• Communications of the Korean Mathematical Society
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• v.30 no.2
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• pp.123-130
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• 2015

The object of the present paper is to study the second order parallel symmetric tensors and Ricci solitons on $(LCS)_n$-manifolds. We found the conditions of Ricci soliton on $(LCS)_n$-manifolds to be shrinking, steady and expanding respectively.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1113-1129
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• 2019

We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.303-319
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• 2019

The aim of the present paper is to study the Eisenhart problems of finding the properties of second order parallel tensors (symmetric and skew-symmetric) on a 3-dimensional LCS-manifold. We also investigate the properties of Ricci solitons, Ricci semisymmetric, locally ${\phi}$-symmetric, ${\eta}$-parallel Ricci tensor and a non-null concircular vector field on $(LCS)_3$-manifolds.

• Smart Structures and Systems
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• v.13 no.2
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• pp.257-280
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• 2014

In this paper, a novel PARAllel FACtor (PARAFAC) decomposition based Blind Source Separation (BSS) algorithm is proposed for modal identification of structures equipped with tuned mass dampers. Tuned mass dampers (TMDs) are extremely effective vibration absorbers in tall flexible structures, but prone to get de-tuned due to accidental changes in structural properties, alteration in operating conditions, and incorrect design forecasts. Presence of closely spaced modes in structures coupled with TMDs renders output-only modal identification difficult. Over the last decade, second-order BSS algorithms have shown significant promise in the area of ambient modal identification. These methods employ joint diagonalization of covariance matrices of measurements to estimate the mixing matrix (mode shape coefficients) and sources (modal responses). Recently, PARAFAC BSS model has evolved as a powerful multi-linear algebra tool for decomposing an $n^{th}$ order tensor into a number of rank-1 tensors. This method is utilized in the context of modal identification in the present study. Covariance matrices of measurements at several lags are used to form a $3^{rd}$ order tensor and then PARAFAC decomposition is employed to obtain the desired number of components, comprising of modal responses and the mixing matrix. The strong uniqueness properties of PARAFAC models enable direct source separation with fine spectral resolution even in cases where the number of sensor observations is less compared to the number of target modes, i.e., the underdetermined case. This capability is exploited to separate closely spaced modes of the TMDs using partial measurements, and subsequently to estimate modal parameters. The proposed method is validated using extensive numerical studies comprising of multi-degree-of-freedom simulation models equipped with TMDs, as well as with an experimental set-up.