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Operational modal analysis (OMA) is a procedure that allows the identification of the modal parameters of a structure using measured responses to unknown excitation. OMA techniques are based on the assumption that the input to the structure is stationary white noise. One of the OMA techniques, which is based on the assumption of a zero mean Gaussian white noise excitation, is the random decrement (RD) technique. In many practical cases, however, periodic excitation is often present in addition to the white noise. In this study, a method based on the concept of RD transformation is proposed to extract the response of a structure to the random input from the measured response that is due to both random and periodic excitations. Applying the RD method to the extracted random response, RD signatures were estimated. Modal parameters were estimated from RD signatures using the Ibrahim time domain algorithm. It is assumed that the period of the periodic excitation is known a priori. To verify the applicability of the method, a numerical simulation of a discrete two-degrees-of-freedom (DOF) dynamic system with a viscous damping is carried out. The results of this method were also compared with the results obtained from the enhanced frequency domain decomposition method. The efficiency of the proposed method, in the cases where the frequencies of harmonic components of periodic excitation are located at the natural frequencies of the system, is also evaluated.

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This paper deals with the performance analysis of a vibration-isolation system for Michelangelo Buonarroti's famous Ronadanini Pietà statue based on the monitoring and analysis of vibration signals. A tuned mass-damper-inerter is introduced in order to increase the effectiveness of the isolator in the horizontal direction. Specifically, a multi-degree-of-freedom (MDOF) model for the system, including non-linear terms, is proposed. The monitoring data of the structure inside the museum were utilized to update the MDOF model of this structure. Then, the effect of different parameters was analysed, and some modifications proposed to enhance the efficiency of the isolation system in its working condition. A combination of tuned mass-dampers (TMD) with an inerter is proposed to attain a considerable increase in the performance of the isolation system based on the main feature of the tuned mass-damper-inerter (TMDI), which can apply high apparent mass to a system without adding considerable real mass to the original system. Various performance functions are used to illustrate the efficiency of the proposed TMDI. It is shown that a significant effect of this passive method is to reduce the level of vibration in the updated model of this sensitive and valuable object.