• 제목/요약/키워드: method of differential equation

검색결과 984건 처리시간 0.028초

객관적 방법에 의한 동해의 반일주조 조석도 (Objective Interpolation Of the $M_2$ Tide in the East Sea)

  • 강용균;최석원
    • 한국수산과학회지
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    • 제20권6호
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    • pp.477-483
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    • 1987
  • 조석방정식에 근거한 객관적 방법으로 동해내 반일주조($M_2$조)의 조석도를 자성하였다. 조석도의 작성은 라프라스 조석방정식으로부터 유도된 해면변위 방정식의 해로서 구하였으며, 이때 연안 검조소에서 관측된 해면변위의 진폭과 위상을 경계조건으로 사용하였다. 본 연구에서는 동해의 해저 지형과 조류에 따른 마찰력이 동해의 조석도 분포에 미치는 영향을 구명하였다. 또한, 동해 전역의 조석도의 견과를 기초로 하여, 한반도 동해안 외해의 국지적 영역의 반일주조에 대한 정밀조석도를 작성하였다.

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Nanotechnology, smartness and orthotropic nonhomogeneous elastic medium effects on buckling of piezoelectric pipes

  • Mosharrafian, Farhad;Kolahchi, Reza
    • Structural Engineering and Mechanics
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    • 제58권5호
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    • pp.931-947
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    • 2016
  • The effects of nanotechnology and smartness on the buckling reduction of pipes are the main contributions of present work. For this ends, the pipe is simulated with classical piezoelectric polymeric cylindrical shell reinforced by armchair double walled boron nitride nanotubes (DWBNNTs), The structure is subjected to combined electro-thermo-mechanical loads. The surrounding elastic foundation is modeled with a novel model namely as orthotropic nonhomogeneous Pasternak medium. Using representative volume element (RVE) based on micromechanical modeling, mechanical, electrical and thermal characteristics of the equivalent composite are determined. Employing nonlinear strains-displacements and stress-strain relations as well as the charge equation for coupling of electrical and mechanical fields, the governing equations are derived based on Hamilton's principal. Based on differential quadrature method (DQM), the buckling load of pipe is calculated. The influences of electrical and thermal loads, geometrical parameters of shell, elastic foundation, orientation angle and volume percent of DWBNNTs in polymer are investigated on the buckling of pipe. Results showed that the generated ${\Phi}$ improved sensor and actuator applications in several process industries, because it increases the stability of structure. Furthermore, using nanotechnology in reinforcing the pipe, the buckling load of structure increases.

Efficient analysis of SSI problems using infinite elements and wavelet theory

  • Bagheripour, Mohamad Hossein;Rahgozar, Reza;Malekinejad, Mohsen
    • Geomechanics and Engineering
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    • 제2권4호
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    • pp.229-252
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    • 2010
  • In this paper, Soil-Structure Interaction (SSI) effect is investigated using a new and integrated approach. Faster solution of time dependant differential equation of motion is achieved using numerical representation of wavelet theory while dynamic Infinite Elements (IFE) concept is utilized to effectively model the unbounded soil domain. Combination of the wavelet theory with IFE concept lead to a robust, efficient and integrated technique for the solution of complex problems. A direct method for soil-structure interaction analysis in a two dimensional medium is also presented in time domain using the frequency dependent transformation matrix. This matrix which represents the far field region is constructed by assembling stiffness matrices of the frequency dependant infinite elements. It maps the problem into the time domain where the equations of motion are to be solved. Accuracy of results obtained in this study is compared to those obtained by other SSI analysis techniques. It is shown that the solution procedure discussed in this paper is reliable, efficient and less time consuming as compared to other existing concepts and procedures.

테이퍼 말뚝의 좌굴 거동 (Buckling Behaviors of Tapered Piles)

  • 이준규;권오일;정태석;박수한
    • 한국지반공학회논문집
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    • 제35권2호
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    • pp.19-27
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    • 2019
  • 본 논문에서는 테이퍼 말뚝의 좌굴 거동을 평가할 수 있는 해석모델을 제안하였다. 말뚝의 변단면과 주면마찰, 지반의 비균질성을 고려하는 지반-말뚝 시스템의 좌굴을 지배하는 미분방정식을 유도하였다. 이 지배방정식을 Runge-Kutta 법을 이용하여 직접 수치 적분하였고, 미분방정식의 고유치인 좌굴하중은 Regula-Falsi 법을 이용하여 산정하였다. 원통형 말뚝에 대한 문헌값과 이 연구의 좌굴하중을 비교하여 연구의 타당성을 검증하였고, 지반-말뚝에 관련된 무차원변수가 좌굴하중, 좌굴모드, 좌굴응력에 미치는 영향을 분석하였다.

3차원 등가자기회로망법을 이용한 초전도 전동기의 자속밀도 분포 해석 (Flux Density Analysis of Superconducting Motor Using 3D Equivalent Magnetic Circuit Network)

  • 이정종;진영우;김영균;조영식;홍정표
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 2002년도 하계학술대회 논문집 B
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    • pp.773-775
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    • 2002
  • This paper deals with 3 Dimensional(3D) analysis of magnetic flux density of High Temperature Superconducting(HTS) motor using 3D Equivalent Magnetic Circuit Network (EMCN). When the Finite Element Method (FEM) is applied to an analysis of 3D models, it takes much time to the pre-process work required for 3D modeling and to solve the differential equation. Compare with 3D FEM, the result of 3D EMCN by using the magnetic resistance and magnetomotive force is exact and rapid. The accuracy of 3D EMCN is verified by comparing the 3D EMCN analysis with that of 3D FEM in HTS motor.

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원료채집기의 제어: 모델링, 계수추정, 견실한 스미스 예측기의 설계 (Reclaimer Control: Modeling , Parameter Estimation, and a Robust Smith Predictor Design)

  • 김성훈;홍금식;강동헌
    • 제어로봇시스템학회논문지
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    • 제5권8호
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    • pp.923-931
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    • 1999
  • In this paper, a modeling and a robust time-delay control for the reclaimer are investigated. Supplying the same amount of a raw material throughout the reclamation process from the raw yard to a sinter plant is important to keep the quality of the molten steel uniform in blast furnaces. As the actual parameter values of the reclaimer are not available, the boom rotational dynamics are modeled as a second order differential equation with unknown coefficients. The unknown parameters in the nominal model are estimated using a recursive estimation method. Another important factor in the control design of the reclaimer is the large time-delay in output measurement. Assuming a multiplicative uncertainty, that accounts for both the unstructured uncertainty neglected in the modeling and the structured uncertainty contained in the parameter estimation, a robust Smith predictor is designed. A robust stability criterion for the multiplicative uncertainty is also derived. Following the work of Goodwin et al. [4], a quantifying procedure of the multiplicative uncertainty bound, through experiments , is described. Experimental and simulation results are provided.

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Free and transient responses of linear complex stiffness system by Hilbert transform and convolution integral

  • Bae, S.H.;Cho, J.R.;Jeong, W.B.
    • Smart Structures and Systems
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    • 제17권5호
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    • pp.753-771
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    • 2016
  • This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.

유사변환기법을 이용한 3차원 모델의 개발 (Developing a Three-dimensional Spectral Model Using Similarity Transform Technique)

  • 강관수;소재귀;정경태;선우중호
    • 한국해안해양공학회지
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    • 제5권2호
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    • pp.107-120
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    • 1993
  • 본 논문은 유사변환기법을 이용한 새로운 3차원 연직 모우드 전개 모델의 개발에 대하여 기술한다. 기본방정식을 External 모우드와 Internal 모우드로 분리시킨 다음 Internal 모우드식에 Galerkin 방법을 적용하고 구성되는 행열방정식에 유사변환기법을 적용, 기저함수의 계수 값을 구하였다. 최종 얻어지는 기저함수의 계수 값은 마찰장을 제외하고는 비연계되어 시간 간격의 제약을 거의 받지않고 연직 구조를 구할 수 있기 때문에 경제성면에서 탁월하다. 수립된 모델은 어떤 기저함수라도 적용 가능하나 현 단계에서는 Chebyshev 다항식함수가 사용되었으며, 바람응력은 일정한 것으로 가정하였다. 모델 테스트로서 정상상태의 균일한 바람응력이 가해지는 장방형 Basin에 적용하여 모델의 적용 가능성을 검증하였다.

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Analytical free vibration solution for angle-ply piezolaminated plate under cylindrical bending: A piezo-elasticity approach

  • Singh, Agyapal;Kumari, Poonam
    • Advances in Computational Design
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    • 제5권1호
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    • pp.55-89
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    • 2020
  • For the first time, an accurate analytical solution, based on coupled three-dimensional (3D) piezoelasticity equations, is presented for free vibration analysis of the angle-ply elastic and piezoelectric flat laminated panels under arbitrary boundary conditions. The present analytical solution is applicable to composite, sandwich and hybrid panels having arbitrary angle-ply lay-up, material properties, and boundary conditions. The modified Hamiltons principle approach has been applied to derive the weak form of governing equations where stresses, displacements, electric potential, and electric displacement field variables are considered as primary variables. Thereafter, multi-term multi-field extended Kantorovich approach (MMEKM) is employed to transform the governing equation into two sets of algebraic-ordinary differential equations (ODEs), one along in-plane (x) and other along the thickness (z) direction, respectively. These ODEs are solved in closed-form manner, which ensures the same order of accuracy for all the variables (stresses, displacements, and electric variables) by satisfying the boundary and continuity equations in exact manners. A robust algorithm is developed for extracting the natural frequencies and mode shapes. The numerical results are reported for various configurations such as elastic panels, sandwich panels and piezoelectric panels under different sets of boundary conditions. The effect of ply-angle and thickness to span ratio (s) on the dynamic behavior of the panels are also investigated. The presented 3D analytical solution will be helpful in the assessment of various 1D theories and numerical methods.

Buckling of simply supported thin plate with variable thickness under bi-axial compression using perturbation technique

  • Fan, Haigui;Chen, Zhiping;Wang, Zewu;Liu, Peiqi
    • Structural Engineering and Mechanics
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    • 제70권5호
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    • pp.525-534
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    • 2019
  • An analytical research on buckling of simply supported thin plate with variable thickness under bi-axial compression is presented in this paper. Combining the perturbation technique, Fourier series expansion and Galerkin methods, the linear governing differential equation of the plate with arbitrary thickness variation under bi-axial compression is solved and the analytical expression of the critical buckling load is obtained. Based on that, numerical analysis is carried out for the plates with different thickness variation forms and aspect ratios under different bi-axial compressions. Four different thickness variation forms including linear, parabolic, stepped and trigonometric have been considered in this paper. The calculated critical buckling loads and buckling modes are presented and compared with the published results in the tables and figures. It shows that the analytical expressions derived by the theoretical method in this paper can be effectively used for buckling analysis of simply supported thin plates with arbitrary thickness variation, especially for the stepped thickness that used in engineering widely.