• Title/Summary/Keyword: Approximate Equation

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Combined resonance of axially moving truncated conical shells in hygro-thermal environment

  • Zhong-Shi Ma;Gui-Lin She
    • Structural Engineering and Mechanics
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    • v.91 no.3
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    • pp.291-300
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    • 2024
  • This paper predicts the combined resonance behavior of the truncated conical shells (TCSs) under transverse and parametric coupled excitation. The motion governing equation is formulated in the framework of high-order shear deformation theory, von Kármán theory and Hamilton principle. The displacements and boundary conditions are characterized by a set of displacement shape functions with double Fourier series. Subsequently, the method of varying amplitude (MVA) is utilized to derive the approximate analytical solution of system response of TCSs. A comparative analysis is conducted to verify the accuracy of the current computational method. Additionally, the interaction mechanism of combined resonance, parametric resonance and primary resonance is examined. And the effect of damping coefficient, the external excitation, initial phase, axial motion speed, temperature variation, humidity variation, material properties and semi-vortex angle on the vibration mechanism are analyzed.

Nonlinear dynamic stability and vibration analysis of sandwich FG-CNTRC shallow spherical shell

  • Kamran Foroutan;Akin Atas;Habib Ahmadi
    • Advances in nano research
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    • v.17 no.2
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    • pp.95-107
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    • 2024
  • In this article, the semi-analytical method was used to analyze the nonlinear dynamic stability and vibration analysis of sandwich shallow spherical shells (SSSS). The SSSS was considered as functionally graded carbon nanotube-reinforced composites (FG-CNTRC) with three new patterns of FG-CNTRC. The governing equation was obtained and discretized utilizing the Galerkin method by implementing the von Kármán-Donnell nonlinear strain-displacement relations. The nonlinear dynamic stability was analyzed by means of the fourth-order Runge-Kutta method. Then the Budiansky-Roth criterion was employed to obtain the critical load for the dynamic post-buckling. The approximate solution for the deflection was represented by suitable mode functions, which consisted of the three modes of transverse nonlinear oscillations, including one symmetrically and two asymmetrical mode shapes. The influences of various geometrical characteristics and material parameters were studied on the nonlinear dynamic stability and vibration response. The results showed that the order of layers had a significant influence on the amplitude of vibration and critical dynamic buckling load.

Investigation into the Causes of Rupturing Ammonia-filled Cylinders (액상 암모니아 충전 용기의 파열 원인 분석)

  • BYOUNGIL JEON;CHANGHYUP PARK
    • Journal of Hydrogen and New Energy
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    • v.35 no.4
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    • pp.451-459
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    • 2024
  • This paper quantitatively analyzes the causes of ammonia-filled- cylinder rupture based on Tait equation and the safety guidelines, focusing on liquid expansion, internal temperature, and overfilling. When there exists a safety volume, i.e., gas-occupied volume within the ammonia cylinder, the internal pressure due to temperature rise corresponds to the vapor pressure at that temperature, with an approximate circumferential stress increase of 1.43 MPa/℃. In the absence of the safety volume, the internal pressure due to temperature rise matches the pressure of the compressed liquid ammonia at that temperature, and the resulting circumferential stress gradient in the cylinder shell is approximately 55.94 MPa/℃.

Dam-Break and Transcritical Flow Simulation of 1D Shallow Water Equations with Discontinuous Galerkin Finite Element Method (불연속 갤러킨 유한요소법을 이용한 1차원 천수방정식의 댐 붕괴류 및 천이류 해석)

  • Yun, Kwang Hee;Lee, Haegyun;Lee, Namjoo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.34 no.5
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    • pp.1383-1393
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    • 2014
  • Recently, with rapid improvement in computer hardware and theoretical development in the field of computational fluid dynamics, high-order accurate schemes also have been applied in the realm of computational hydraulics. In this study, numerical solutions of 1D shallow water equations are presented with TVD Runge-Kutta discontinuous Galerkin (RKDG) finite element method. The transcritical flows such as dam-break flows due to instant dam failure and transcritical flow with bottom elevation change were studied. As a formulation of approximate Riemann solver, the local Lax-Friedrichs (LLF), Roe, HLL flux schemes were employed and MUSCL slope limiter was used to eliminate unnecessary numerical oscillations. The developed model was applied to 1D dam break and transcritical flow. The results were compared to the exact solutions and experimental data.

One-dimensional Hydraulic Modeling of Open Channel Flow Using the Riemann Approximate Solver - Application for Natural River (Riemann 해법을 이용한 1차원 개수로 수리해석 - 자연하도 적용)

  • Kim, Ji-Sung;Han, Kun-Yeun
    • Journal of Korea Water Resources Association
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    • v.42 no.4
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    • pp.271-279
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    • 2009
  • The objective of this study is to develop the scheme to apply one-dimensional finite volume method (FVM) to natural river with complex geometry. In the previous study, FVM using the Riemann approximate solver was performed successfully in the various cases of dam-break, flood propagation, etc. with simple and rectangular cross-sections. We introduced the transform the natural into equivalent rectangular cross-sections. As a result of this way, the momentum equation was modified. The accuracy and applicability of newly developed scheme are demonstrated by means of a test example with exact solution, which uses triangular cross-sections. Secondly, this model is applied to natural river with irregular cross-sections and non-uniform lengths between cross-sections. The results shows that the aspect of flood propagation, location and height of hydraulic jump, and numerical solutions of maximum water level are in good agreement with the measured data. Using the developed scheme in this study, existing numerical schemes conducted in simple cross-sections can be directly applied to natural river without complicated numerical treatment.

Impact Force Applied on the Spent Nuclear Fuel Disposal Canister that Accidentally Drops and Collides onto the Ground (사고로 지면에 추락낙하 충돌하는 고준위폐기물 처분용기에 발생하는 충격력)

  • Kwon, Young Joo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.40 no.5
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    • pp.469-481
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    • 2016
  • In this paper, a mathematical methodology was theoretically studied to obtain the impact force caused by the collision between rigid bodies. This theoretical methodology was applied to compute the impact force applied on the spent nuclear fuel disposal canister that accidentally drops and collides onto the ground. From this study, the impact force required to ensure a structurally safe canister design was theoretically formulated. The main content of the theoretical study concerns the rigid body kinematics and equation of motion during collision between two rigid bodies. On the basis of this study, a general impact theory to compute the impact force caused by the collision between two bodies was developed. This general impact theory was applied to theoretically formulate the approximate mathematical solution of the impact force that affects the spent nuclear fuel disposal canister that accidentally falls to the ground. Simultaneously, a numerical analysis was performed using the computer code to compute the numerical solution of the impact force, and the numerical result was compared with the approximate mathematical solution.

Approximate Solution for Finding the Buckling Strength of Orthotropic Rectangular Plates (직교이방성판의 좌굴강도를 구하기 위한 근사식의 개발)

  • J. H. Jung;S. J. Yoon;S. K. You
    • Composites Research
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    • v.16 no.5
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    • pp.28-38
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    • 2003
  • In this study, the analytical investigation of orthotropic rectangular plate is presented. The loaded edges are assumed to be simply supported and the unloaded edges could have elastically restrained boundary conditions including the extreme boundary condition such as simple, fixed, and free. Using the closed-form solutions, the buckling analyses of orthotropic plate with arbitrary boundary conditions are performed. Based on the data obtained by conducting numerical analysis, the simplified form of equation for finding the buckling coefficient of plate with elastically restrained boundary conditions at the unloaded edges is suggested as a function of aspect ratio, elastic restraint. and material properties of the plate. The results of buckling analyses by closed-form solution and simplified form of solution are compared for various orthotropic material properties. It is confirmed that the difference of results is less than 1.5%.

Natural Frequency of 2-Dimensional Cylinders in Heaving; Frequency-Domain Analysis (상하동요하는 2차원 주상체의 고유진동수; 주파수 영역 해석)

  • Song, Je-Ha;Lee, Seung-Joon
    • Journal of the Society of Naval Architects of Korea
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    • v.52 no.1
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    • pp.25-33
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    • 2015
  • Following the previous works on the natural frequency of heaving circular cylinder, i.e. Lee and Lee (2013) and Kim and Lee (2013), an investigation of the same spirit on the 2-dimensional cylinder of Lewis form has been conducted. As before, the natural frequency is defined as that corresponding to the local maximum of the MCFR (Modulus of Complex Frequency Response), which is given by the equation of motion in the frequency domain analysis. Hydrodynamic coefficients were found by using the Ursell-Tasai method, and numerical results for them were obtained up to much higher frequencies than before, for which the method was known as numerically unstable in the past. For a wide range of H, the beam-draft ratio, and ${\sigma}$, the sectional area coefficient, including their practical ranges for a ship, results for the natural frequency were computed and presented in this work. Two approximate values for the natural frequency, one proposed by Lee (2008) and another one by the damped harmonic oscillator, were also compared with the current results, and for most cases it was observed that the current result is between the two values. Our numerical results showed that the values of the local maximum of MCFR as well as the natural frequencye increase as ${\sigma}$ increases while H decreases. At present, extension of the present finding to the 3-dimensional ship via the approximate theory like the strip method looks promising.

MPA-based IDA Using the Inelastic Displacement ratio, CR and the Collapse Intensity, RC (비탄성변위비와 붕괴강도비를 이용한 MPA기반의 IDA 해석법)

  • Han, Sang-Whan;Seok, Seung-Wook;Lee, Tae-Sub
    • Journal of the Earthquake Engineering Society of Korea
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    • v.14 no.5
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    • pp.33-39
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    • 2010
  • This study develops an approximate procedure for incremental dynamic analysis (IDA) using modal pushover analysis (MPA) with empirical equations of the inelastic displacement ratio ($C_R$) and the collapse strength ratio ($R_C$). By using this procedure, it is not required to conduct linear or nonlinear response history analyses of multi- or single- degree of freedom (MDF) systems. Thus, IDA curves can be effortlessly obtained. For verification of the proposed procedure, the 6-, 9- and 20-story steel moment frames are tested under an ensemble of 44 ground motions. The results show that the MPA-based IDA with empirical equations of $C_R$ and $R_C$ produced accurate IDA curves of the MDF systems. The computing time is almost negligible compared to the exact IDA using repeated nonlinear response history analysis (RHA) of a structure and the original MPA-based IDA using repeated nonlinear RHA of modal SDF systems.

Depth Averaged Numerical Model for Sediment Transport by Transcritical Flows (급변류에 의한 하상변동 예측을 위한 수심적분 수치모형)

  • Kim, Boram;Kim, Dae-Hong
    • Journal of Korea Water Resources Association
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    • v.47 no.11
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    • pp.1061-1066
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    • 2014
  • A stable second-order finite volume method was proposed to predict sediment transport under rapidly varied flow conditions such as transcritical flow. For the use under unsteady flow conditions, a sediment transport model was coupled with shallow water equations. HLLC approximate Riemann solver based on a monotone upstream-centered schemes for conservation laws (MUSCL) reconstruction was used for the computation of the flux terms. From the comparisons of dam break flow experiments on erodible beds in one- and two-dimensional channels, good agreements were obtained when proper parameters were provided. Lastly, dam surface erosion problem by overtopped water was simulated. Overall, the numerical solutions showed reasonable results, which demonstrated that the proposed numerical scheme could provide stable and physical results in the cases of subcritical and supercritical flow conditions.