• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.363-379
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• 2016

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we introduce here the family of the incomplete generalized ${\tau}$-hypergeometric functions $2{\gamma}_1^{\tau}(z)$ and $2{\Gamma}_1^{\tau}(z)$. The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second ${\tau}$-Appell hypergeometric functions ${\Gamma}_2^{{\tau}_1,{\tau}_2}$ and ${\gamma}_2^{{\tau}_1,{\tau}_2}$ of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.2
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• pp.225-235
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• 2001

본 연구는 물리·역학적 특성을 고려한 점탄성 감쇠기의 수치모델에 의한 강뼈대구조물의 지진응답개선에 관해서 조사하고자 한다. 온도변화에 의한 감쇠기 이력거동에 미치는 영향을 고려하기 위하여, 점탄성 감쇠기의 모델은 온도-주기 등가원리와 더불어 개선된 분수도함수법에 기초하여 정식화하였다. 본 감쇠기 모델의 알고리즘을 일반화된 강뼈대구조물의 비선형 동적 해석 프로그램에 추가하였다. 강뼈대구조물에 대한 해석 예를 통하여, 제시된 모델에 의한 점탄성 감쇠기의 지진응답개선에 관한 효과를 확인할 수 있었다.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1951-1967
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• 2017

We aim to introduce a further extension of a family of the extended Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate several interesting properties of the extended function such as its integral representations which provide extensions of various earlier corresponding results of two and one variables, its summation formula, its Mellin-Barnes type contour integral representations, its computational representation and fractional derivative formulas. A multi-parameter extension of the extended Hurwitz-Lerch Zeta function of two variables is also introduced. Relevant connections of certain special cases of the main results presented here with some known identities are pointed out.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.1023-1026
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• 2007

Optimal damping layout of the constrained viscoelastic damping layer on beam is identified with temperatures by using a gradient-based numerical search algorithm. An optimal design problem is defined in order to determine the constrained damping layer configuration. A finite element formulation is introduced to model the constrained damping layer beam. The four-parameter fractional derivative model and the Arrhenius shift factor are used to describe dynamic characteristics of viscoelastic material with respect to frequency and temperature. Frequency-dependent complex-valued eigenvalue problems are solved by using a simple resubstitution algorithm in order to obtain the loss factor of each mode and responses of the structure. The results of the numerical example show that the proposed method can reduce frequency responses of beam at peaks only by reconfiguring the layout of constrained damping layer within a limited weight constraint.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.1136-1140
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• 2001

Viscous fluid damper is used for vibration isolation of piping system, presses, turbo-generator and other heavy industrial equipments, as well as seismic isolation of buildings structure. So dynamic characteristic of viscous fluid damper is very important. This paper presents the result of the study of dynamic characteristic of viscous fluid damper. And the force-displacement relation of the viscous damper is described by experimentally calibrated fractional derivative Maxwell Model. The proposed model is validated by dynamic testing and A good agreement between predicted and experimental results is obtained.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1351-1370
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• 2018

In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2011.04a
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• pp.744-749
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• 2011

Silicon oil in viscous fluid damper has a viscoelastic feature that show stiffness besides damping. These properties depend on frequency and are non-linear. A lot of research has been conducted in order to identify viscoelastic damper with mathematical model. Fractional Derivative Maxwell Model has been widely used, but this model did not explain the effect of damper size change on the damper performance. In this paper, the experimental study was conducted to validate damper's dynamic behaviors when total damper's size is changed while maintaining same aspect ratio and orifice size.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.83-98
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• 2024

In this paper, we investigate the existence and uniqueness of solutions to a new class of integro-differential equation boundary value problems (BVPs) with ㄒ-Hilfer operator. Our problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed points coincide with the solutions to the given problem. Using Banach's and Schauder's fixed point techniques, the uniqueness and existence result for the given problem are demonstrated. The stability results for solutions of the given problem are also discussed. In the end. One example is provided to demonstrate the obtained results

• The KIPS Transactions:PartC
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• v.11C no.3
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• pp.395-400
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• 2004

Being aware of growing needs for wireless communication led to the development of UWB systems, this study proposed an impulse for single band UWB systems which does not count a carrier; analyzed the characteristics and the problems of pulses suggested by the existing poise of the Un system; finally, proposed TDMG(Time Delay Multiple Gaussian) pulse that generates signals of UWB without attenuation of pulse width. The hardware structure of the TDMC pulse for the single band UWB system was modelled after describing the pulse in a mathematical method in an attempt to compare with performances of the existing pulses through computer simulation. The outcome of the test unveiled the fact that each center frequency of the TDMG pulse rose approximately 1GHz, and also each l0dB fractional bandwidth of the TDMG pulse was widened over 1GHz. In the case of derivative, center frequencies of the TDMG pulse rose over 1GHz each. As a consequence, the TDMG pulse appeared to have better quality frequency, satisfying the characteristics of spectrum and the band of frequency recommended by the FCC and decreasing interference with other wireless communication systems.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.6
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• pp.553-562
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• 2013

Vehicle vibrations arise from engine and road surface excitations. The engine mount system of a passenger car sustains the engine weight and insulates the excitation force from the engine system. The dynamic properties of viscoelastic material used for the vehicle engine mounts have large variation due to environmental factors such as environmental temperature and humidity etc. The present study aims to investigate the variability of dynamic characteristics in rubber engine mounts considering both environmental temperature change and material model errors/uncertainty. The engine mounts for a passenger car were modeled using finite element method. Then, the dynamic stiffness variability of the engine mounts were estimated using Monte Carlo simulation method. In order to estimate the variations in the storage and loss moduli of the viscoelastic materials, the material properties of the synthetic rubber were expressed as a fractional-derivative model. Next, in order to simulate the uncertainty propagation of the dynamic stiffness for the engine mounts due to the storage and loss moduli variations, the Monte Carlo simulation was used. The Monte Carlo simulation results showed large variation of the engine-mount stiffness along frequency axis.