• Title/Summary/Keyword: harmonic functions

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Free Vibrations of Arches in Cartesian Coordinates (직교좌표계에 의한 아치의 자유진동)

  • Lee, Byoung-Koo;Lee, Yong-Soo;Kim, Il-Jung;Choi, Kou-Moon
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.12 no.12
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    • pp.970-978
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    • 2002
  • The differential equations governing free vibrations of the elastic arches with unsymmetric axis are derived in Cartesian coordinates rather than in polar coordinates. in which the effect of rotatory inertia is included. Frequencies and mode shapes are computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters are reported, with and without the rotatory inertia, as functions of three non-dimensional system parameters the rise to chord length ratio. the span length to chord length ratio, and the slenderness ratio. Also typical mode shapes of vibrating arches are presented.

Dynamic analysis of buildings considering the effect of masonry infills in the global structural stiffness

  • de Souza Bastos, Leonardo;Guerrero, Carolina Andrea Sanchez;Barile, Alan;da Silva, Jose Guilherme Santos
    • Coupled systems mechanics
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    • v.8 no.2
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    • pp.169-184
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    • 2019
  • This research work presents a study that aims to assess the dynamic structural behaviour and also investigate the human comfort levels of a reinforced concrete building, when subjected to nondeterministic wind dynamic loadings, considering the effect of masonry infills on the global stiffness of the structural model. In general, the masonry fills most of the empty areas within the structural frames of the buildings. Although these masonry infills present structural stiffness, the common practice of engineers is to adopt them as static loads, disregarding the effect of the masonry infills on the global stiffness of the structural system. This way, in this study a numerical model based on sixteen-storey reinforced concrete building with 48 m high and dimensions of $14.20m{\times}15m$ was analysed. This way, static, modal and dynamic analyses were carried out in order to simulate the structural model based on two different strategies: no masonry infills and masonry infills simulated by shell finite elements. In this investigation, the wind action is considered as a nondeterministic process with unstable properties and also random characteristics. The fluctuating parcel of the wind is decomposed into a finite number of harmonic functions proportional to the structure resonant frequency with phase angles randomly determined. The nondeterministic dynamic analysis clearly demonstrates the relevance of a more realistic numerical modelling of the masonry infills, due to the modifications on the global structural stiffness of the building. The maximum displacements and peak accelerations values were reduced when the effect of the masonry infills (structural stiffness) were considered in the dynamic analysis. Finally, it can be concluded that the human comfort evaluation of the sixteen-storey reinforced concrete building can be altered in a favourable way to design.

Elastic solutions for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface

  • Wang, Ling;Zou, Jin-Feng;Yang, Tao;Wang, Feng
    • Geomechanics and Engineering
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    • v.19 no.3
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    • pp.201-215
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    • 2019
  • A new approach of analyzing the displacements and stress of the surrounding rock for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface is investigated in this study. In the proposed approach, by using a virtual image technique, the shear stress of the vertical ground surface is revised to be zero, and elastic solutions of the surrounding rock are obtained before stress revision. To revise the vertical normal stress and shear stress of horizontal ground surface generated by the combined action of the actual and image sinks, the harmonic functions and corresponding stress function solutions were adopted. Based on the Boussinesq's solutions and integral method, the horizontal normal stress of the vertical ground surface is revised to be zero. Based on the linear superposition principle, the final solution of the displacements and stress were proposed by superimposing the solutions obtained by the virtual image technique and the stress revision on the horizontal and vertical ground surfaces. Furthermore, the ground settlements and lateral displacements of the horizontal and vertical ground surfaces are derived by the proposed approach. The proposed approach was well verified by comparing with the numerical method. The discussion based on the proposed approach in the manuscript shows that smaller horizontal ground settlements will be induced by lower tunnel buried depths and smaller limb distances. The proposed approach for the displacement and stress of the surrounding rocks can provide some practical information about the surrounding rock stability analysis of shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface.

Numerical simulation in time domain to study cross-flow VIV of catenary riser subject to vessel motion-induced oscillatory current

  • Liu, Kun;Wang, Kunpeng;Wang, Yihui;Li, Yulong
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.12 no.1
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    • pp.491-500
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    • 2020
  • The present study proposes a time domain model for the Vortex-induced Vibration (VIV) simulation of a catenary riser under the combination of the current and oscillatory flow induced by vessel motion. In this model, the hydrodynamic force of VIV comprises excitation force, hydrodynamic damping and added mass, which are taken as functions of the non-dimensional frequency and amplitude ratio. The non-dimensional frequency is related with the response frequency, natural frequency, lock-in range and the fluid velocity. The relatively oscillatory flow induced by vessel motion is taken into account in the fluid velocity. Considering that the added mass coefficient and the non-dimensional frequency can affect each other, an iterative analysis is conducted at each time step to update the added mass coefficient and the natural frequency. This model is in detail validated against the published test models. The results show that the model can reasonably reflect the effect of the added mass coefficient on the VIV, and can well predict the riser's VIV under stationary and oscillatory flow induced by vessel motion. Based on the model, this study carries out the VIV simulation of a catenary riser with harmonic vessel motion. By analyzing the bending moment near the touchdown point, it is found that under the combination of the ocean current and oscillatory flow the vessel motion may decrease the VIV response, while increase the excited frequencies. In addition, the decreasing rate of the VIV under vessel surge is larger than that under vessel heave at small vessel motion velocity, while the situation becomes opposite at large vessel motion velocity.

A quasi 3D solution for thermodynamic response of FG sandwich plates lying on variable elastic foundation with arbitrary boundary conditions

  • Bouiadjra, Rabbab Bachir;Mahmoudi, Abdelkader;Sekkal, Mohamed;Benyoucef, Samir;Selim, Mahmoud M.;Tounsi, Abdelouahed;Hussain, Muzamal
    • Steel and Composite Structures
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    • v.41 no.6
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    • pp.873-886
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    • 2021
  • In this paper, an analytical solution for thermodynamic response of functionally graded (FG) sandwich plates resting on variable elastic foundation is performed by using a quasi 3D shear deformation plate theory. The displacement field used in the present study contains undetermined integral terms and involves only four unknown functions with including stretching effect. The FG sandwich plate is considered to be subject to a time harmonic sinusoidal temperature field across its thickness with any combined boundary conditions. Equations of motion are derived from Hamilton's principle. The numerical results are compared with the existing results of quasi-3D shear deformation theories and an excellent agreement is observed. Several numerical examples for fundamental frequency, deflection, stress and variable elastic foundation parameter's analysis of FG sandwich plates are presented and discussed considering different material gradients, layer thickness ratios, thickness-to-length ratios and boundary conditions. The results of the present study reveal that the nature of the elastic foundation, the boundary conditions and the thermodynamic loading affect the response of the FG plate especially in the case of a thick plate.

Buckling of FGM elliptical cylindrical shell under follower lateral pressure

  • Moradi, Alireza;Poorveis, Davood;Khajehdezfuly, Amin
    • Steel and Composite Structures
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    • v.45 no.2
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    • pp.175-191
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    • 2022
  • A review of previous studies shows that although there is a considerable difference between buckling loads of structures under follower and non-follower lateral loads, only the buckling load of FGM elliptical cylindrical shell under non-follower lateral load was investigated in the literature. This study is the first to obtain the buckling load of elliptical FGM cylindrical shells under follower lateral load and also make a comparison between buckling loads of elliptical FGM cylindrical shells under follower and non-follower lateral loads. Moreover, this research is the first one to derive the load potential function of elliptical cylindrical shell. In this regard, the FGM cylindrical elliptical shell was modeled using the semi-analytical finite strip method and based on the First Shear Deformation Theory (FSDT). The shell is discretized by strip elements aligned in the longitudinal direction. The Lagrangian and harmonic shape functions were considered in the circumference and longitudinal directions, respectively. The buckling pressure of the shell under follower and non-follower lateral loads was obtained from eigenvalue problem. The results obtained from the model were compared with those presented in the literature to evaluate the validity of the model. A comparison index was defined to compare the buckling loads of the shell under follower and non-follower lateral load. A parametric study was carried out to investigate the effects of material properties and shell geometry characteristics on the comparison index. For the elliptical cylindrical shells with length-to-radius ratio greater than 16 and major-to-minor axis ratio greater than 0.6, the comparison index reaches to more than 20 percent which is significant. Moreover, the maximum difference is about 30 percent in some cases. The results obtained from the parametric study indicate that the buckling load of long elliptical cylindrical shell under non-follower load is not reliable.

Higher Order Shimming for Ultra-fast Spiral-Scan Imaging at 3 Tesla MRI System (3 Tesla MRI 시스템에서 초고속 나선주사영상을 위한 고차 shimming)

  • Kim, P.K.;Lim, J.W.;Ahn, C.B.
    • Investigative Magnetic Resonance Imaging
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    • v.11 no.2
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    • pp.95-102
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    • 2007
  • Purpose: To acquire high-resolution spiral-scan images at higher magnetic field, high homogeneous magnetic field is needed. Field inhomogeneity mapping and in-vivo shimming are important for rapid imaging such as spiral-scan imaging. The rapid scanning sequences are very susceptible to inhomogeneity. In this paper, we proposed a higher-order shimming method to obtain homogeneous magnetic field. Materials and Methods: To reduce measurement time for field inhomogeneity mapping, simultaneous axial/ sagittal, and coronal acquisitions are done using multi-slice based Fast Spin echo sequence. Acquired field inhomogeneity map is analyzed using the spherical harmonic functions, and shim currents are obtained by the multiplication of the pseudo-inverse of the field pattern with the inhomogeneity map. Results: Since the field inhomogeneity is increasing in proportion to the magnetic field, higher order shimming to reduce the inhomogeneity becomes more important in high field imaging. The shimming technique in which axial, sagittal, and coronal section inhomogeneity maps are obtained in one scan is developed, and the shimming method based on the analysis of spherical harmonics of the imhomogenity map is applied. The proposed technique is applicable to a localized shimming as well. High resolution spiral-scan imaging was successfully obtained with the proposed higher order shimming. Conclusion: Proposed pulse sequence for rapid measurement of inhomogeneity map and higher order shimming based on the inhomogeneity map work very well at 3 Tesla MRI system. With the proposed higher order shimming and localized higher order shimming techniques, high resolution spiral-scan images are successfully obtained at 3 T MRI system.

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Gravity modeling and application to the gravity referenced navigation (중력모델링과 중력참조항법에의 적용)

  • Lee, Ji-Sun;Kwon, Jay-Hyoun;Yu, Myeong-Jong
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.29 no.5
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    • pp.543-550
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    • 2011
  • The gravity anomaly is a basic geophysical data applied in various fields such as geophysics, geodesy and national defense. In general, the gravity anomaly is used through a interpolation process based on the constructed database. The gravity variation, however, is appeared in various shapes depending on the topography and the density of the underground structures. Therefore, the interpolation could lead to a large differences if the gravity fields do not satisfy the assumptions on the signal behavior like linear or a certain degree polynomials. Furthermore, the interpolation does not reflect the physical characteristics of the gravity such as the harmonic condition. In this study, the gravity modeling using the plane Fourier series and radial basis functions are performed to overcome the problems in the usual interpolation. The results of the modeling is analyzed for the case of the gravity referenced navigation focused on the signal characteristics. Based on the study, it was found that the results from modeling are not much different to that from the interpolation in a smoothly varied area. In case of the highly varied area, however, a large differences are appeared among the three methods. Especially, the Fourier series shows the most smooth variations in the modeled gravity values while the highest variations appeared in the interpolation. Applying to the gravity referenced navigation, it was found that the modeling is more effective in calculation cost. It is considered that the results from this study provides a basis on effective modeling of the gravity fields in terms of the signal characteristics and resolution for various application fields.

A Study on the Interference of Harmonic Frequency during the Change of Urban Transit's Signalling Systems (도시철도 신호시스템의 절체에 따른 주파수 간섭 연구)

  • Jeong, Rag-Gyo;Kim, Beak-Hyun;Joung, Eui-Jin
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.11 no.2
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    • pp.469-475
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    • 2010
  • The railway signalling system plays an essential role in the safe and efficient train operation as serving control functions of train operation intervals and train routes. The reliability and safety of the system are very important because the failure of the railway signalling system can lead to train collision or derailment as well as train operation stop. Until now, in railway signalling system the conventional wayside signal mode has been used generally. There are, however, the risk of accidents such as human mistakes caused by that the driver identifies the signal lamp status and controls train speed with the naked eye. It is also necessary to refurbish the obsolete system. Thereby, It is being effective that the onboard signal mode has been recently introduced and applied in order to transmit the speed control information to train by using the computer and communication equipment. It is necessary to switch over the system in a way while providing passengers with an operation service to replace the obsolete signal system. In this paper, we verify the cases through trial assessment which are solved by the way of adding specific functionalities in the problems of interference among the procedure of switch-over processes and a serial of processes for system verification while a train is operated in the new system in parallel to the existing system.

Electrical Characteristics Measurement of Eddy Current Testing Instrument for Steam Generator in NPP (원전 증기발생기 와전류검사 장치의 전기적 특성 측정)

  • Lee, Hee-Jong;Cho, Chan-Hee;Yoo, Hyun-Joo;Moon, Gyoon-Young;Lee, Tae-Hun
    • Journal of the Korean Society for Nondestructive Testing
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    • v.33 no.5
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    • pp.465-471
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    • 2013
  • A steam generator in nuclear power plant is a heatexchager which is used to convert water into steam from heat produced in a nuclear reactor core, and the steam produced in steam generator is delivered to the turbine to generate electricity. Because of damage to steam generator tubing may impair its ability to adequately perform required safety functions in terms of both structural integrity and leakage integrity, eddy current testing is periodically performed to evaluate the integrity of tubes in steam generator. This assessment is normally performed during a reactor refueling outage. Currently, the eddy current testing for steam generator of nuclear power plant in Korea is performed in accordance with KEPIC & ASME Code requirements, the eddy current testing system is consists of remote data acquisition unit and data analysis program to evaluate the acquired data. The KEPIC & ASME Code require that the electrical properties of remote data acquisition unit, such as total harmonic distortion, input & output impedance, amplifier linearity & stability, phase linearity, bandwidth & demodulation filter response, analog-to-digital conversion, and channel crosstalk shall be measured in accordance with the KEPIC & ASME Code requirements. In this paper, the measurement requirements of electrical properties for eddy current testing instrument described in KEPIC & ASME Code are presented, and the measurement results of newly developed eddy current testing instrument by KHNP(Korea Hydro & Nuclear Power Co., LTD) are presented.