Stability and Nonlinear Dynamics of a Horizontally Base-Excited Rigid Rod With Unsymmetric End Stiffnesses

Abstract

This paper presents a dynamic analysis of a horizontally base-excited rigid rod with unsymmetric end stiffnesses. This is to model a shaker/mould structure with gripper imperfections. The study explains the large rotational and transverse vibrations of the mould at specific operating frequencies observed in the experiments. The governing equations consist of a time-dependent coefficient which indicates the existence of parametric excitation effects. It is concluded that differences between the gripper stiffnesses are responsible for this phenomenon and could destabilize the system. The value of the time-varying parameter is related to the horizontal vibration amplitude of the mould and hence is a function of the system parameters and excitation frequency. The mould’s rotational motion is directly parametrically excited while its transverse vibration is excited indirectly through coupling with the rotational motion. A thorough analysis of this class of mechanical systems has not been performed in the past. In this research, studies are conducted to identify the contributions of various system parameters, such as gripper stiffness, damping, mould inertia, and excitation amplitude to the system dynamic characteristics. The results provide new insight and guidelines toward optimizing such mechanical systems.