Identification of pseudo-natural frequencies in a beam-moving mass system with periodic passages

Abstract

The response of a linear time-invariant (LTI) system to harmonic input generates a harmonic output with constant frequency but varying magnitude and phase. Many structural dynamic systems have been modeled as linear time-varying periodic (LTP) systems. Previous studies have reported that the response of an LTP system to an exponential input establishes an infinite number of frequencies. These studies have presented a new, exponentially modulated periodic signal space and a corresponding harmonic transfer function as useful tools in the operational modal analysis of LTP systems. In consideration of this new approach, this study mainly identifies the frequencies of a typical LTP system, such as a beam that is subject to the intermittent passage of moving masses. Upon obtaining the harmonic transfer function for the beam-moving mass system, conventional frequency domain methods for LTI systems are used to derive the frequency characteristics of the LTP system from the system response. These methods include the peak-picking method. As expected in an LTP system, an infinite number of pseudo-natural frequencies resonate in the beam-moving mass system.