• Structural Engineering and Mechanics
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• v.74 no.4
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• pp.471-479
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• 2020

This paper aims to study the effect of the elastic nonlocality on the transient waves in a two-dimensional thermoelastic medium influenced by thermal loading due to the laser pulse. The bounding plane surface is heated by a non-Gaussian laser beam. The problem is discussed under the Eringen's nonlocal elasticity model and the Green-Naghdi (G-N) theory with and without energy dissipation. The normal mode analysis method is used to get the exact expressions for the physical quantities which illustrated graphically by comparison and discussion. The effects of nonlocality and different values of time on the displacement, the stresses, and the temperature were made numerically. All the computed results obtained have been depicted graphically and explained.

• Journal of The Korean Astronomical Society
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• v.19 no.2
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• pp.91-107
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• 1986

Making use of our extended version of $\ddot{O}pik's$ convection theory, we have calculated magnetic cycle periods of the sun and late type stars by using Parker's dynamo theory, where we have included the non-linear effect. We presented a relationship between the computed cycle period and spectral type to analyze observed magnetic activities of the late type stars and long-term luminosity variations. It is found that (1) the stellar magentic-cycle period increases towards the later spectral type, (2) the rapid rotation facilitates the activity-related luminosity variation of stars later than about K5, (3) differential rotation plays a critical role in determining the magnetic activity-cycle period, and (4) the non-local effect should be taken into account in order to understand the observed long-term luminosity variations.

• Journal of Advanced Marine Engineering and Technology
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• v.29 no.7
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• pp.779-784
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• 2005

This paper presents the theory of similarity transformations applied to the momentum and energy equations for laminar, forced, external boundary layer flow over a horizontal flat plate which leads to a set of non-linear, ordinary differential equations of phase change material slurry(PCM Slurry). The momentum and energy equation set numerically to obtain the non-dimensional velocity and temperature profiles in a laminar boundary layer are solved. The heat transfer characteristics of PCM slurry was numerically investigated with similar method. It is clarified that the similar solution method of Newtonian fluid can be used reasonably this type of PCM slurry which has low concentration. The data of local wall heat flux and convective heat transfer coefficient of PCM slurry are higher than those of water more than 150$\~$200$\%$, approximately.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.21-59
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• 2020

Let L_K denote the hypothetical automorphic Langlands group of a number field K. In our recent study, we briefly introduced a certain unconditional non-commutative topological group ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$, called the Weil-Arthur idèle group of K, which, assuming the existence of L_K, comes equipped with a natural topological group homomorphism $NR{\frac{\varphi}{K}^{Langlands}}$ : ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ → L_K that we called the "Langlands form" of the global nonabelian norm-residue symbol of K. In this work, we present a detailed construction of ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ and $NR{\frac{\varphi}{K}^{Langlands}}$ : ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ → L_K, and discuss their basic properties.

• Advances in nano research
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• v.16 no.2
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• pp.141-154
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• 2024

This study aims to develop explicit models to investigate thermo-mechanical interactions in moving nanobeams. These models aim to capture the small-scale effects that arise in continuous mechanical systems. Assumptions are made based on the Euler-Bernoulli beam concept and the fractional Zener beam-matter model. The viscoelastic material law can be formulated using the fractional Caputo derivative. The non-local Eringen model and the two-phase delayed heat transfer theory are also taken into account. By comparing the numerical results to those obtained using conventional heat transfer models, it becomes evident that non-localization, fractional derivatives and dual-phase delays influence the magnitude of thermally induced physical fields. The results validate the significant role of the damping coefficient in the system's stability, which is further dependent on the values of relaxation stiffness and fractional order.

• Structural Engineering and Mechanics
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• v.87 no.6
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• pp.529-540
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• 2023

A novel laminated-hybrid-composite-beam (LHCB) of glass-epoxy infused with flyash and graphene is constructed for this study. The conventional mixture-rule and constitutive-relationship are modified to incorporate filler and lamina orientation. Eringen's non-local-theory is used to include the filler effect. Hamilton's principle based on fifth-order-layer-wise-shear-deformation-theory is applied to formulate the equation of motion. The analogous shear-spring-models for LHCB with multiple-cracks are employed in finite-element-analysis (FEA). Modal-experimentations are conducted (B&K-analyser) and the findings are compared with theoretical and FEA results. In terms of dimensionless relative-natural-frequencies (RNF), the dynamic-response in cantilevered support is investigated for various relative-crack-severities (RCSs) and relative-crack-positions (RCPs). The increase of RCS increases local-flexibility in LHCB thus reductions in RNFs are observed. RCP is found to play an important role, cracks present near the end-support cause an abrupt drop in RNFs. Further, multiple cracks are observed to enhance the nonlinearity of LHCB strength. Introduction of the first to third crack in an intact LHCB results drop of RNFs by 8%, 10%, and 11.5% correspondingly. Also, it is demonstrated that the RNF varies because of the lamina-orientation, and filler addition. For 0° lamina-orientation the RNF is maximum. Similarly, it is studied that the addition of graphene reduces weight and increases the stiffness of LHCB in contrast to the addition of flyash. Additionally, the response of LHCB to moving mass is accessed by appropriately modifying the numerical programs, and it is noted that the successive introduction of the first to ninth crack results in an approximately 40% to 120% increase in the dynamic-amplitude-ratio.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.916-919
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• 2004

The monopole theory has long been used to model air-pumped effect from the elastic cavities in car tire. This approach models the change of an air as a piston moving backward and forward on a spring and equates local air movements exactly with the volume changes of the system. Thus, the monopole theory has a restricted domain of applicability due to the usual assumption of a small amplitude acoustic wave equation and acoustic monopole theory. This paper describes an approach to predict the air-pumping noise of a car ave with CFD/Kirchhoff integral method. The type groove is simply modeled as piston-cavity-sliding door geometry and with the aid of CFD technique flow properties in the groove of rolling car tyre are acquired. And these unsteady flow data are used as a air-pumping source in the next Cm calculation of full tyre-road geometry. Acoustic far field is predicted from Kirchhoff integral method by using unsteady flow data in space and time, which is provided by the CFD calculation of full tyre-road domain. This approach can cover the non-linearity of acoustic monopole theory with the aid of using Non-linear governing equation in CFD calculation. The method proposed in this paper is applied to the prediction of air-pumping noise of modeled car tyre and the predicted results are qualitatively compared with the experimental data.

• Journal of the Earthquake Engineering Society of Korea
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• v.26 no.6
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• pp.237-246
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• 2022

Based on the random-vibration-theory methodology, dynamic responses of nuclear facilities subjected to obliquely incidental and incoherent earthquake ground motions are calculated. The spectral power density functions of the 6-degree-of-freedom motions of a rigid foundation due to the incoherent ground motions are obtained with the local wave scattering and wave passage effects taken into consideration. The spectral power density function for the pseudo-acceleration of equipment installed on a structural floor is derived. The spectral acceleration of the equipment or the in-structure response spectrum is then estimated using the peak factors of random vibration. The approach is applied to nuclear power plant structures installed on half-spaces, and the reduction of high-frequency earthquake responses due to obliquely incident incoherent earthquake ground motions is examined. The influences of local wave scattering and wave passage effects are investigated for three half-spaces with different shear-wave velocities. When the shear-wave velocity is sufficiently large like hard rock, the local wave scattering significantly affects the reduction of the earthquake responses. In the cases of rock or soft rock, the earthquake responses of structures are further affected by the incident angles of seismic waves or the wave passage effects.

• Computers and Concrete
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• v.12 no.5
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• pp.585-612
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• 2013

The paper presents quasi-static numerical simulations of the behaviour of short reinforced concrete beams without shear reinforcement under mixed shear-tension failure using the FEM and four various constitutive continuum models for concrete. First, an isotropic elasto-plastic model with a Drucker-Prager criterion defined in compression and with a Rankine criterion defined in tension was used. Next, an anisotropic smeared crack and isotropic damage model were applied. Finally, an elasto-plastic-damage model was used. To ensure mesh-independent FE results, to describe strain localization in concrete and to capture a deterministic size effect, all models were enhanced in a softening regime by a characteristic length of micro-structure by means of a non-local theory. Bond-slip between concrete and reinforcement was considered. The numerical results were directly compared with the corresponding laboratory tests performed by Walraven and Lehwalter (1994). The advantages and disadvantages of enhanced models to model the reinforced concrete behaviour were outlined.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.51-62
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• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.