Truncation error analysis on modal flexibility-based deflections: application to mass regular and irregular structures

It is of interest in the fields of vibration-based structural identification and damage detection to analyze the truncation effects introduced on modal flexibility (MF) based deflections that are estimated using only a subset of structural modes. To address this problem, an approach for truncation error analysis on MF-based deflections of structural systems subjected to a generic load is proposed in this paper. The approach is based on the determination of the relative contribution of each mode to the deflection by means of a proposed load participation factor (LPF). This factor, as derived analytically, depends both on the applied load and on the distribution of the structural masses. The validation of the proposed approach was carried out both on numerical models of shear-type frame buildings and on experimental data of a steel frame structure tested under ambient vibrations (i.e. the benchmark study sponsored by the IASC-ASCE Task Group on SHM). In both cases, results show that the LPF factors can give an a priori indication of the truncation effects expected on the MF-based deflections. The relationship between the proposed approach and the approach based on the mass participation factors, introduced by Zhang and Aktan (1998) for the case of uniform load (UL) deflections, is discussed since the two approaches are equal only if a special load, which is a mass proportional load (MPL), is considered. Thus, the application of this MPL load for mass irregular structures is also investigated. Numerical analyses performed both on a shear-type frame building and on a simply-supported beam, showed that for the great majority of the analyzed configurations, the truncation errors on the MF-based deflections due to the MPL are lower compared to those related to the UL.