Updating method of the time history response for dynamic similitude models with dissimilar damping ratios

During dynamic similitude model experiments, it is generally difficult to assure the same damping ratio of the scaled model with its original structure. As a result, the measured dynamic response of the scaled model with damping errors cannot be used directly to predict the response of the structural prototype. 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 damping of the actual and ideal scaled models can be expressed as a classical damping model, and then based on the linear superposition principle and modal superposition method, the updating equations to solve the updating value are deduced from the forced vibration equations of the practical and ideal scaled models. These updating equations show that the calculation of the updating value can be transformed into a dynamic response solution of the ideal scaled model forced by an equivalent additional exciting force. Considering that response measurement points in a practical experiment are usually limited, a reduced order modal method is proposed to reconstruct the responses of those non-measured points. For the proposed updating method, just modal damping ratios, mass and stiffness matrices of the structural prototype and the actual scaled model are needed, and these required conditions are easy to satisfy. Finally, this updating method is used to update the dynamic response of a scaled model of a fighter wing beam structure. The updating results show that the updated displacement power spectrum density (PSD) and root mean square (RMS) values are consistent with real measured responses, which verifies the feasibility and validity of the proposed updating method.