Estimation of structural static displacements based on vibration data using known mass perturbation

Abstract

This note presents a new method for conveniently estimating static displacements of a structure based on its vibration data. In the proposed method, structural static displacements can be estimated using a normalized modal flexibility matrix assisted by a known mass perturbation method in order to overcome several shortcomings of existing displacement sensors (e.g., linear variable differential transformers, laser Doppler vibrometer, etc) such as limitations on installation due to surrounding environments and inconvenience to the public during static loading tests. For validating the feasibility of the proposed method, experimental validation was carried out on a simply-supported beam model. In the experimental tests, the vibration data under excitation by wind loads was first measured with eight accelerometers. Then the known masses were added on a specific location on the beam and the measurements were carried out under the same settings as the first experiment. The determination of the changes in modal parameters allows estimation of the scaling constants to obtain mass-normalized mode shapes. Finally, the normalized modal flexibility matrix was calculated by using the mass-normalized mode shapes based on the scaling constants and the displacements were estimated by the normalized modal flexibility matrix. These results were compared with real static displacements estimated from the laser-type displacement sensor. It was found that they matched each other well. Therefore, the proposed method can be an effective alternative to conventional static displacement estimation.