*Corresponding author:Livija Cveticanin, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21000 Novi Sad, Serbia
Received: July 25, 2018; Published: August 16, 2018
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Objectives: The aim of the paper is to give a new explanation of motion of human head-neck structure modelled as a nonlinear two-degree-of-freedom system. The influence of the excitation parameter on steady state motions (periodic and chaotic) is analyzed. A method for chaos control is discussed.
Methods: Mathematical model, given with two nonhomogenous and nonlinear coupled second order differential equations, is analyzed. The nonlinearity is assumed to be of any order given with a real number (integer or noninteger). For qualitative analysis of the motion the numerical simulation is applied. For determination of chaos the method based on the sign of Lyapunov’s exponents and bifurcation diagram is used. Method of chaos suppression is incorporated into the investigation.
Result: Due to nonlinearity steady state periodic and chaotic motion may appear. The type of motion depends on the parameter of excitation which acts apart from the apparent mass modeling the human head. Chaos suppression is achieved with a control function added to the system.
Conclusion: Knowing the limits of excitation and biomechanical parameters, it is possible to obtain the type of the steady-state motion of the head as appointed mass. We think that the transition between steady-state motions is useful in explanation of the injury of head-neck system. It is believed that in the human body a control mechanism must exist which transforms the chaotic motion to a simple periodical steady state one.
Keywords: Nonlinear Vibration; Chaos; Bifurcation Diagram; Chaos; Control of Motion