• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.656-661
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• 2005

An optimization formulation of unconstrained damping treatment on beams is proposed to minimize vibration responses using a numerical search method. The fractional derivative model is combined with RUK's equivalent stiffness approach in order to represent nonlinearity of complex modulus of damping materials with frequency and temperature. The loss factors of partially covered unconstrained beam are calculated by the modal strain energy method. Vibration responses are calculated by using the modal superposition method, and of which design sensitivity formula with respect to damping layout is derived analytically. Plugging the sensitivity formula into optimization software, we can determine optimally damping treatment region that gives minimum forced response under a given boundary condition. A numerical example shows that the proposed method is very effective in minimizing vibration responses with unconstrained damping layer treatment.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.805-812
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• 2006

An optimization formulation is proposed to minimize sound pressures in a two-dimensional cavity by controlling the attachment area of unconstrained damping materials. For the analysis of structural-acoustic systems, a hybrid approach that uses finite elements for structures and boundary elements for cavity is adopted. Four-parameter fractional derivative model is used to accurately represent dynamic characteristics oJ the viscoelastic materials with frequency and temperature. Optimal layouts of the unconstrained damping layer on structural wall of cavity are identified according to temperatures and the amount of damping material by using a numerical search algorithm.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.7 s.100
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• pp.829-835
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• 2005

An optimization formulation of unconstrained damping treatment on beam is proposed to minimize vibration responses using a numerical search method. The fractional derivative model is combined with RUK's equivalent stiffness approach in order to represent nonlinearity of complex modulus of damping materials with frequency and temperature. Vibration responses are calculated by using the modal superposition principle, and of which design sensitivity formula with respect to damping layout is derived analytically. Plugging the sensitivity formula into optimization software, we can determine optimally damping treatment region that gives minimum forced response under a given boundary condition. A numerical example shows that the proposed method is very effective in suppressing nitration responses by means of unconstrained damping layer treatment.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.12
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• pp.938-946
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• 2003

Length of an unconstrained viscoelastic damping layer on beams is determined to maximizeloss factor using a numerical search method. The fractional derivative model can describe damping characteristics of viscoelastic damping materials accurately, and is used to represent nonlinearity of complex modulus with frequencies and temperatures. Equivalent flexural rigidity of the unconstrained beam is obtained using Ross, Ungar, Kelvin[RUK] equation. The loss factors of partially covered unconstrained beam are calculated by a modal strain energy method. Optimal lengths of the unconstrained viscoelastic damping layer of beams are identified with ambient temperatures and thickness ratios of beam and damping layer by using a finite-difference-based steepest descent method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.665-671
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• 2003

Length of an unconstrained viscoelastic damping layer on beams is determined to maximize loss factor using a numerical search method. The fractional derivative model can describe damping characteristics of the viscoelastic damping material, and is used to represent nonlinearity of complex modulus with frequencies and temperatures. Equivalent flexural rigidity of the unconstrained beam is obtained using Ross, Ungar, Kerwin(RUK) equation. The loss factors of partially covered unconstrained beam are calculated by a modal strain energy method. Optimal lengths of the unconstrained viscoelastic damping layer of beams are obtained with respect to ambient temperatures and thickness ratios of beam and damping layer.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.12 s.255
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• pp.1581-1587
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• 2006

An optimization formulation is proposed to minimize sound pressures in a two-dimensional cavity by controlling the attachment area of viscoelastic unconstrained damping materials. For the analysis of structural- acoustic systems, a hybrid approach that uses finite elements for structures and boundary elements for cavity is adopted. Four-parameter fractional derivative model is used to accurately represent dynamic characteristics of the viscoelastic materials with respect to frequency and temperature. Optimal layouts of the unconstrained damping layer on structural wall of cavity are identified according to temperatures and the amount of damping material by using a numerical search algorithm.

• Structural Engineering and Mechanics
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• v.41 no.1
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• pp.113-137
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• 2012

Frame structures with viscoelastic (VE) dampers mounted on them are considered in this paper. It is the aim of this paper to compare the dynamic characteristics of frame structures with VE dampers when the dampers are modelled by means of different models. The classical rheological models, the model with the fractional order derivative, and the complex modulus model are used. A relatively large structure with VE dampers is considered in order to make the results of comparison more representative. The formulae for dissipation energy are derived. The finite element method is used to derive the equations of motion of the structure with dampers and such equations are written in terms of both physical and state-space variables. The solution to motion equations in the frequency domain is given and the dynamic properties of the structure with VE dampers are determined as a solution to the appropriately defined eigenvalue problem. Several conclusions concerning the applicability of a family of models of VE dampers are formulated on the basis of results of an extensive numerical analysis.

• Steel and Composite Structures
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• v.48 no.6
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• pp.611-623
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• 2023

This work considered an optimal control formulation in the sense of Caputo derivatives. The optimality of the fractional optimal control problem. The tumor immune interaction in fractional form provides an excellent tool for the description of memory and hereditary properties of inter and intra cells. So the interaction between effector-cells, tumor cells and are modeled by using the definition of Caputo fractional order derivative that provides the system with long-time memory and gives extra degree of freedom. In addiltion, existence and local stability of fixed points are investigated for discrete model. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Our technique likewise allows the advancement of results, such as return time to baseline that are unrealistic with current model solvers.

• Steel and Composite Structures
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• v.24 no.3
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• pp.297-307
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• 2017

A unified mathematical model of phase-lag Green-Naghdi magneto-thermoelasticty theories based on fractional derivative heat transfer for perfectly conducting media in the presence of a constant magnetic field is given. The GN theories as well as the theories of coupled and of generalized magneto-thermoelasticity with thermal relaxation follow as limit cases. The resulting nondimensional coupled equations together with the Laplace transforms techniques are applied to a half space, which is assumed to be traction free and subjected to a thermal shock that is a function of time. The inverse transforms are obtained by using a numerical method based on Fourier expansion techniques. The predictions of the theory are discussed and compared with those for the generalized theory of magneto-thermoelasticity with one relaxation time. The effects of Alfven velocity and the fractional order parameter on copper-like material are discussed in different types of GN theories.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.1
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• pp.53-60
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• 2012

To reduce the vibration in industrial settings, the viscous fluid dampers have been widely used. Since the damper shows a viscoelastic behavior, many methods to predict the behavior have been investigated. But the methods did not consider a change of damper size that is important factor for practical design engineer. In this study, to predict a change of damper ability with respect to a change of damper size, the dynamic experiment were conducted with fixed aspect ratio and gap. The damping coefficient at zero frequency was computed through theoretical and experiment approach in order to fit the experimental results using fractional derivative Maxwell model.