• 대한수학회논문집
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• 제29권1호
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• pp.205-212
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• 2014

This paper investigates mean square exponential dissipativity of singularly perturbed stochastic delay differential equations. The L-operator delay differential inequality and stochastic analysis technique are used to establish sufficient conditions ensuring the mean square exponential dissipativity of singularly perturbed stochastic delay differential equations for sufficiently small ${\varepsilon}$ > 0. An example is presented to illustrate the efficiency of the obtained results.

• Wind and Structures
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• 제22권1호
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• pp.107-131
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• 2016

The need for a more affordable, reliable, clean and secure energy has led to explorations in non-traditional sources, particularly renewable energies. Wind is one of the cleanest energy sources that plays a significant role in augmenting sustainability. Wind turbines, as energy convertors, are usually tall and slender structures, and depending on their location (inland or offshore), they can be subject to high wind and/or strong wave loadings. These loads can cause severe vibrations with detrimental effects on energy production, structural lifecycle and initial cost. A dissipativity analysis study was carried out to know whether wind turbine towers require damping enhancement or rigidity modifications for vibration suppression. The results suggest that wind turbines are lightly damped structures and damping enhancement is a potential solution for vibration lessening. Accordingly, the paper investigates different damping enhancement techniques for vibration mitigation. The efficacy of tuned mass damper (TMD), tuned liquid column damper (TLCD), tuned sloshing damper (TSD), and viscous damper (VD) to reduce vibrations is investigated. A comparison among these devices, in terms of robustness and effectiveness, is conducted. The VD can reduce both displacement and acceleration responses of the tower, better than other types of dampers, for the same control effort, followed by TMD, TSD, and finally TLCD. Nevertheless, the use of VDs raises concerns about where they should be located in the structure, and their application may require additional design considerations.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.521-535
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• 2023

In this work, some various types of Dissipativity in random dynamical systems are introduced and studied: point, compact, local, bounded and weak. Moreover, the notion of random Levinson center for compactly dissipative random dynamical systems presented and prove some essential results related with this notion.