Constructing Second-Order Models of Mechanical Systems from Identified State Space Realizations. Part II: Numerical Investigations

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Abstract
This paper presents various numerical investigations about obtaining physical parameters of second-order mechanical systems using the algorithms that were investigated in detail in the first part of this study. To discuss in detail the computational aspects and the limitations of each of these algorithms, the first example presented is the identification of the physical parameters of a three-degrees-of-freedom (3-DOF) system. It is shown that when the input/output data used in the identification is noise free, then each of the methodologies can exactly retrieve the second-order coefficient matrices, provided that the sensor/actuator requirements imposed by each of them are satisfied accordingly. To investigate the effects of noisy data on the identified second-order parameters, Monte Carlo simulations are performed on the 3-DOF system at different noise-to-signal ratios, and the results show that the three algorithms perform quite satisfactorily. The analysis is then extended to a 120-DOF, three-dimensional structural system, and in this part of the presentation issues such as modal truncation, insufficient instrumentation, and alternative colocation requirements are discussed. The last section of the paper is devoted to a detailed evaluation of the performance of each of the algorithms discussed in this work.

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