• Structural Engineering and Mechanics
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• v.86 no.1
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• pp.1-16
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• 2023

The free vibration of temperature-dependent functionally graded plates (FGPs) resting on a viscoelastic foundation is investigated in this paper using a newly developed simple first-order shear deformation theory (FSDT). Unlike other first order shear deformation (FSDT) theories, the proposed model contains only four variables' unknowns in which the transverse shear stress and strain follow a parabolic distribution along the plates' thickness, and they vanish at the top and bottom surfaces of the plate by considering a new shape function. For this reason, the present theory requires no shear correction factor. Linear steady-state thermal loads and power-law material properties are supposed to be graded across the plate's thickness. Uniform, linear, non-linear, and sinusoidal thermal rises are applied at the two surfaces for simply supported FGP. Hamilton's principle and Navier's approach are utilized to develop motion equations and analytical solutions. The developed theory shows progress in predicting the frequencies of temperature-dependent FGP. Numerical research is conducted to explain the effect of the power law index, temperature fields, and damping coefficient on the dynamic behavior of temperature-dependent FGPs. It can be concluded that the equation and transformation of the proposed model are as simple as the FSDT.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.04a
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• pp.1-6
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• 2003

In injection molding of an optical disk, a toric lens, etc., their performance depends on the transcription preciseness of fine surface structure of a mold. However, transcription behavior has not been made clear yet, because transcription is made in very short time and the structure is very small. In this paper, transcription properties have been examined, by using V-grooves of various sizes. machined on mold surfaces, and the following results are obtained. (1) Transcription properties have been made clear experimentally and it was found that the mold temperature $T_D$ makes great influence on the transcription property and that compression applying time $t_c$ should be taken more than 2.0s for fine transcription. (2) A mechanical model of transcription process, in consideration with strain recovery due to viscoelastic property of polymer. is proposed. (3) Simulation results agree with experimental ones fairly well. It means that the transcription model is useful for estimation of transcription property in advance of an actual. injection molding.

• Preventive Nutrition and Food Science
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• v.22 no.1
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• pp.56-61
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• 2017

Rheological properties of waxy barley flour (WBF) dispersions mixed with various gums (carboxyl methyl celluleose, guar gum, gum arabic, konjac gum, locust bean gum, tara gum, and xanthan gum) at different gum concentrations were examined in steady and dynamic shear. WBF-gum mixture samples showed a clear trend of shear-thinning behavior and had a non-Newtonian nature with yield stress. Rheological tests indicated that the flow and dynamic rheological parameter (apparent viscosity, consistency index, yield stress, storage modulus, and loss modulus) values of WBF dispersions mixed with gums, except for gum arabic, were significantly higher than those of WBF with no gum, and also increased with an increase in gum concentration. In particular, konjac gum at 0.6% among other gums showed the highest rheological parameter values. Tan ${\delta}$ values of WBF-xanthan gum mixtures were lower than those of other gums, showing that there is a more pronounced synergistic effect on the elastic properties of WBF in the presence of xanthan gum. Such synergistic effect was hypothesized by considering thermodynamic compatibility between xanthan gum and WBF. These rheological results suggest that in the WBF-gum mixture systems, the addition of gums modified the flow and viscoelastic properties of WBF, and that these modifications were dependent on the type of gum and gum concentration.

• Journal of Mechanical Science and Technology
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• v.20 no.5
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• pp.658-667
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• 2006

Fractional derivative models, which are used to describe the viscoelastic behavior of material, have received considerable attention. Thus it is necessary to put forward the analysis solutions of dynamic systems containing a fractional derivative. Although previously reported such kind of fractional calculus-based constitutive models, it only handles the particularity of rational number in part, has great limitation by reason of only handling with particular rational number field. Simultaneously, the former study has great unreliability by reason of using the complementary error function which can't ensure uniform real number. In this paper, a new approach is proposed for an analytical scheme for dynamic system of a spring-mass-damper system of single-degree of freedom under general forcing conditions, whose damping is described by a fractional derivative of the order $0<{\alpha}<1$ which can be both irrational number and rational number. The new approach combines the fractional Green's function and Laplace transform of fractional derivative. Analytical examples of dynamic system under general forcing conditions obtained by means of this approach verify the feasibility very well with much higher reliability and universality.

• Korea-Australia Rheology Journal
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• v.17 no.3
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• pp.99-110
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• 2005

This work presents results of finite element analysis of isothermal incompressible creeping viscoelastic flows with the tensor-logarithmic formulation of the Leonov model especially for the planar geometry with singular comers in the domain. In the case of 4:1 contraction flow, for all 5 meshes we have obtained solutions over the Deborah number of 100, even though there exists slight decrease of convergence limit as the mesh becomes finer. From this analysis, singular behavior of the comer vortex has been clearly seen and proper interpolation of variables in terms of the logarithmic transformation is demonstrated. Solutions of 4:1:4 contraction/expansion flow are also presented, where there exists 2 singular comers. 5 different types spatial resolutions are also employed, in which convergent solutions are obtained over the Deborah number of 10. Although the convergence limit is rather low in comparison with the result of the contraction flow, the results presented herein seem to be the only numerical outcome available for this flow type. As the flow rate increases, the upstream vortex increases, but the downstream vortex decreases in their size. In addition, peculiar deflection of the streamlines near the exit comer has been found. When the spatial resolution is fine enough and the Deborah number is high, small lip vortex just before the exit comer has been observed. It seems to occur due to abrupt expansion of the elastic liquid through the constriction exit that accompanies sudden relaxation of elastic deformation.

• Korea-Australia Rheology Journal
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• v.20 no.3
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• pp.165-173
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• 2008

Multiple particle tracking microrheology is used to characterize the viscoelastic properties of biomaterial and synthetic polymer gels near the liquid-solid transition. Probe particles are dispersed in the gel precursors, and their dynamics are measured as a function of the extent of reaction during gel formation. We interpret the dynamics using the generalized Stokes-Einstein relationship (GSER), using a form of the GSER that emphasizes the relationship between the probe particle mean-squared displacement and the material creep compliance. We show that long-standing concepts in gel bulk rheology are applicable to microrheological data, including time-cure superposition to identify the gel point and critical scaling exponents, and the power-law behavior of incipient network's viscoelastic response. These experiments provide valuable insight into the rheology, structure, and kinetics of gelling materials, and are especially powerful for studying the weak incipient networks of dilute gelators, as well as scarce materials, due to the small sample size requirements and rapid data acquisition.

• Composites Research
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• v.25 no.1
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• pp.9-13
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• 2012

In this research, biomechanical characteristics of the bone tissue are experimentally investigated. By using specimens of the bovine bone, the mechanical properties are obtained through tension and shear tests. In experiments, non-homogeneous and anisotropic properties with respect to longitudinal and transversal directions are observed. Moreover, the viscoelastic behavior in which modulus and strength properties are dependent on strain rates is analyzed. It is expected that a numerical damage model of the bone be efficiently established based on the results.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.713-722
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• 2020

This article aims to illustrate the damped dynamic responses of layered functionally graded (FG) thick 2D beam under dynamic pulse sinusoidal load by using finite element method, for the first time. To investigate the response of thick beam accurately, two-dimensional plane stress problem is assumed to describe the constitutive behavior of thick beam structure. The material is distributed gradually through the thickness of each layer by generalized power law function. The Kelvin-Voigt viscoelastic constitutive model is exploited to include the material internal damping effect. The governing equations are obtained by using Lagrange's equations and solved by using finite element method with twelve -node 2D plane element. The dynamic equation of motion is solved numerically by Newmark implicit time integration procedure. Numerical studies are presented to illustrate stacking sequence and material gradation index on the displacement-time response of cantilever beam structure. It is found that, the number of waves increases by increasing the graduation distribution parameter. The presented mathematical model is useful in analysis and design of nuclear, marine, vehicle and aerospace structures those manufactured from functionally graded materials (FGM).

• Geomechanics and Engineering
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• v.19 no.1
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• pp.61-70
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• 2019

Yieldable steel ribs have been widely applied in tunnels excavated in rheological rocks. For further understanding the influence of yieldable steel ribs on supporting effect, mechanical behavior of tunnels supported by them in rheological rocks is investigated in this paper. Taking into account the deformation characteristic of yieldable steel ribs, their deformation is divided into three stages. In order to modify the stiffness of yieldable steel ribs in different deformation stages, two stiffness correction factors are introduced in the latter two stages. Viscoelastic analytical solutions for the displacement and pressure in the rock-support interface in each deformation stage are obtained. The reliability of the theoretical analysis is verified by use of numerical simulation. It could be concluded that yieldable steel ribs are able to reduce pressure acting on them without becoming damaged through accommodating the rock deformation. The influence of stiffness correction factor in yielding deformation stage on pressure and displacement could be neglected with it remaining at a low level. Furthermore, there is a linearly descending relationship of pressure with yielding displacement in linear viscoelastic rocks.

• Geomechanics and Engineering
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• v.29 no.1
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• pp.53-63
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• 2022

Simplified analytical solutions are developed for the dynamic analyses of an axially loaded pile foundation embedded in a transverse-isotropic, fluid-filled, poro-visco-elastic soil with rigid substratum. The pile is modeled as a viscoelastic Rayleigh-Love rod, while the surrounding soil is regarded as a transversely isotropic, liquid-saturated, viscoelastic, porous medium of which the mechanical behavior is represented by the Boer's poroelastic media model and the fractional derivative model. Upon the separation of variables, the frequency-domain responses for the impedance function of the pile top, and the vertical displacement and the axial force along the pile shaft are gained. Then by virtue of the convolution theorem and the inverse Fourier transform, the time-domain velocity response of the pile head is derived. The presented solutions are validated, compared to the existing solution, the finite element model (FEM) results, and the field test data. Parametric analyses are made to show the effect of the soil anisotropy and the excitation frequency on the pile-soil dynamic responses.