Mechanical Systems and Signal Processing (1990) 4(S), 393-404 MODAL PA RA M ETER IDENTIFICATION IN THE TIM E DOMAIN FROM A RANDOM EXCITATION FORCE PAULO R. G. KURKA Departamento de Projeto Mecanico, FEM, CJNICAMP, Caixa Postal 6051, CEP 13081, Campinas, Sa’o Paulo, Brazil AND ALAN COWLEY Department of Mechanical Engineering, University of Manchester Institute of Science and Technology, PO Box 88, Manchester M60 1 QD, U.K. (Received 13 March 1989, accepted 8 January 1990) A time domain algorithm for calculating frequencies, damping ratios and modal shape information of a discrete dynamic system is presented. Input and output samples of the system’s dynamic excitation and response signals are used to determine the parameters. The algorithm is based on Prony’s solution to the complex exponential interpolation of the system’s unit impulse response function. The problem of determining resonant fre- quencies of a steel beam is presented to illustrate a practical application of the algorithm. 1. INTRODUCTION Time domain techniques are used for identification of dynamic characteristics of vibrating systems i.e. natural frequencies, damping ratios and mode shapes (or modal vectors). The Prony technique of complex exponential interpolation [l-4] is used for the determina- tion of modal parameters from the freely decaying movement of a system, after an initial disturbance of the same. Such a technique is not able to determine the modal vectors of a vibrating system due to the arbitrary nature of its initial conditions of motion. The autoregressive-moving average approach (ARMA) [5-71 represents a way of calculating natural frequencies, damping ratios and mode shapes of a system in the time domain from the knowledge of its response to an arbitrary excitation. Coefficients of the autoregressive and moving average branches in the ARMA process form the basic set of parameters from which the system’s modal information is derived. A relation between the coefficients of the ARMA approach and the system’s modal parameters is obtained via the application of Z-transform techniques. The present work introduces a method [8] which derives the system’s natural fre- quencies, damping ratios and modal vectors from coefficients of a complex exponential interpolation of the Prony type. A simple linear system of equations is solved prior to the application of Prony’s scheme in order to find the dynamic system’s unit impulse response vector. Coefficients of such a system of equations are taken from samples of the dynamic system’s excitation and response signals. 2. PARAMETRIC REPRESENTATION OF A DYNAMIC SYSTEM The dynamic system under investigation is assumed to have the following rep- resentation: Mii+Ci+Ku=f (1) 393 0888-3270/90/050393+ 12 %03.00/O @ 1990 Academic Press Limited