ANALISIS KESALAHAN FUNGSI RESPON FREKUENSI AKIBAT KETERBATASAN WAKTU REKAM PADA PENGUJIAN GETARAN DENGAN EKSITASI IMPAK KASUS DOMAIN WAKTU KONTINU

Abstract

This paper derives mathematical equation describing the relation between errors in FRF due to limited record time length, record time and the time constant of a vibration system modelled by the I- dof vibration system with viscious damping. It is assumed in derivation of the equations that both impact excitation as well as response signals are not contaminated by noises. Moreover, the impact excitation is assumed to be a delta Dirac function. Consequently, the spectrum of the excitation is constant for all frequencies. The derived mathematical equations results show that the FRF error is a complex function so that is can be expressed by the magnitude anf phase functions. The magnitude of FRF error represent the maximum possible error occuring in the FRF magnitude. The maximum possible error occuring in the FRF magnitude at fn is influenced by parameters, such as record time and time constant of the structures. This maximum possible error shows an exponentially decreasing nature as the ratio of these parameters increases. Based on the derived equation, a recording of the response signal within three times of the system time constant results in the maximum possible error at fn in the FRF magnitude in the order of 5% of the theoritical FRF magnitude. Such recording can be performed if the peak amplitude of the response signal ceases to about 5% of the initial peak amplitude at the end of the record time for between 0.001 and 0,1.