A STUDY ON USE OF NONLINEAR SITFFNESS IN 3-DIMEN-SIONAL SPACE TO REDUCE ROTATIONAL VIBRATION

Abstract

This study presents the effect and use of nonlinear stiffness on 3-dimensional rigid body vibration. The system is modeled as a simple cylinder with vibration mounts attached at three points on the fixed boundary and is 6 degree-of-freedom system considering rotational coordinates. The posture of the rigid body is defined using the 3-2-1 Euler angle convention. The equations of motion are derived using the Lagrange equation. The mode shapes of the system are derived and the effect of nonlinear stiffness on the rotational mode was investigated. The duffing oscillator is used for modeling the nonlinearity. By assuming that the mass is placed on the mounts and is equilibrium state with gravity, nonlinear stiffness becomes asymmetric with respect to displacement of mount. This asymmetry in displacement results in asymmetric vibrational response of the system with respect to displacement. With linear stiffness, the response rotates repeatedly along the same path, while with asymmetric nonlinear stiffness, the response represents a continuous rotation. The change of the response results in decrease of peak amplitude in frequency domain and reducing the rotational vibration.