DISPLACEMENT AND FREQUENCY ANALYSES OF VIBRATORY-SYSTEMS

This paper deals with the frequency and response studies of vibratory systems, which are represented by a set of n coupled second-order diff erential equations. The following numerical methods are used in the re sponse analysis: central difference, fourth-order Runge-Kutta and moda l methods. Data generated in the response analysis are processed to ob tain the system frequencies by using the fast Fourier transform (FFT) or harmonic response methods. Two types of the windows are used in the FFT analysis: rectangular and Hanning windows. Examples of two, four and seven degrees of freedom systems are considered, to illustrate the proposed algorithms. Comparisons with those existing results confirm the validity of the proposed methods. The Hanning window attenuates th e results that give a narrower bandwidth around the peak if compared w ith those using the rectangular window. It is also found that in free vibrations of a multi-mass system, the masses will vibrate in a manner that is the superposition of the natural frequencies of the system, w hile the system will vibrate at the driving frequency in forced vibrat ions.