Dynamic Stability of a Vibrating Hammer

Abstract

This paper deals with the stability of motion of an elastically suspended vibrating hammer that impacts upon an energy absorbing surface referring to the dynamical interaction between a vibrating hammer and a motor. Assuming an ideal source [1] of energy is characteristic of a motor, then the force mr ω2 cosωt appears to be the vertical component of the inertia force of the mass m . The mass m is located the distance r from the axis 0 and rotates by frequency ω. Hence the basic equation of a vibrating system takes the form of a linear system. Fu [2] has investigated the regions of stability of the system as the linear system. In the case of practical use, however, a limited power source called a “nonideal source of energy” is the characteristic of a motor. Accordingly, it follows that the motion of an oscillating system with a nonideal source of energy may be formulated as a nonlinear system. The local stability of the sytem desired by a nonlinear equation is presented in our paper. Finally, the results of the regions of stability are compared with those studied in Fu.