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Modal identification is a key step in modal analysis. It enables the researcher to extract modal parameters, such as natural frequency, amplitude, and damping from a given structure. There are a considerable number of techniques in the state of the art aiming to address this problem, where multi-mode approaches arise as an appealing choice due to their ability to deal with mode coupling. This tutorial paper focuses on the complex-curve fitting technique, originally conceived for an application distinct from modal analysis. It aims at guiding other researchers by providing a tutorial-like and in-depth analysis of this important method, associated with a nonlinear weighting procedure for improved precision. Additionally, this paper fills a gap on the original technique, which is limited to the ratio of two polynomials, by proposing an automatic parameter extraction technique. The original and improved methods are applied on both simulated and experimental data, highlighting the effectiveness of the proposed changes. The proposed procedure is also compared with the rational fraction polynomial method. [ABSTRACT FROM AUTHOR]

In this paper, we give some extensions for Mortenson's identities in series with the Bell polynomial using the partial fraction decomposition. As applications, we obtain some combinatorial identities involving the harmonic numbers. [ABSTRACT FROM AUTHOR]

Recently, Melham computed some finite sums in which the denominator of the summand includes products of ‘sine’ or ‘cosine’. In this paper, generalizations of the sums, which he studied in 2016, are presented, by allowing arbitrary factors in the denominator of the summand. Our approach uses the elementary technique of partial fraction decomposition. Furthermore, some of the sums, which he studied in 2017, are treated in the same style. [ABSTRACT FROM AUTHOR]

Recently Melham [1] gives closed formulæ for certain finite reciprocal sums. In this paper, we present a different approach to compute these sums in closed form. Our approach is straight-forward and simple. First we convert the sums in q-notation, then use partial fraction decomposition and telescoping to derive closed formulæ. [ABSTRACT FROM AUTHOR]