Abstract:
The paper introduces a model of two identical coupled 4-DOF mechanical
linear sliding systems with dry friction coupled with each other by a linear torsional
spring. The appropriate components (bodies) of the coupled systems are riding on two
separated driving belts, which are driven at constant velocities, and stick-slip
vibrations can be observed. In this case the physical interpretation of the considered
model could be two rows of carriages laying on the guideways and coupled by an
elastic shaft, which are moving at constant velocity with respect to the guideways as a
foundation. From a mathematical point of view the analyzed problem is governed by
eight nonlinear ordinary second order differential equations of motion yielded by the
second kind Lagrange equations. Numerical analysis is performed in Mathematica
software using the qualitative and quantitative theories of differential equations. Some
interesting non-linear system dynamics are detected and reported using the phase
portraits and the Poincaré maps. Next, power spectra obtained by the FFT technique
are reported. The presented results show periodic, quasi-periodic, chaotic and hyperchaotic orbits. Moreover, synchronization effects between the coupled systems are
also detected and studied.
