• Title/Summary/Keyword: power series equation

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A transfer matrix method for in-plane bending vibrations of tapered beams with axial force and multiple edge cracks

  • Lee, Jung Woo;Lee, Jung Youn
    • Structural Engineering and Mechanics
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    • v.66 no.1
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    • pp.125-138
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    • 2018
  • This paper proposes a transfer matrix method for the bending vibration of two types of tapered beams subjected to axial force, and it is applied to analyze tapered beams with an edge or multiple edge open cracks. One beam type is assumed to be reduced linearly in the cross-section height along the beam length. The other type is a tapered beam in which the cross-section height and width with the same taper ratio is linearly reduced simultaneously. Each crack is modeled as two sub-elements connected by a rotational spring, and the method can evaluate the effect of cracking on the desired number of eigenfrequencies using a minimum number of subdivisions. Among the power series available for the solutions, the roots of the differential equation are computed using the Frobenius method. The computed results confirm the accuracy of the method and are compared with previously reported results. The effectiveness of the proposed methods is demonstrated by examining specific examples, and the effects of cracking and axial loading are carefully examined by a comparison of the single and double tapered beam results.

Numerical Analysis for Hydrodynamic Performance of OWC Devices with Multiple Chambers in Waves

  • Kim, Jeong-Seok;Nam, Bo Woo
    • Journal of Ocean Engineering and Technology
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    • v.36 no.1
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    • pp.21-31
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    • 2022
  • In recent years, various studies have been conducted on oscillating-water-column-type wave energy converters (OWC-WECs) with multiple chambers with the objective of efficiently utilizing the limited space of offshore/onshore structures. In this study, a numerical investigation based on a numerical wave tank was conducted on single, dual, and triple OWC chambers to examine the hydrodynamic performances and the energy conversion characteristics of the multiple water columns. The boundary value problem with the Laplace equation was solved by using a numerical wave tank based on a finite element method. The validity of the current numerical method was confirmed by comparing it with the measured data in the previous experimental research. We undertook a series of numerical simulations and observed that the water column motion of sloshing mode in a single chamber can be changed into the piston motion of different phases in multiple OWC chambers. Therefore, the piston motion in the multiple chambers can generate considerable airflow at a specific resonant frequency. In addition, the division of the OWC chamber results in a reduction of the time-dependent variability of the final output power from the device. As a result, the application of the multiple chambers leads to an increase of the energy conversion performance as well as a decrease of the variability of the wave energy converter.

Lubrication phenomenon in the stagnation point flow of Walters-B nanofluid

  • Muhammad Taj;Manzoor Ahmad;Mohamed A. Khadimallah;Saima Akram;Muzamal Hussain;Madeeha Tahir;Faisal Mehmood Butt;Abdelouahed Tounsi
    • Advances in concrete construction
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    • v.15 no.5
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    • pp.303-312
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    • 2023
  • The present study investigates the effects of Cattaneo-Christov thermal effects of stagnation point in Walters-B nanofluid flow through lubrication of power-law fluid by taking the slip at the interfacial condition. For the solution, the governing partial differential equation is transformed into a series of non-linear ordinary differential equations. With the help of hybrid homotopy analysis method; that consists of both the homotopy analysis and shooting method these equations can be solved. The influence of different involved constraints on quantities of interest are sketched and discussed. The viscoelastic parameter, slip parameters on velocity component and temperature are analyzed. The velocity varies by increase in viscoelastic parameter in the presence of slip parameter. The slip on the surface has major effect and mask the effect of stagnation point for whole slip condition and throughout the surface velocity remained same. Matched the present solution with previously published data and observed good agreement. It can be seen that the slip effects dominates the effects of free stream and for the large values of viscoelastic parameter the temperature as well as the concentration profile both decreases.

Pile tip grouting diffusion height prediction considering unloading effect based on cavity reverse expansion model

  • Jiaqi Zhang;Chunfeng Zhao;Cheng Zhao;Yue Wu;Xin Gong
    • Geomechanics and Engineering
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    • v.37 no.2
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    • pp.97-107
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    • 2024
  • The accurate prediction of grouting upward diffusion height is crucial for estimating the bearing capacity of tip-grouted piles. Borehole construction during the installation of bored piles induces soil unloading, resulting in both radial stress loss in the surrounding soil and an impact on grouting fluid diffusion. In this study, a modified model is developed for predicting grout diffusion height. This model incorporates the classical rheological equation of power-law cement grout and the cavity reverse expansion model to account for different degrees of unloading. A series of single-pile tip grouting and static load tests are conducted with varying initial grouting pressures. The test results demonstrate a significant effect of vertical grout diffusion on improving pile lateral friction resistance and bearing capacity. Increasing the grouting pressure leads to an increase in the vertical height of the grout. A comparison between the predicted values using the proposed model and the actual measured results reveals a model error ranging from -12.3% to 8.0%. Parametric analysis shows that grout diffusion height increases with an increase in the degree of unloading, with a more pronounced effect observed at higher grouting pressures. Two case studies are presented to verify the applicability of the proposed model. Field measurements of grout diffusion height correspond to unloading ratios of 0.68 and 0.71, respectively, as predicted by the model. Neglecting the unloading effect would result in a conservative estimate.

Exact Solutions for Vibration and Buckling of Rectangular Plates Loaded at Two Simply-Supported Opposite Edges by In-Plane Moments, Free along the Other Two Edges (면내(面內) 모멘트를 받는 단순지지된 두 모서리와 자유경계인 나머지 두 모서리를 갖는 직사각형 판의 진동과 좌굴의 엄밀해)

  • Shim, Hyun-Ju;Woo, Ha-Young;Kang, Jae-Hoon
    • Journal of Korean Association for Spatial Structures
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    • v.6 no.4 s.22
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    • pp.81-92
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    • 2006
  • This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon Poisson's ratio ( V ), results are shown for $0{\leq}v{\leq}0.5$, valid for isotropic materials.

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Wave Analysis and Spectrum Estimation for the Optimal Design of the Wave Energy Converter in the Hupo Coastal Sea (파력발전장치 설계를 위한후포 연안의 파랑 분석 및 스펙트럼 추정)

  • Kweon, Hyuck-Min;Cho, Hongyeon;Jeong, Weon-Mu
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.25 no.3
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    • pp.147-153
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    • 2013
  • There exist various types of the WEC (Wave Energy Converter), and among them, the point absorber is the most popularly investigated type. However, it is difficult to find examples of systematically measured data analysis for the design of the point absorber type of power buoy in the world. The study investigates the wave load acting on the point absorber type resonance power buoy wave energy extraction system proposed by Kweon et al. (2010). This study analyzes the time series spectra with respect to the three-year wave data (2002.05.01~2005.03.29) measured using the pressure type wave gage at the seaside of north breakwater of Hupo harbor located in the east coast of the Korean peninsula. From the analysis results, it could be deduced that monthly wave period and wave height variations were apparent and that monthly wave powers were unevenly distributed annually. The average wave steepness of the usual wave was 0.01, lower than that of the wind wave range of 0.02-0.04. The mode of the average wave period has the value of 5.31 sec, while mode of the wave height of the applicable period has the value of 0.29 m. The occurrence probability of the peak period is a bi-modal type, with a mode value between 4.47 sec and 6.78 sec. The design wave period can be selected from the above four values of 0.01, 5.31, 4.47, 6.78. About 95% of measured wave heights are below 1 m. Through this study, it was found that a resonance power buoy system is necessary in coastal areas with low wave energy and that the optimal design for overcoming the uneven monthly distribution of wave power is a major task in the development of a WEF (Wave Energy Farm). Finding it impossible to express the average spectrum of the usual wave in terms of the standard spectrum equation, this study proposes a new spectrum equation with three parameters, with which basic data for the prediction of the power production using wave power buoy and the fatigue analysis of the system can be given.

A Numerical Study of the 2-D Cold Flow for a Qubec City Stoker Incinerator (큐벡시 스토커 소각로 2차원 비반응 유동장 수치해석)

  • 박지영;송은영;장동순
    • Journal of Energy Engineering
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    • v.2 no.3
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    • pp.268-275
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    • 1993
  • A series of parametric investigations are performed in order to resolve the flow characteristic of a Quebec city stoker incinerator. The parameters considered in this study are five internal configurations of the Quebec city stoker itself and its modified ones, primary air velocity, the injection velocity and angle of the secondary air, and the reduction of the stoker exit area. A control-volume based finite-difference method by Patankar together with the power-law scheme is employed for discretization. The resolution of the pressure-velocity coupling is made by the use of SIMPLEC algorithm. The standard, two equation, k-$\varepsilon$ model is incorporated for the closure of turbulence. The size of recirculation region, turbulent viscosity, the mass fraction of the secondary air and pressure drop are calculated in order to analyze the characteristics of flow field. The results are physically acceptable and discussed in detail. The flow field of the Quebec city stoker shows the strong recirculation zone together with the high turbulence intensity over the upper part of the incinerator.

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The solar cell modeling using Lambert W-function (Lambert W 함수를 이용한 태양전지 모델링)

  • Bae, Jong-Guk;Kang, Gi-Hwan;Kim, Kyung-Soo;Yu, Gwon-Jong;Ahn, Hyung-Geun;Han, Deuk-Young
    • 한국태양에너지학회:학술대회논문집
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    • 2011.11a
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    • pp.278-281
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    • 2011
  • This system can predict the maximum output about all illumination levels so that the PV system designer can design the system having the best efficiency. For the output prediction exact about the solar cell, that is the device the basis most in the PV system, the basis has to be in order to try this way. The solution based on Lambert W-function are presented to express the transcendental current-voltage characteristic containing parasitic power consuming parameters like series and shunt resistances. A simple and efficient method for the extraction of a single current-voltage (I-V) curve under the constant illumination level is proposed. With the help of the Lambert W function, the explicit analytic expression for I is obtained. And the explicit analytic expression for V is obtained. This analytic expression is directly used to fit the experimental data and extract the device parameters. The I-V curve of the solar cell was expressed through the modeling using Lambert W-function and the numerical formula where there is the difficulty could be logarithmically expressed This method expresses with the I-V curve through the modeling using Lambert W-function which adds other loss ingredients to the equation2 as to the research afterward. And the solar cell goes as small and this I-V curve can predict the power penalty in the system unit.

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Stream flow estimation in small to large size streams using Sentinel-1 Synthetic Aperture Radar (SAR) data in Han River Basin, Korea

  • Ahmad, Waqas;Kim, Dongkyun
    • Proceedings of the Korea Water Resources Association Conference
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    • 2019.05a
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    • pp.152-152
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    • 2019
  • This study demonstrates a novel approach of remotely sensed estimates of stream flow at fifteen hydrological station in the Han River Basin, Korea. Multi-temporal data of the European Space Agency's Sentinel-1 SAR satellite from 19 January, 2015 to 25 August, 2018 is used to develop and validate the flow estimation model for each station. The flow estimation model is based on a power law relationship established between the remotely sensed surface area of water at a selected reach of the stream and the observed discharge. The satellite images were pre-processed for thermal noise, radiometric, speckle and terrain correction. The difference in SAR image brightness caused by the differences in SAR satellite look angle and atmospheric condition are corrected using the histogram matching technique. Selective area filtering is applied to identify the extent of the selected stream reach where the change in water surface area is highly sensitive to the change in stream discharge. Following this, an iterative procedure called the Optimum Threshold Classification Algorithm (OTC) is applied to the multi-temporal selective areas to extract a series of water surface areas. It is observed that the extracted water surface area and the stream discharge are related by the power law equation. A strong correlation coefficient ranging from 0.68 to 0.98 (mean=0.89) was observed for thirteen hydrological stations, while at two stations the relationship was highly affected by the hydraulic structures such as dam. It is further identified that the availability of remotely sensed data for a range of discharge conditions and the geometric properties of the selected stream reach such as the stream width and side slope influence the accuracy of the flow estimation model.

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Closed-Form Solutions to Free Vibration Response of Single Degree of Freedom Systems with Coulomb Friction (쿨롱마찰을 갖는 단자유도계의 자유진동응답에 관한 닫힌 해)

  • Lee, Sung-Kyung
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.33 no.1
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    • pp.9-16
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    • 2020
  • The objective of this study is to propose closed-form solutions to the free vibration response of single-degree-of-freedom (SDOF) systems, as part of fundamental research on dynamic systems with Coulomb friction. The motion of a dynamic system with Coulomb friction is described by a nonlinear differential equation, and, due to the variation in the sign of friction force term with the direction of motion, it is difficult to obtain the closed-form solution. To solve this problem, the nonlinear differential equation is directly computed by numerical integration, or an approximated solution is indirectly obtained using a linear differential equation wherein the damping effect due to Coulomb friction is replaced by an equivalent viscous damping term. However, these conventional methods do not provide a closed-form solution from a mathematical point of view. In this regard, closed-form solutions to the free vibration response of SDOF systems with Coulomb friction are derived herein by considering that the sign of the friction force term is reversed in each half-cycle of motion and by expanding it to the entire time history using the power series function. In addition, for a given initial condition, both the number of free vibration half-cycles and the response at the instant when free vibration motion stops are predicted under the condition that the motion of free vibration is stopped when the amplitude of the friction force is higher than that of the restoring force due to stiffness.