• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.161-169
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• 2017

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler-Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

• Steel and Composite Structures
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• v.26 no.6
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• Ocean and Polar Research
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• v.25 no.4
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• pp.437-446
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• 2003

Field measurements of directional waves were carried out during the summer of 2002 at two coastal sites in water of finite depth. A couple of general purpose instruments were used employing acoustic Doppler technology. The aim of the study was to investigate the spatial behavior of the directional movement of waves as they come ashore. In total,74 tests were carried out during which sea states of low to moderate intensity were recorded. A great number of these runs displayed bimodal characteristics of the spreading function at high frequencies. It was found that in general, the frequency-integrated directional width tends to broaden as the water shoals and when refraction effects are negligible. This is attributed to wave-wave interactions that become pronounced in shallow water. The same directional width showed, also, a tendency to increase with increasing peak frequency of the sea state spectrum. The behavior of the kurtosis of the spreading function was also examined. It was found that for higher frequencies this index tends to increase in wave spectra above a certain sea severity threshold.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1993.11a
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• pp.39-42
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• 1993

In this paper, we performed theoretical simulation for directional coupler using BPM program. Simulation results shored that the optimum optical waveguide refractive index between the guides were 3$\mu\textrm{m}$. Using the parameters of n$_1$=2.25, n$_2$=2.25, n$_3$=2.2, gap=3$\mu\textrm{m}$, W= 30$\mu\textrm{m}$, $\Delta$z=0.l$\mu\textrm{m}$, λ=1.5$\mu\textrm{m}$, we decided other design parameters. When we applied 40[V] in the optimum condition of the directional coupling effect, we concluded the refractive index variation of 0.001.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2000.05a
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• pp.156-159
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• 2000

A new analysis method of Tap-Off for CATV, DBS, CS systems was proposed and investigated by using 4-port and Lport equivalent circuits. As an analysis method the even$.$odd-mode theory for a symmetrical coupled-line directional coupler was introduced, and then it was applied to transformer type directional couple By comparing the results of simulation and measurement, the validity of the proposed analysis method was confirmed. Furthermore, the Tap-off has been broadened from 5 MHz to 4,000 MHz by adopting the propose theory.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.23 no.7
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• pp.1764-1769
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• 1998

The FE-BI (finite element- boundary integral) method is used for the characterization of an arbitrary-shaped multiaperture-coupled directional coupler between two retangular waveguides crossing with an arbitrary angle. The method is shown to be much more effective than the ordinary FEM for the structures under consideration. the computation time is compared with that of the ordinary FEM. The results of other papers for Moreno coupler are compared with the theoretical prediction and a good agreement is obtained.

• Advances in nano research
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• v.12 no.3
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• pp.281-290
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• 2022

In the current research, the thermal buckling characteristics of the bi-directional functionally graded nano-scale tapered beam on the basis of a couple of nonlocal Eringen and classical beam theories are scrutinized. The nonlocal governing equation and associated nonlocal boundary conditions are constructed using the conservation energy principle, and the resulting equations are solved using the generalized differential quadrature method (GDQM). The mechanical characteristics of the produced material are altered along both the beam length and thickness direction, indicating that it is a two-dimensional functionally graded material (2D-FGM). It is thought that the nanostructures are defective because to the presence of porosity voids. Finally, the obtained results are used to design small-scale sensors and make an excellent panorama of developing the production of nanostructures.

• Advances in nano research
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• v.8 no.2
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• pp.115-134
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• 2020

In this paper, the free vibrations analysis of the nanoplates made of three-directional functionally graded material (TDFGM) with small scale effects is presented. To study the small-scale effects on natural frequency, modified strain gradient theory (MSGT) has been used. Material properties of the nanoplate follow an arbitrary function that changes in three directions along the length, width and thickness of the plate. The equilibrium equations and boundary conditions of nanoplate are obtained using the Hamilton's principle. The generalized differential quadrature method (GDQM) is used to solve the governing equations and different boundary conditions for obtaining the natural frequency of nanoplate made of three-directional functionally graded material. The present model can be transformed into a couple stress plate model or a classic plate model if two or all parameters of the length scales set to zero. Finally, numerical results are presented to study the small-scale effect and heterogeneity constants and the aspect ratio with different boundary conditions on the free vibrations of nanoplates. To the best of the researchers' knowledge, in the literature, there is no study carried out into MSGT for free vibration analysis of FGM nanoplate with arbitrary functions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.7
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• pp.680-695
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• 1991

In this paper, the conditions on the number of required copies of a self-routing network with and without extra stages in back-to-back manner are presented respectively for a nonblocking $Multi-Log_2N$ multiconnection network. Actually the obained results hold regardless of connection patterns, i.e., whether a network deploys on-to-one connections or multiconnections. Thus open problems on the nonblocking condition for a multi $Multi-Log_2N$ multiconnection network are solved. Interestingly some of the given formulas comprise the Benes network and the Canto network as a special case repectively. A novel switching system architecture deploying a distributed calls-distribution algorithm is provided to design a nonblocking $Multi-Log_2N$ photonic switching network using a directional coupler. And a directional couplex based call holding demultiplexer is introduced to hold a call until blocking disappears in a switching network and let it enter to a network, provided that the number of switching networks is less than that of required switching networks for a nonblocking $Multi-Log_2N$ network.

• Steel and Composite Structures
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• v.52 no.5
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• pp.501-513
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• 2024

Two-directional functionally graded materials (2D-FGMs) show extraordinary physical properties which makes them ideal candidates for designing smart micro-switches. Pull-in instability is one of the most critical challenges in the design of electrostatically-actuated microswitches. The present research aims to bridge the gap in the static pull-in instability analysis of microswitches composed of 2D-FGM. Euler-Bernoulli beam theory with geometrical nonlinearity effect (i.e. von-Karman nonlinearity) in conjunction with the modified couple stress theory (MCST) are employed for mathematical formulation. The micro-switch is subjected to electrostatic actuation with fringing field effect and Casimir force. Hamilton's principle is utilized to derive the governing equations of the system and corresponding boundary conditions. Due to the extreme nonlinear coupling of the governing equations and boundary conditions as well as the existence of terms with variable coefficients, it was difficult to solve the obtained equations analytically. Therefore, differential quadrature method (DQM) is hired to discretize the obtained nonlinear coupled equations and non-classical boundary conditions. The result is a system of nonlinear coupled algebraic equations, which are solved via Newton-Raphson method. A parametric study is then implemented for clamped-clamped and cantilever switches to explore the static pull-in response of the system. The influences of the FG indexes in two directions, length scale parameter, and initial gap are discussed in detail.