Journal of Advances in Applied Mathematics

Download PDF (757.9 KB) PP. 135 - 145 Pub. Date: July 1, 2021

DOI: 10.22606/jaam.2021.63001

• Lawrence Atepor^*
  Department of Mechanical Engineering, Cape Coast Technical University, Cape Coast, Ghana
• Richard Nii Ayitey Akoto
  School of Graduate Studies, University of Professional Studies, Box LG 149, Accra, Ghana

Chaotic Vibrations are considered for a quarter-car model excited by the road surface profile. The equation of motion is obtained in the form of a classical Duffing equation and it is modeled with deliberate introduction of parametric excitation force term to enable us manipulate the behavior of the system. The equation of motion is solved using the Method of Multiple Scales. The steady-state solutions with and without the parametric excitation force term is investigated using NDSolve MathematicaTM Code and the nonlinear dynamical system’s analysis is by a study of the Bifurcations that are observed from the analysis of the trajectories, and the calculation of the Lyapunov. In making the system more strongly nonlinear the excitation amplitude value is artificially increased to various multiples of the actual value. Results show that the system’s response can be extremely sensitive to changes in the amplitude and the that chaos is evident as the system is made more nonlinear and that with the introduction of parametric excitation force term the system’s motion becomes periodic resulting in the elimination of chaos and the reduction in amplitude of vibration.

chaotic vibration, parametric excitation, excitation frequency, quarter-car, magnetorheological dampers.

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