• Title/Summary/Keyword: the maximum principle

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Comprehensive study of internal modals interactions: Comparison of various axial nonlinear beam theories

  • Somaye Jamali Shakhlavi;Reza Nazemnezhad
    • Advances in nano research
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    • v.16 no.3
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    • pp.273-288
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    • 2024
  • The geometrical nonlinear vibrations of the gold nanoscale rod are investigated for the first time by considering the internal modals interactions using different nonlinear beam theories. This phenomenon is usually one of the important features of nonlinear vibration systems. For a more detailed analysis, the von-Karman effects, preserving all the nonlinear terms in the strain-displacement relationships of gold nanoscale rods in three displacement directions, are considered to analyze the nonlinear axial vibrations of gold nanoscale rods. It uses highly accurate analytical-numerical solutions for the clamped-clamped and clamped-free boundary conditions of nanoscale gold rods. Also, with the help of Hamilton's principle, the governing equation and boundary conditions are derived based on Eringen's theory. The influence of nonlinear and nonlocal factors on axial vibrations was investigated separately for all three theories: Simple (ST), Rayleigh (RT) and Bishop (BT). Using different theories, the effects of inertia and shear on the internal resonances of gold nanorods were studied and compared in terms of twoto-one and three-to-one internal resonances. As the nonlocal parameter of the gold nanorod increases, the maximum nonlinear amplitude occurs. So, by adding nonlocal effects in a gold nanorod, the internal modal interactions resulting from the unique structure can be enhanced. It is worth noting that shear and inertial analysis have a significant effect on internal modal interactions in gold nanorods.

Dynamic analysis of concrete beams reinforced with Tio2 nano particles under earthquake load

  • Sharifi, Morteza;Kolahchi, Reza;Bidgoli, Mahmood Rabani
    • Wind and Structures
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    • v.26 no.1
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    • pp.1-9
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    • 2018
  • This research studies the dynamic analysis of a concrete column reinforced with titanium dioxide ($TiO_2$) nanoparticles under earthquake load. The effect of nanoparticles accumulation in a region of concrete column is examined using Mori-Tanaka model. The structure is simulated mathematically based on the theory of sinusoidal shear deformation theory (SSDT). By calculating strain-displacement and stress-strain relations, the system energies include potential energy, kinetic energy, and external works are derived. Then, using the Hamilton's principle, the governing equations for the structure are extracted. Using these equations, the response of the concrete column under earthquake load is investigated using the numerical methods of differential quadrature (DQ) and Newark. The purpose of this study is to study the effects of percentage of nanoparticles, nanoparticles agglomeration, geometric parameters and boundary conditions on the dynamic response of the structure. The results indicate that by increasing the volume percent of $TiO_2$ nanoparticles, the maximum dynamic deflection of the structure decreases.

A Study on Treatment Efficiency of Toluene and CO2 using Vortex Cyclones (보텍스 사이클론을 이용한 Toluene과 CO2 처리효율에 관한 연구)

  • 임계규
    • Journal of Korean Society for Atmospheric Environment
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    • v.20 no.4
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    • pp.493-501
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    • 2004
  • The principle of vortex tube and cyclone was introduced to enhance the treatment efficiency of waste air streams containing particulate matters, toluene, and others developed by Hangreen Tech, Ltd. and Hoseo Chemical and Industrial Technology R&D Center. Adsorption, condensation, and/or coagulation could be induced at low temperature zone formed by vortex tube and Joule-Thomson expansion. The pressurized air was introduced at the tangential direction into the cyclone system applied with the coaxial funnel tube. Easily condensible vapors such as toluene. carbon dioxide, and water vapor were adsorbed enforcedly on coagulated or condensed materials which were formed as cores for coagulation or condensation by themselves. These types of coagulation or condensation rates were rapidly promoted as the diameter being growing up. The maximum removal efficiency for carbon dioxide and toluene was achieved to about 87 and 90 percent, respectively. The Joule-Thomson coefficients were increased with the pressure of air injected in the range of the relative humidities between 10% and 30%. An optimum value was observed within the range of the tested temperatures at a fixed pressure. In conclusion. it could be identified that the treatment efficiency would be depended on the pressure of the process air introduced and physical and chemical characteristics of waste air streams containing target materials for a designed system. The final design parameters should be decided depending upon the given system and target materials.

A Study on the Structure of Axial-Symmetric Two-Phase Spray and Flame (축대칭 이류체 분무화염의 구조에 관한 연구)

  • Jung, Bo-Yoon;Ko, Dae-Kwon;Ahn, Soo-Kil
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.24 no.1
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    • pp.36-43
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    • 1988
  • Boilers and diesel engines have many problems because their exhaust particles, i.e., soot have lots of bad influence on environment. And it's spray and flame have fundamentally axial symmetric shape. To investigate the relationship between fuel concentration distribution of spray and soot concentration distribution as well as temperature distribution of flame, we made a axial symmetric two phase spray-flame and analyzed the structure of is. The measuring method is the principle of the light extinction method for the spray-flame and onion peeling model is applied to analyze the radial distribution of fuel and soot concentration. The temperature of flame is measured by ø 0.4mm Pt-Pt.RH 3% thermocouple. The oils for the experiments are diesel oil and 10% water emulsified diesel oil. It was found that the soot concentration becomes higher as it comes near to the center of flame, and the fuel concentration does, too. And the soot concentration level of diesel oil is generally higher than that of the 10% water emulsified fuel. The maximum flame temperature of diesel oil is 1,17$0^{\circ}C$, however, 10% water emulsified diesel oil is 1,27$0^{\circ}C$.

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Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM

  • Mohammadimehr, M.;Alimirzaei, S.
    • Structural Engineering and Mechanics
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    • v.59 no.3
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    • pp.431-454
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    • 2016
  • In this paper, the nonlinear static and free vibration analysis of Euler-Bernoulli composite beam model reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) with initial geometrical imperfection under uniformly distributed load using finite element method (FEM) is investigated. The governing equations of equilibrium are derived by the Hamilton's principle and von Karman type nonlinear strain-displacement relationships are employed. Also the influences of various loadings, amplitude of the waviness, UD, USFG, and SFG distributions of carbon nanotube (CNT) and different boundary conditions on the dimensionless transverse displacements and nonlinear frequency ratio are presented. It is seen that with increasing load, the displacement of USFG beam under force loads is more than for the other states. Moreover it can be seen that the nonlinear to linear natural frequency ratio decreases with increasing aspect ratio (h/L) for UD, USFG and SFG beam. Also, it is shown that at the specified value of (h/L), the natural frequency ratio increases with the increasing the values amplitude of waviness while the dimensionless nonlinear to linear maximum deflection decreases. Moreover, with considering the amplitude of waviness, the stiffness of Euler-Bernoulli beam model reinforced by FG-CNT increases. It is concluded that the R parameter increases with increasing of volume fraction while the rate of this parameter decreases. Thus one can be obtained the optimum value of FG-CNT volume fraction to prevent from resonance phenomenon.

A Self-Driven Active Clamp Forward Converter Using the Auxiliary Winding of the Power Transformer (변압기 보조권선을 이용한 자기 구동 능동 클램프 포워드 컨버터)

  • 이광운;임범선;김희준
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.40 no.5
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    • pp.350-354
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    • 2003
  • This study proposes a new self-driven active clamp forward converter eliminating the extra drive circuit for the active clamp switch. The converter used the auxiliary winding of the power transformer to drive the active clamp switch and a simple R-C circuit to get the dead time between the two switches. The operation principle was presented and experimental results were used to verify theoretical predictions. A 100-W (5V/20A) prototype converter built that only exhibited 1.5-turn winding number in the auxiliary winding was sufficient to drive the active clamp switch on the input of 50V. Finally, the measured efficiency of the converter was presented and the maximum efficiency of 91% was obtained.

Static and dynamic bending of ball reinforced by CNTs considering agglomeration effect

  • Chenghong Long;Dan Wang;H.B. Xiang
    • Steel and Composite Structures
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    • v.48 no.4
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    • pp.419-428
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    • 2023
  • In this paper, dynamic and static bending of ball modelled by nanocomposite microbeam by nanoparticles seeing agglomeration is presented. The structural damping is considered by Kelvin-Voigt model. The agglomeration effects are assumed using Mori-Tanaka model. The football ball is modeled by third order shear deformation theory (TSDT). The motion equations are derived by principle of Hamilton's and energy method assuming size effects on the basis of Eringen theory. Using differential quadrature method (DQM) and Newmark method, the static and dynamic deflections of the structure are obtained. The effects of agglomeration and CNTs volume percent, damping of structure, nonlocal parameter, length and thickness of micro-beam are presented on the static and dynamic deflections of the nanocomposite structure. Results show that with increasing CNTs volume percent, the maximum dimensionless dynamic deflection is reduced about 17%. In addition, assuming CNTs agglomeration increases the dimensionless dynamic deflection about 14%. It is also found that with increasing the CNTs volume percent from 0 to 0.15, the static deflection is decreased about 3 times due to the enhance in the stiffness of the structure. In addition, with enhancing the nonlocal parameters, the dynamic deflection is increased about 3.1 times.

Nonlinear vibration analysis of an embedded multi-walled carbon nanotube

  • Wu, Chih-Ping;Chen, Yan-Hong;Hong, Zong-Li;Lin, Chia-Hao
    • Advances in nano research
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    • v.6 no.2
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    • pp.163-182
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    • 2018
  • Based on the Reissner mixed variational theorem (RMVT), the authors present a nonlocal Timoshenko beam theory (TBT) for the nonlinear free vibration analysis of multi-walled carbon nanotubes (MWCNT) embedded in an elastic medium. In this formulation, four different edge conditions of the embedded MWCNT are considered, two different models with regard to the van der Waals interaction between each pair of walls constituting the MWCNT are considered, and the interaction between the MWCNT and its surrounding medium is simulated using the Pasternak-type foundation. The motion equations of an individual wall and the associated boundary conditions are derived using Hamilton's principle, in which the von $K{\acute{a}}rm{\acute{a}}n$ geometrical nonlinearity is considered. Eringen's nonlocal elasticity theory is used to account for the effects of the small length scale. Variations of the lowest frequency parameters with the maximum modal deflection of the embedded MWCNT are obtained using the differential quadrature method in conjunction with a direct iterative approach.

Robust Design of Coordinated Set Planning with the Non-Ideal Channel

  • Dai, Jianxin;Liu, Shuai;Chen, Ming;Zhou, Jun;Qi, Jie;Liang, Jingwei
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.8 no.5
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    • pp.1654-1675
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    • 2014
  • In practical wireless systems, the erroneous channel state information (CSI) sometimes deteriorates the performance drastically. This paper focuses on robust design of coordinated set planning of coordinated multi-point (CoMP) transmission, with respect to the feedback delay and link error. The non-ideal channel models involving various uncertainty conditions are given. After defining a penalty factor, the robust net ergodic capacity optimization problem is derived, whose variables to be optimized are the number of coordinated base stations (BSs) and the divided area's radius. By the maximum minimum criterion, upper and lower bounds of the robust capacity are investigated. A practical scheme is proposed to determine the optimal number of cooperative BSs. The simulation results indicate that the robust design based on maxmin principle is better than other precoding schemes. The gap between two bounds gets smaller as transmission power increases. Besides, as the large scale fading is higher or the channel is less reliable, the number of the cooperated BSs shall be greater.

Feasibility Study on Similarity Principle in Discrete Element Analysis (이산요소법을 이용한 수치해석에서의 상사성 이론의 적용성 검토)

  • Yun, Taeyoung;Park, Hee Mun
    • International Journal of Highway Engineering
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    • v.18 no.2
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    • pp.51-60
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    • 2016
  • PURPOSES : The applicability of the mechanics-based similarity concept (suggested by Feng et al.) for determining scaled variables, including length and load, via laboratory-scale tests and discrete element analysis, was evaluated. METHODS: Several studies on the similarity concept were reviewed. The exact scaling approach, a similarity concept described by Feng, was applied in order to determine an analytical solution of a free-falling ball. This solution can be considered one of the simplest conditions for discrete element analysis. RESULTS : The results revealed that 1) the exact scaling approach can be used to determine the scale of variables in laboratory tests and numerical analysis, 2) applying only a scale factor, via the exact scaling approach, is inadequate for the error-free replacement of small particles by large ones during discrete element analysis, 3) the level of continuity of flowable materials such as SCC and cement mortar seems to be an important criterion for evaluating the applicability of the similarity concept, and 4) additional conditions, such as the kinetics of particle, contact model, and geometry, must be taken into consideration to achieve the maximum radius of replacement particles during discrete element analysis. CONCLUSIONS : The concept of similarity is a convenient tool to evaluate the correspondence of scaled laboratory test or numerical analysis to physical condition. However, to achieve excellent correspondence, additional factors, such as the kinetics of particles, contact model, and geometry, must be taken into consideration.