Abstract
In this paper, we have shown an electronic circuit equivalence of a mechanical system consisting of two oscillators coupled with each other. The mechanical design has the effects of the magnetic spring force resistance force, and the spring constant of the system is periodically varying. We have shown that the system’s state variables, such as the displacements and the velocities, under the effects of different forces, lead to some nonlinear behaviors, like a transition from the fixed point attractors to the chaotic attractors through the periodic and quasi-periodic oscillations. We have verified those numerically obtained phenomena using the analog electronic circuit of this mechanical system.
Highlights
There are a large number of physical and feigned systems, especially in the machine industry, where we can see the effects of magnetic and electrical fields [1,2,3,4]
When the non-dimensional velocity has the positive values, the non-dimensional dry-friction term reaches the 0.2413 value, equal to the value of t1. Those values are well agreed with the definition of a dry-friction in mechanical systems
From the Equation (15), we can say that the linear frequency f of the applied sine wave is dependent on the nondimensional angular frequency ωnd of the considered mechanical system
Summary
There are a large number of physical and feigned systems, especially in the machine industry, where we can see the effects of magnetic and electrical fields [1,2,3,4]. Have shown that the dry-friction force can be implemented by using two antiparallel diodes in the circuit. Many works have already been shown regarding the equivalence of the electrical and mechanical systems, the mechanical systems under different forces and coupling schemes are not yet conducted in a more general way in an electronic circuit. We have shown how, in another way, using op-amps and the multipliers, this dry-friction term and different forces can be implemented. In this paper, we have shown the electronic circuit equivalence of a coupled mechanical system having different forces, like magnetic, resistive, etc., and verified the numerical predictions using the equivalent electronic circuit.
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