A Stochastic Model for the Random Impact Series Method in Modal Testing

Abstract

A novel stochastic model is developed to describe a random series of impacts in modal testing that can be performed manually or by using a specially designed random impact device. The number of the force pulses, representing the impacts, is modeled as a Poisson process with stationary increments. The force pulses are assumed to have an arbitrary, deterministic shape function, and random amplitudes and arrival times. The force signal in a finite time interval is shown to consist of a wide-sense stationary part and two nonstationary parts. The expectation of the force spectrum is obtained from two approaches. The expectations of the average power densities associated with the entire force signal and the stationary part of it are determined and compared. The analytical expressions are validated by numerical solutions for two different types of shape functions. A numerical example is given to illustrate the advantages of the random impact series over a single impact and an impact series with deterministic arrival times of the pulses in estimating the frequency response function. The model developed can be used to describe a random series of pulses in other applications.