An-Najah Staff

The presence of fixed points in a frequency response of vibrating systems can complicate the vibration reduction if these points were not recognized.  In this paper, the fixed points of vibrating discrete systems with n-degrees of freedom are investigated. A procedure for determining the frequencies at which mass and/or stiffness fixed points of discrete systems with n-degrees of freedom occur, is presented. A mass fixed point is an intersection of all amplitude curves which occurs in a frequency response of a vibrating system during a parametric variation of a mass. At the frequency where this point occurs, the vibration amplitudes remain constant regardless of the mass values. A stiffness fixed point is defined as in a similar manner. To verify the analysis performed, all frequencies at which mass and/or stiffness fixed points of a vibrating 3-mass system occur, are determined analytically.