• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1017-1034
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• 2023

In this paper, we work two different problems. First, we investigate a new class of fractional differential equations involving Caputo sequential derivative with some (e₁, e₂, θ)-periodic conditions. The existence and uniqueness of solutions are proven. The stability of solutions is also discussed. The second part includes studying traveling wave solutions of a conformable fractional Korteweg-de Vries-Burger (KdV Burger) equation through the Tanh method. Graphs of some of the waves are plotted and discussed, and a conclusion follows.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.12 s.117
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• pp.1192-1200
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• 2006

Viscoelastic damping materials are widely used to reduce noise and vibration because of its low cost and easy implementation, for examples, on the body structure of passenger cars, air planes, electric appliances and ships. To design the damped structures, the material property such as elastic modulus and loss factor is essential information. The four-parameter fractional derivative model well describes the dynamic characteristics of the viscoelastic damping materials with respect to both frequency and temperature. However, the identification procedure of the four-parameter is very time-consuming one. In this study a new identification procedure of the four-parameters is proposed by using an FE model and a gradient-based numerical search algorithm. The identification procedure goes two sequential steps to make measured frequency response functions(FRF) coincident with simulated FRFs: the first one is a peak alignment step and the second one is an amplitude adjustment step. A numerical example shows that the proposed method is useful in identifying the viscoelastic material parameters of fractional derivative model.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1235-1242
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• 2006

Viscoelastic damping materials are widely used to reduce noise and vibration because of its low cost and easy implementation, for examples, on the body structure of passenger cars, air planes, electric appliances and ships. To design the damped structures, the material property such as elastic modulus and loss factor is essential information. The four-parameter fractional derivative model well describes the nonlinear dynamic characteristics of the viscoelastic damping materials with respect to both frequency and temperature with fewer parameters than conventional spring-dashpot models. However the identification procedure of the four-parameter is very time-consuming one. An efficient identification procedure of the four-parameters is proposed by using an FE model and a gradient-based numerical search algorithm. The identification procedure goes two sequential steps to make measured FRFs coincident with simulated FRFs: the first one is a peak alignment step and the second one is an amplitude adjustment. A numerical example shows that the proposed method is efficient and robust in identifying the viscoelastic material parameters of fractional derivative model.