• Title/Summary/Keyword: Equation of Motion Solution

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Developing girder distribution factors in bridge analysis through B-WIM measurements: An empirical study

  • Widi Nugraha;Winarputro Adi Riyono;Indra Djati Sidi;Made Suarjana;Ediansjah Zulkifli
    • Structural Monitoring and Maintenance
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    • v.10 no.3
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    • pp.207-220
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    • 2023
  • The safety of bridges are critical in our transportation infrastructure. Bridge design and analysis require complex structural analysis procedures to ensure their safety and stability. One common method is to calculate the maximum moment in the girders to determine the appropriate bridge section. Girder distribution factors (GDFs) provide a simpler approach for performing this analysis. A GDF is a ratio between the response of a single girder and the total response of all girders in the bridge. This paper explores the significance of GDFs in bridge analysis and design, including their importance in the evaluation of existing bridges. We utilized Bridge Weigh-in-motion (B-WIM) measurements of five simple supported girder bridge in Indonesia to develop a simple GDF provisions for the Indonesia's bridge design code. The B-WIM measurements enable us to know each girder strain as a response due to vehicle loading as the vehicle passes the bridge. The calculated GDF obtained from the B-WIM measurements were compared with the code-specified GDF and the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) bridge design specification. Our study found that the code specified GDF was adequate or conservative compared to the GDF obtained from the B-WIM measurements. The proposed GDF equation correlates well with the AASHTO LRFD bridge design specification. Developing appropriate provisions for GDFs in Indonesian bridge design codes can provides a practical solution for designing girder bridges in Indonesia, ensuring safety while allowing for easier calculations and assessments based on B-WIM measurements.

A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory

  • Mokhtar, Youcef;Heireche, Houari;Bousahla, Abdelmoumen Anis;Houari, Mohammed Sid Ahmed;Tounsi, Abdelouahed;Mahmoud, S.R.
    • Smart Structures and Systems
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    • v.21 no.4
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    • pp.397-405
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    • 2018
  • In this paper, a novel simple shear deformation theory for buckling analysis of single layer graphene sheet is formulated using the nonlocal differential constitutive relations of Eringen. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal elasticity theory is employed to investigate effects of small scale on buckling of the rectangular nano-plate. The equations of motion of the nonlocal theories are derived and solved via Navier's procedure for all edges simply supported boundary conditions. The results are verified with the known results in the literature. The influences played by Effects of nonlocal parameter, length, thickness of the graphene sheets and shear deformation effect on the critical buckling load are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the buckling nanoplates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

Effectiveness of Wave Resonator for Secondary Undulation under Real Sea Conditions (실해역에서 공진장치를 이용한 부진동의 제어)

  • Jeong, Jin-Woo;Kim, Do-Sam;Park, Jong-Bae;An, Sung-Wook
    • Journal of Ocean Engineering and Technology
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    • v.24 no.6
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    • pp.51-60
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    • 2010
  • In this study, the performance evaluation of a conventional wave resonator at the entrance of a port or a pier against secondary undulation has been performed using 2D hydrodynamic modeling within port. A wave resonator has been designed for the attenuation of the secondary undulation induced by the long-periodic waves. The controlled performance of the wave resonator has been numerically investigated for CGWAVE MODULE of finite-element model of SMS (Surface water Modeling System) based on the elliptic mild-slope wave equation. SMS was verified though the comparisons with analytical solution performed by Ippen and Goda (1963). Also, It was confirmed that a wave resonator of a rectangular model harbor is effective enough to control the secondary undulation when it compares variation of water level with the case of no resonance system. From the above results, amplification phenomenon induced by long-period waves transferred from 1900 sec to 2100 sec when it applied a wave resonator in Busan Gamcheon Port which is a deep-sea. And it was confirmed that a wave resonator of Pohang New Port attenuates largely long-period waves which are within the range of 300 sec induced by long-period motion of the moored ship.

Development of Cable Excitation System for Evaluating Dynamic Characteristics of Stay Cables (사장교 케이블 동특성 평가를 위한 케이블 가진시스템 개발)

  • Kim, Nam-Sik;Jeong, Woon;Seo, Ju-Won;Ahn, Sang-Sup
    • Journal of the Earthquake Engineering Society of Korea
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    • v.7 no.4
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    • pp.71-79
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    • 2003
  • As a critical member of cable-stayed bridges, stay cables play on important role of supporting the entire structure. Traffic, wind or rain-wind induced vibrations of stay cables would be a major cause of degrading both safety and serviceability of the bridge. One of the effective alternatives to solve this problem is to employ the cable dampers. In order to design the cable damper optimally, it is necessary to exactly estimate the dynamic characteristics of the existing cables. To achieve more reliable dynamic properties of stay cables, precise excitations inducing forced vibration are needed. Therefore, in this study, a cable excitation system(exciter) controlled digitally was developed. And to evaluate the performance of the cable exciter developed, a solution of the differential equation of cable motion considering the exciter was derived, Using the cable exciter, sine sweeping and resonance tests on a cable model were carried out to obtain the dynamic characteristics effectively.

Dynamical Predictions of the Structural Connection by the Reduced Approach (축약법에 의한 구조물 결합부의 동적 거동 예측)

  • Yun, Seong-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.27 no.6
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    • pp.589-596
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    • 2014
  • Joints, fasteners or connected parts frequently have a significant effect on the dynamical behavior of assembled mechanical structures. Therefore, the analytical prediction of structural responses depends on the accuracy of joint modeling. This paper deals with the formulation and analysis of dynamic mechanism for joint flexibilities whose relevant magnitudes of stiffnesses are investigated by using linear and torsional springs. The equation of motion is derived by using a generic joint in the middle of clamped-clamped beam. A reanalysis due to changes in magnitudes of joint stiffnesses is based on the reduced analysis where the binomial series terms are used as basis vectors. The solution procedures are straightforward and the method can be readily used with a general finite element method. The computational effort needed by this approach is usually much smaller than the effort needed for complete vibration analysis. Two numerical examples show that accurate results are obtained efficiently by reducing the number of degree in the reduced model.

Finite Element Analysis of Continuous Beam Vibration under Pedestrian Loading Considering Moving Mass Effect (이동 질량 효과를 고려한 연속 보의 보행하중 진동 유한요소 해석)

  • Park, Wonsuk
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.35 no.5
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    • pp.309-316
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    • 2022
  • This study proposes a finite element analysis method that can analyze the vibration of a beam by considering the inertia effect of moving masses in a vertical direction. The proposed method is effective when a precise interaction analysis is not required. The inertial effects of the moving masses are included in the equation of motion, and the interaction forces between the masses and the beam are considered only as external loads. Time domain analyses were performed using Abaqus, a general-purpose finite element analysis software, and an implementation method using multi-point constraints wais presented to link the displacements of the beam element nodes and moving rigid masses. The proposed method was verified by comparing its solution with that obtained using an existing analytical method, and the analysis results for continuous beam vibrations under dynamic gait loadings were used to examine the mass effect of pedestrians.

Undamped Forced Vibration Response of Curved Composite Panels using Enhanced Assumed Strain Finite Element-Direct Integration Method (추가변형률 유한요소-직접적분법을 이용한 복합적층 곡선패널의 비감쇠 강제진동응답)

  • Park, Won-Tae;Chun, Kyoung-Sik;Son, Byung-Jik
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.8 no.2
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    • pp.247-258
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    • 2004
  • The composite shell element is developed for the solution of undamped forced vibration problem of composite curved panels. The finite element used in the current study is an 4-node enhanced assumed shell element with six degrees of freedom per node. The composite shell element is free of both shear and membrane locking phenomenon by using the enhanced assumed strain(EAS) method. A modification to the first-order shear deformation shell theory is proposed, which results in parabolic thorough-thickness distribution of the transverse shear strains and stresses. It eliminates the need for shear correction factors in the first order theory. Newmark's direct integration technique is used for carrying out the integration of the equation motion, to obtain the repones history. Parametric studies of curved composite panels are carried out for forced vibration analysis by geometrical shapes and by laminated composite; such as fiber orientation, stacking sequence.

Development of Attitude Heading Reference System based on MEMS for High Speed Autonomous Underwater Vehicle (고속 자율 무인잠수정 적용을 위한 MEMS 기술기반 자세 측정 장치 개발)

  • Hwang, A-Rom;Ahn, Nam-Hyun;Yoon, Seon-Il
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.19 no.6
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    • pp.666-673
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    • 2013
  • This paper proposes the performance evaluation test of attitude heading reference system (AHRS) suitable for small high speed autonomous underwater vehicle(AUV). Although IMU can provides the detail attitude information, it is sometime not suitable for small AUV with short operation time in view of price and the electrical power consumption. One of alternative for tactical grade IMU is the AHRS based micro-machined electro mechanical system(MEMS) which can overcome many problems that have inhibited the adoption of inertial system for small AUV such as cost and power consumption. A cost effective and small size AHRS which incorporates measurements from 3-axis MEMS gyroscopes, accelerometers, and 3-axis magnetometers has been developed to provide a complete attitude solution for AUV and the attitude calculation algorithm is derived based the coordinate transform equation and Kalman filter. The developed AHRS was validated through various performance tests as like the magnetometer calibration, operating experiments using land mobile vehicle and flight motion simulator (FMS). The test of magnetometer calibration shows the developed MEMS AHRS is robust to the external magent field change and the test with land vehicle proves the leveling error of developed MEMS AHRS is below $0.5^{\circ}/hr$. The results of FMS test shows the fact that AHRS provides the measurement with $0.5^{\circ}/hr$ error during 5 minutes operation time. These results of performance evaluation tests showed that the developed AHRS provides attitude information which error of roll and pitch are below $1^{\circ}$ and the error of yaw is below $5^{\circ}$ and satisfies the required specification. It is expected that developed AHRS can provide the precise attitude measurement under sea trial with real AUV.

Inference of the Probability Distribution of Phase Difference and the Path Duration of Ground Motion from Markov Envelope (Markov Envelope를 이용한 지진동의 위상차 확률분포와 전파지연시간의 추정)

  • Choi, Hang;Yoon, Byung-Ick
    • Journal of the Earthquake Engineering Society of Korea
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    • v.26 no.5
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    • pp.191-202
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    • 2022
  • Markov envelope as a theoretical solution of the parabolic wave equation with Markov approximation for the von Kármán type random medium is studied and approximated with the convolution of two probability density functions (pdf) of normal and gamma distributions considering the previous studies on the applications of Radiative Transfer Theory (RTT) and the analysis results of earthquake records. Through the approximation with gamma pdf, the constant shape parameter of 2 was determined regardless of the source distance ro. This finding means that the scattering process has the property of an inhomogeneous single-scattering Poisson process, unlike the previous studies, which resulted in a homogeneous multiple-scattering Poisson process. Approximated Markov envelope can be treated as the normalized mean square (MS) envelope for ground acceleration because of the flat source Fourier spectrum. Based on such characteristics, the path duration is estimated from the approximated MS envelope and compared to the empirical formula derived by Boore and Thompson. The results clearly show that the path duration increases proportionately to ro1/2-ro2, and the peak value of the RMS envelope is attenuated by exp (-0.0033ro), excluding the geometrical attenuation. The attenuation slope for ro≤100 km is quite similar to that of effective attenuation for shallow crustal earthquakes, and it may be difficult to distinguish the contribution of intrinsic attenuation from effective attenuation. Slowly varying dispersive delay, also called the medium effect, represented by regular pdf, governs the path duration for the source distance shorter than 100 km. Moreover, the diffraction term, also called the distance effect because of scattering, fully controls the path duration beyond the source distance of 300 km and has a steep gradient compared to the medium effect. Source distance 100-300 km is a transition range of the path duration governing effect from random medium to distance. This means that the scattering may not be the prime cause of peak attenuation and envelope broadening for the source distance of less than 200 km. Furthermore, it is also shown that normal distribution is appropriate for the probability distribution of phase difference, as asserted in the previous studies.

Hydrogen Bond Effect on Chain Behavior at the Semidilute Regime of Poly(vinyl alcohol) Aqueous Solution (폴리(비닐 알코올) 수용액의 준희박농도 영역에서 사슬 거동에 대한 수소결합의 효과)

  • Park Il-Hyun;Yu Young-Chol;Park Ki-Sang;Lee Dong-Il;Lyoo Won-Seok
    • Polymer(Korea)
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    • v.30 no.3
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    • pp.271-278
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    • 2006
  • In order to investigate the structure and dynamics of atatic poly (vinyl alcohol) (PVA)/water system, laser light scattering experiment has been done in the semi-dilute concentration regime at $25^{\circ}C$. The scattering intensity I(q) can be analyzed with the fractal equation of $I(q){\sim}q^{-m}$ instead of Onstein-Zernike type equation. The fractal dimensionality m was found to be constant after reaching the plateau value of $m=2.6{\pm}0.3$ above C=3wt%. The time correlation function of dynamic light scattering has always two different modes such as fast mode and slow one. The cooperative diffusion of fast mode showed concentration independence contrary 4o the reptation theory's concentration dependent exponent of 3/4. The slow mode can be interpreted as the motion of large scale heterogeneities and its strong concentration dependence is apparent with a large negative exponent of -3.0. It is considered that the stereo-regular arrangement with four successive meso units of -OH plays as a key role in forming such heterogeneity.