An expansion technique for the estimation of unmeasured rotational frequency response functions

Abstract

Often numerical and measured data are not compatible both in type and number of degrees of freedom (DOFs). While finite element modelling can provide a full data set, the conventional vibration testing is usually limited, allowing only the measurement of part of the receptance matrix, namely the responses at translational DOFs due to applied forces. Therefore, the experimental frequency response function (FRF) matrix usually does not contain any information regarding rotational DOFs, especially those related to pure moment excitations. In this work, the authors propose a process that starts with a set of translational FRFs, conventionally measured, and expand it to estimate the entire receptance matrix. A generalized version of Kidder’s method, together with the principle of reciprocity, is used in the expansion process, which has the advantage of avoiding modal identification. The accuracy of the estimated FRFs is assessed by comparing the results with those of experimental data collected at a simple structure. It is worth mentioning that the use of a T-block is considered to obtain experimental rotational FRFs with the simple purpose of accuracy assessment.