Estimation of steady loss factor with decay rate method

Abstract

Steady loss factor is derived according to its definition, and a conclusion is obtained that steady loss factor is not always among modal loss factors but related to contributions of each modal response to vibration response. To obtain the conclusions about the range of steady loss factor, four cases are discussed according to positions of the two natural frequencies related to the central frequency. 1) Both natural frequencies are lower than the central frequency. 2) Both natural frequencies are higher than the central frequency. 3) One natural frequency, whose modal loss factor is smaller, is higher than the central frequency and the other natural frequency is lower than the central frequency. 4) One natural frequency, whose modal loss factor is larger, is higher than the central frequency and the other natural frequency is lower than the central frequency. Steady loss factor ranges between modal loss factors only if the frequency, whose value of multiplying modal loss factor is largest, is lower than central frequency of frequency band and at the same time, the frequency, whose value of multiplying modal loss factor is the smallest, is higher than the central frequency. Process loss factor which is a time-dependent function is proposed for the description of loss factor of decay process. Meanwhile, the way to calculate process loss factor with modal frequency, loss factor and amplitude is presented. Process loss factor tends to steady loss factor contributed by the mode with smallest loss factor over time. The accuracy is good enough for traditional decay rate method to estimate steady loss factor when there is only one mode or lots of modes in the frequency band. It is difficult for traditional decay rate method to be used to evaluate steady loss factor in the mid-frequency band where frequency density is not enough. A new method is proposed to estimate steady loss factor through separating the smallest modal loss factor components in the frequency band with time decay curve step by step according to the different decay characteristics. Simulation and experimental results indicate that the proposed method can cover the shortage of traditional decay rate method of estimating the steady loss factor in mid-frequency band.