Estimation of the Mass, Stiffness and Damping Matrices in the Frequency- Domain by Nonlinear Regression Techniques

Resumo

A frequency-domain method for estimating the mass, stiffness and damping matrices of the mass-spring-
dumper model is presented. The developed estimation is based on the Least Squares Method in the Nonlinear

Regression Approach, where the input data are the elements of the Complex Frequency Response Inverse Matrix
and frequencies, which were chosen randomly from the range of frequencies. The amount of frequencies for
an accurate result is described in this work. It is shown that each element of the mass, stiffness and damping
matrices can be estimated independently, using the corresponding element of the Complex Frequency Response
Inverse Matrix, when the nonlinear regression is adopted properly. Although the method is developed for viscous
damping, it can be generalized for other types of damping, material or hysteresis, for example. Three examples are
employed in order to illustrate the applicability of the proposed method and the results are quite accurate.