• Structural Engineering and Mechanics
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• 제85권3호
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• pp.305-314
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• 2023

The article is about the theoretical analysis of the transmission and reflection of elastic waves through the interface of perfectly connected materials. The solid continuum mediums considered are piezoelectric semiconductors and transversely isotropic in nature. The connection among the mediums is considered in such a way that it holds the continuity property of field variables at the interface. The concept of strain and stress introduced by non-local theory is also being involved to make the study more applicable It is found that, the incident wave results in the generation of four reflected and three transmitted waves including the thermal and elastic waves. The thermal waves generated in the medium are encountered by using the concept of three phase lag heat model along with fractional ordered time thermoelasticity. The results obtained are calculated graphically for a ZnO material with piezoelectric semiconductor properties for medium M₁ and CdSc material with transversely isotropic elastic properties for medium M₂. The influence of fractional order parameter, non-local parameter, and steady carrier density parameter on the amplitude ratios of reflected and refraction waves are studied graphically by MATLAB.

• Advances in nano research
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• 제10권4호
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• pp.359-371
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• 2021

A tumor immune interaction is a main topic of interest in the last couple of decades because majority of human population suffered by tumor, formed by the abnormal growth of cells and is continuously interacted with the immune system. Because of its wide range of applications, many researchers have modeled this tumor immune interaction in the form of ordinary, delay and fractional order differential equations as the majority of biological models have a long range temporal memory. So in the present work, 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 interleukin-2 (IL-2) 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. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Furthermore, existence and local stability of fixed points are investigated for discrete model. Moreover, it is proved that two types of bifurcations such as Neimark-Sacker and flip bifurcations are studied. Finally, numerical examples are presented to support our analytical results.

• Korea-Australia Rheology Journal
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• 제18권2호
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• pp.67-81
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• 2006

Using a strain-controlled rheometer, the dynamic viscoelastic properties of aqueous xanthan gum solutions with different concentrations were measured over a wide range of strain amplitudes and then the linear viscoelastic behavior in small amplitude oscillatory shear flow fields was investigated over a broad range of angular frequencies. In this article, both the strain amplitude and concentration dependencies of dynamic viscoelastic behavior were reported at full length from the experimental data obtained from strain-sweep tests. In addition, the linear viscoelastic behavior was explained in detail and the effects of angular frequency and concentration on this behavior were discussed using the well-known power-law type equations. Finally, a fractional derivative model originally developed by Ma and Barbosa-Canovas (1996) was employed to make a quantitative description of a linear viscoelastic behavior and then the applicability of this model was examined with a brief comment on its limitations. Main findings obtained from this study can be summarized as follows: (1) At strain amplitude range larger than 10%, the storage modulus shows a nonlinear strain-thinning behavior, indicating a decrease in storage modulus as an increase in strain amplitude. (2) At strain amplitude range larger than 80%, the loss modulus exhibits an exceptional nonlinear strain-overshoot behavior, indicating that the loss modulus is first increased up to a certain strain amplitude(${\gamma}_0{\approx}150%$) beyond which followed by a decrease in loss modulus with an increase in strain amplitude. (3) At sufficiently large strain amplitude range (${\gamma}_0>200%$), a viscous behavior becomes superior to an elastic behavior. (4) An ability to flow without fracture at large strain amplitudes is one of the most important differences between typical strong gel systems and concentrated xanthan gum solutions. (5) The linear viscoelastic behavior of concentrated xanthan gum solutions is dominated by an elastic nature rather than a viscous nature and a gel-like structure is present in these systems. (6) As the polymer concentration is increased, xanthan gum solutions become more elastic and can be characterized by a slower relaxation mechanism. (7) Concentrated xanthan gum solutions do not form a chemically cross-linked stable (strong) gel but exhibit a weak gel-like behavior. (8) A fractional derivative model may be an attractive means for predicting a linear viscoelastic behavior of concentrated xanthan gum solutions but classified as a semi-empirical relationship because there exists no real physical meaning for the model parameters.

• 대한수학회논문집
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• 제18권3호
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• pp.449-457
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• 2003

On the setting of the upper half-space of the Euclidean space $R^{n}$, we show that to each weighted harmonic Bergman function $u\;\epsilon\;b^p_{\alpha}$, there corresponds a unique conjugate system ($upsilon$_1,…, $upsilon_{n-1}$) of u satisfying $upsilon_j{\epsilon}\;b^p_{\alpha}$ with an appropriate norm bound.

• Steel and Composite Structures
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• 제45권3호
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• pp.409-423
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• 2022

Nowadays, there is a high demand for great structural implementation and multifunctionality with excellent mechanical properties. The porous structures reinforced by graphene platelets (GPLs) having valuable properties, such as heat resistance, lightweight, and excellent energy absorption, have been considerably used in different engineering implementations. However, stiffness of porous structures reduces significantly, due to the internal cavities, by adding GPLs into porous medium, effective mechanical properties of the porous structure considerably enhance. This paper is relating to vibration analysis of fluidconveying cantilever porous graphene platelet reinforced (GPLR) pipe with fractional viscoelastic model resting on foundations. A dynamical model of cantilever porous GPLR pipes conveying fluid and resting on a foundation is proposed, and the vibration, natural frequencies and primary resonant of such a system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with the fractional viscoelastic model is used to govern the construction relation of nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied to the pipe and the excitation frequency is close to the first natural frequency. The governing equation for transverse motions of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.

• Steel and Composite Structures
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• 제50권2호
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• pp.201-216
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• 2024

This paper is motivated by the lack of studies relating to vibration and nonlinear resonance of fluid-conveying cantilever porous GPLR pipes with fractional viscoelastic model resting on nonlinear foundations. A dynamical model of cantilever porous Graphene Platelet Reinforced (GPLR) pipes conveying fluid and resting on nonlinear foundation is proposed, and the vibration, natural frequencies and primary resonant of such system are explored. The pipe body is considered to be composed of GPLR viscoelastic polymeric pipe with porosity in which Halpin-Tsai scheme in conjunction with fractional viscoelastic model is used to govern the construction relation of the nanocomposite pipe. Three different porosity distributions through the pipe thickness are introduced. The harmonic concentrated force is also applied on pipe and excitation frequency is close to the first natural frequency. The governing equation for transverse motion of the pipe is derived by the Hamilton principle and then discretized by the Galerkin procedure. In order to obtain the frequency-response equation, the differential equation is solved with the assumption of small displacement, damping coefficient, and excitation amplitude by the multiple scale method. A parametric sensitivity analysis is carried out to reveal the influence of different parameters, such as nanocomposite pipe properties, fluid velocity and nonlinear viscoelastic foundation coefficients, on the primary resonance and linear natural frequency. Results indicate that the GPLs weight fraction porosity coefficient, fractional derivative order and the retardation time have substantial influences on the dynamic response of the system.

• Transactions on Electrical and Electronic Materials
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• 제18권5호
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• pp.287-297
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• 2017

Novel power system stabilizers (PSSs) have been proposed to effectively dampen low frequency oscillations (LFOs) in multi-machine power systems and have attracted increasing research interest in recent years. Due to this attention, recently, fractional order controllers (FOCs) have found new applications in power system stability issues. Here, a tilt-integral-derivative power system stabilizer (TID-PSS) is proposed to enhance the dynamic stability of a multi-machine power system by providing additional damping to the LFOs. The TID is an extended version of the classical proportional-integral-derivative (PID) applying fractional calculus. The design of the proposed three-parameter tunable TID-PSS is systematized as a nonlinear time domain optimization problem in which the tunable parameters are adjusted concurrently using a modified group search optimization (MGSO) algorithm. An integral of the time multiplied squared error (ITSE) performance index is considered as the objective function. The proposed stabilizer is simulated in the MATLAB/SIMULINK environment using the FOMCON toolbox and the dynamic performance is evaluated on a 3-machine 6-bus power system. The TID-PSS is compared with both classical PID-PSS (PID-PSS) and conventional PSS (CPSS) using eigenvalue analysis and time domain simulations. Sensitivity analyses are performed to assess the robustness of the proposed controller against large changes in system loading conditions and parameters. The results indicate that the proposed TID-PSS provides the better dynamic performance and robustness compared with the PID-PSS and CPSS.

• Journal of Pharmaceutical Investigation
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• 제41권3호
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• pp.161-171
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• 2011

The objective of the present study is to systematically characterize a linear viscoelastic behavior of petroleum jelly in small amplitude oscillatory shear flow fields correspondent to the rheological ground state. With this aim, using a strain-controlled rheometer, the dynamic viscoelastic properties of commercially available petroleum jelly have been measured at $37^{\circ}C$ (body temperature) over a wide range of angular frequencies at an extremely small strain amplitude of 0.1 %. In this article, the linear viscoelastic behavior was reported in detail and then explained from a structural view-point of petroleum jelly and discussed in depth with respect to the consumer's requirements. Main findings obtained from this study can be summarized as follows : (1) The storage modulus is always greater than the loss modulus over an entire range of angular frequencies studied, meaning that the linear viscoelastic behavior of petroleum jelly is dominated by an elastic nature rather than a viscous nature. (2) Petroleum jelly shows a desirable linear viscoelastic behavior with respect to the consumer's requirements because it is undesirable for the product to flow down from the skin at an initial stage upon contact with the human skin. (3) A fractional derivative model shows an excellent applicability to describe a linear viscoelastic behavior of petroleum jelly. However, this model should be used with a special caution because there exists no physical meaning for the model parameters. (4) A modified form of the Cox-Merz rule gives a good ability to predict the relationship between steady shear flow properties (nonlinear behavior) and dynamic viscoelastic properties (linear behavior) for petroleum jelly.

• 한국전산구조공학회논문집
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• 제24권4호
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• pp.383-389
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• 2011

본 논문에서는 통계적인 방법을 이용하여 점탄성 제진재인 합성고무의 물성에 대한 변동성을 평가하는 방법을 제안하고 측정데이터를 이용하여 합성고무에 대한 평가를 수행하고 합성고무로 이루어진 고무 마운트에 대한 동특성 해석을 수행하였다. 고무 물성의 불확실성 인자로는 외기 온도의 변화와 실험 데이터의 오차 및 점탄성 물질모델의 오차를 고려하였다. 고무는 분수차 미분모델로 표현되었고, 온도의 영향은 비선형 이동계수모델을 도입하여 복소계수로 나타내어 동강성과 감쇠를 표현하였다. 이러한 물성모델을 바탕으로 고무에 대한 물성 실험데이터와 물성계수의 확률밀도함수 사이에 정의된 우도함수를 최대화하는 통계적 보정방법을 이용하여 물성모델의 물질계수들에 대한 변동성을 추정하였다. 합성고무로 이루어진 제진용 고무 마운트에 대하여 유한요소모델을 이용하여 동특성을 계산하였다. 동특성의 계산시 추정된 물성의 통계값을 적용하고 몬테카를로 해석을 통하여 동강성의 변동성을 살펴서 그 변동성이 매우 큼을 확인하였다.

• 한국군사과학기술학회지
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• 제26권3호
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• pp.262-272
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• 2023

A polymer-based mechanical low-pass filter(m-LPF) for high-g accelerometers makes it possible to remove high-frequency transient noises from acceleration signals, thus ensuring repeatable and reliable measurement on high-g acceleration. We establish a prediction model for performance of m-LPF by combining a fundamental vibration model with the fractional derivative standard linear solid(FD SLS) model describing the storage modulus and loss modulus of polymers. Here, the FD SLS model is modified to consider the effect of m-LPF shape factor (i.e., thickness) on storage modulus and loss modulus. The prediction accuracy is verified by comparing the displacement transmissibility(or cut-off frequency) estimated using our model with that measured from 3 kinds of polymers(polysulfide rubber(PSR), silicone rubber(SR), and polydimethylsiloxane(PDMS)). Our findings will contribute a significant growth of m-LPF for high-g accelerometers.