical results obtained using the proposed scheme is observed.
Vibrational behavior of harmonically excited MDOF oscillators subjected to multiple contact constraints is investigated in this paper using the combination of the Newmark integration scheme and the Linear complementarity problem (LCP) formulation. An oscillator with gap-activated non-smooth spring constraints exhibits various complex behavior such as sub-harmonic resonances, bifurcations and chaos, which are effectively predicted using the proposed method. Numerical results were obtained and presented for SDOF and 5-DOF systems with frequency and stiffness parameters varying in wide ranges to validate the Newmark-LCP method and to demonstrate its effectiveness in dealing with MDOF systems with multiple contact constraints.
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