Papers by Keyword: Piecewise Linear System

Abstract: This paper investigates the bifurcations of the periodic solutions in the piecewise linear systems. Firstly the equation about amplitude-frequency response is deduced by the averaging method. Then the bifurcation classification is conducted by applying the singularity theory. The effects of the two parameters, the mass and the excitation amplitude, are discussed. The balance position will be changed when the quality changed, So the system is divided into two kinds of state. The results show that the parameter plane is divided into thirteen regions where bifurcation types are different. At last, discussing the amplitude- frequency response of different regions. this paper provides some theoretical guidance for system of considering load variation, and it is significant to help research the change in amplitude-frequency characteristic of piecewise linear system.

Abstract: The clearances, which universally exist in the joint parts of mechanical systems, are a main cause of various operation deteriorating problems, including noises generating, material wearing, even the early fatigue of members. In this paper, a new method to determine the clearance magnitude in the beam support is proposed with the description of a numerical example. The growing clearance will increase the vibration period of realistic system, and the accurateness of measurement is relevant to the frequency resolution of the instrument. Through the time series of the midpoint response of a simply supported beam, the period of the first modal free vibration can be obtained using the FFT Algorithm. Only two responses from different initial conditions are needed to identify the magnitude of the clearance. It is estimated the accurateness could be below 15%. The investigation also suggests this free vibration period approach may be adapted to handle the energy losses situations with the damping ratio considered in the formulas.