Abstract
Magnetorheological damper (MR damper) is the vibration reduction equipment which is filled with MR fluid in the cylinder and it is used for the purpose of reducing the vibration effects in structural, civil, and mechanical engineering systems. MR damper is different from the ormal passive damper because of the tiny magnetic particles in the cylinder. Therefore, when the applied magnetic field is increased, the suspended magnetic particles become the chain structure, and the effective stiffness of MR damper becomes large. In the absence of magnetic field, the MR fluid behaves like a normal passive damping component. In order to modulate the MR damper force and adjust the associated parameters, various modelling techniques are proposed to identify the MR damper behaviour from researches. The most well-known techniques are Bouc-Wen and Bingham models. These two existing mathematical models of MR damper, including discontinuous and piecewise functions, are non-ideal for numerical computation, stability analysis, and control design. This thesis proposes the Duffing equation for the modelling of MR damper system. Duffing equation is a well-known, continuous, second-order nonlinear differential equation and it has been used to analyse the behaviour of chaotic dynamics, a hardening spring, and structural systems under excitations. By adjusting each parameter of equation analyse the influence of the hysteresis curve and fit the hysteresis curve in order to find the dynamic equation of the MR damper.