A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives

Lin, Rong; Mottershead, John E.; Ng, TP

doi:10.1016/j.ymssp.2019.106536

“…(the explicit derivative 𝜕 2 𝑓 /𝜕 𝑝 𝑖 𝜕 𝑝 𝑗 = 0). The obtained formula (24) allows determining the second-order sensitivities with the use of AVM. Similar to DDM, the matrices on the left side of Eqs.…”

Section: Adjoint Variables Methods (Avm)mentioning

confidence: 99%

A smart fault identification system for ball bearing using simulation-driven vibration analysis

Khaire,

Phalle

2023

Archive of Mechanical Engineering

0

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This paper discusses the different methods used for calculating first-and secondorder sensitivity: the direct differentiation method, the adjoint variables method, and the hybrid method. The solutions obtained allow determining the sensitivity of dynamic characteristics such as eigenvalues and eigenvectors, natural frequencies, and nondimensional damping ratios. The methods were applied for analyzing systems with viscoelastic damping elements, whose behavior can be described by classical and fractional rheological models. However, the derived formulas are general and can also be applied to systems with damping elements described by other models. Their advantage is a compact and easy to code form. The paper also presents a comparison of the computational costs of the discussed methods. The correctness of all the proposed methods has been illustrated with numerical examples.

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“…In [23] the authors used the eigensensitivity method to optimize the damper location in trusses. A comprehensive description of design sensitivity analysis and its applications can be found in [24].…”

Section: Introductionmentioning

confidence: 99%

Studying the thermo-gas-dynamic process in a muzzle brake compensator

Nguyen,

Bui,

Nguyen

et al. 2023

Archive of Mechanical Engineering

1

0

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This paper discusses the different methods used for calculating first-and secondorder sensitivity: the direct differentiation method, the adjoint variables method, and the hybrid method. The solutions obtained allow determining the sensitivity of dynamic characteristics such as eigenvalues and eigenvectors, natural frequencies, and nondimensional damping ratios. The methods were applied for analyzing systems with viscoelastic damping elements, whose behavior can be described by classical and fractional rheological models. However, the derived formulas are general and can also be applied to systems with damping elements described by other models. Their advantage is a compact and easy to code form. The paper also presents a comparison of the computational costs of the discussed methods. The correctness of all the proposed methods has been illustrated with numerical examples.

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“…This is called operational modal analysis or output-only modal analysis. The method is based on the transmissibility function (TF), and several review articles have been reported (Chesne and Deraemaeker, 2013, Yan, et al, 2019, Lin, et al, 2020, Hou and Xia, 2021, Avci, et al, 2021. Methods based on the TF can be broadly divided into Global TF-and Local TF-based methods.…”

Section: Introductionmentioning

confidence: 99%

Structural health monitoring for layered structures using transmissibility functions

Kawamura

¹

,

YAMAGUCHI

²

,

Matsubara

³

et al. 2022

Mechanical Engineering Journal

2

0

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In this study, we proposed a structural health monitoring and diagnostic method for layered structures using the transmissibility function. This method belongs to the primary diagnosis one, and its purpose is to identify the location of abnormality quickly after abnormality detection. It focuses on the following fact. When the ceiling or foundation of the first floor is excited in the horizontal direction, the transmissibility function of the top floor is constructed with only the characteristics of the top floor, and in the case of descending to the lower floor, only the characteristics of the floor of interest are unknown parameters. In the diagnosis of an actual structure, there may be a difference between the actual vibration characteristics and those obtained from the mathematical model. We also proposed a method for predicting the resonance and peak frequencies in an abnormal condition based on the difference between the actual measurement and the mathematical model under a normal condition. First, we considered a three-layered structure as a numerical example and verified the validity of the proposed method. When the method was applied to the three types of abnormal conditions, it was shown that the abnormal diagnosis could be performed correctly. Next, we constructed an experimental model of a three-layered structure, and verified the applicability of the proposed method. We realized three types of abnormal states similar to the numerical examples and showed that correct abnormal diagnosis was possible. As described above, the validity and applicability of the proposed method were clarified.

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A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives

Cited by 54 publications

References 316 publications

A smart fault identification system for ball bearing using simulation-driven vibration analysis

A smart fault identification system for ball bearing using simulation-driven vibration analysis

Studying the thermo-gas-dynamic process in a muzzle brake compensator

Structural health monitoring for layered structures using transmissibility functions

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