Updating vibration response for a scale model with dissimilar damping ratios

During dynamic similitude model experiments, it is generally difficult to assure the damping ratio of scale model is same with its original structure. This problem results in that the measured dynamic response of scaled model with damping errors cannot be used directly to predict the original structure's response. An updating method of the time history response for dynamic similitude models with dissimilar damping ratios is proposed to solve the problem. It is assumed that the practical and ideal scaled models' damping can be expressed as classical damping model and then the updating equations are deduced from the relationship between the practical and ideal scaled models' vibration equations. These updating equations show that the calculation of the updating value can be transformed as a dynamic response solution of the ideal scale model forced by an equivalent additional exciting force. Considering that the response measurement points in the realistic experiment are usually limited, a model reduced order method is proposed to reconstruct the responses of those non-measured points. The proposed updating method just need to know modal damping ratios, mass and stiffuess matrixes of the original structure and practical scaled model, and these conditions are easy to be satisfied. Finally, this updating method is used to update the dynamic response of a scaled model of fighter's wing beam structure. Updating results show that the after-updated displacement power spectrum density and root mean square values are consistent with practical measured responses, which verifies the feasibility and validity of the proposed updating method.