• Title/Summary/Keyword: Euler Method

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Dynamic characteristics analysis of partial-interaction composite continuous beams

  • Fang, Genshen;Wang, Jingquan;Li, Shuai;Zhang, Shubin
    • Steel and Composite Structures
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    • v.21 no.1
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    • pp.195-216
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    • 2016
  • The dynamic characteristics of continuous steel-concrete composite beams considering the effect of interlayer slip were investigated based on Euler Bernoulli's beam theory. A simplified calculation model was presented, in which the Mode Stiffness Matrix (MSM) was developed. The natural frequencies and modes of partial-interaction composite continuous beams can be calculated accurately and easily by the use of MSM. Proceeding from the present method, the natural frequencies of two-span steel-concrete composite continuous beams with different span-ratios (0.53, 0.73, 0.85, 1) and different shear connection stiffnesses on the interface are calculated. The influence pattern of interfacial stiffness on bending vibration frequency was found. With the decrease of shear connection stiffness on the interface, the flexural vibration frequencies decrease obviously. And the influence on low order modes is more obvious while the reduction degree of high order is more sizeable. The real natural frequencies of partial-interaction continuous beams commonly used could have a 20% to 40% reduction compared with the fully-interaction ones. Furthermore, the reduction-ratios of natural frequencies for different span-ratios two-span composite beams with uniform shear connection stiffnesses are totally the same. The span-ratio mainly impacts on the mode shape. Four kinds of shear connection stiffnesses of steel-concrete composite continuous beams are calculated and compared with the experimental data and the FEM results. The calculated results using the proposed method agree well with the experimental and FEM ones on the low order modes which mainly determine the vibration properties.

Prediction of vibration and noise from steel/composite bridges based on receptance and statistical energy analysis

  • Liu, Quanmin;Liu, Linya;Chen, Huapeng;Zhou, Yunlai;Lei, Xiaoyan
    • Steel and Composite Structures
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    • v.37 no.3
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    • pp.291-306
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    • 2020
  • The noise from the elevated lines of rail transit has become a growing problem. This paper presents a new method for the rapid prediction of the structure-borne noise from steel or composite bridges, based on the receptance and Statistical Energy Analysis (SEA), which is essential to the study of the generation mechanism and the design of a low-noise bridge. First, the vertical track-bridge coupled vibration equations in the frequency domain are constructed by simplifying the rail and the bridge as an infinite Timoshenko beam and a finite Euler-Bernoulli beam respectively. Second, all wheel/rail forces acting upon the track are computed by taking a moving wheel-rail roughness spectrum as the excitation to the train-track-bridge system. The displacements of rail and bridge are obtained by substituting wheel/rail forces into the track-bridge coupled vibration equations, and all spring forces on the bridge are calculated by multiplying the stiffness by the deformation of each spring. Then, the input power to the bridge in the SEA model is derived from spring forces and the bridge receptance. The vibration response of the bridge is derived from the solution to the power balance equations of the bridge, and then the structure-borne noise from the bridge is obtained. Finally, a tri-span continuous steel-concrete composite bridge is taken as a numerical example, and the theoretical calculations in terms of the vibration and noise induced by a passing train agree well with the field measurements, verifying the method. The influence of various factors on wheel/rail and spring forces is investigated to simplify the train-track-bridge interaction calculation for predicting the vibration and noise from steel or composite bridges.

A Study on Mathematical Model of Caprine Arthritis Encephalitis (CAE) and Development of Animal Quarantine Information System Adapted for Small Island

  • Hirata, Teppei;Yonahara, Yoshihito;Asharif, Faramarz;Omatsu, Tsutomu;Miyagi, Takeshi;Nagata, Yasunori;Mizutani, Tetsuya;Tamaki, Shiro
    • IEIE Transactions on Smart Processing and Computing
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    • v.2 no.5
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    • pp.302-309
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    • 2013
  • This paper proposes a mathematical model of Caprine arthritis encephalitis (CAE), which is a disease causing significant economic damage to the goat farming industry, and reports the application of this model to the development of an information management system of animal quarantine to overcome this disease. The mathematical model of CAE was derived from the AIDs model in human case because epidemical characteristics of these diseases including infection pass are similar. This model can be expressed by simultaneous differential equations. Simulations using a new model were performed according Euler's and Runge-Kutta method using numerical analysis software. In each method, strong convergence was observed and the results were similar. The design of an information management system of animal quarantine was proposed as an application of the new model. System design was constructed on the assumption that in subtropical islands, the expected development of information infrastructure and utilization will become valuable in the future.

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Transverse Vibration Analysis of the Deploying Beam by Simulation and Experiment (시뮬레이션과 실험을 통한 전개하는 보의 횡 방향 진동 분석)

  • Kim, Jaewon;Zhu, Kefei;Chung, Jintai
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.25 no.12
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    • pp.866-873
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    • 2015
  • The transverse vibration of the deploying beam from rigid hub was analyzed by simulation and experiment. The linear governing equation of the deploying beam was obtained using the Euler-Bernoulli beam theory. To discretize the governing equation, the Galerkin method was used. After transforming the governing equation into the weak form, the weak form was discretized. The discretized equation was expressed by the matrix-vector form, and then the Newmark method was applied to simulate. To consider the damping effect of the beam, we conducted the modal test with various beam length. The mass proportional damping was selected by the relation of the first and second damping ratio. The proportional damping coefficient was calculated using the acquired natural frequency and damping ratio through the modal test. The experiment was set up to measure the transverse vibration of the deploying beam. The fixed beam at the carriage of the linear actuator was moved by moving the carriage. The transverse vibration of the deploying beam was observed by the Eulerian description near the hub. The deploying or retraction motion of the beam had the constant velocity and the velocity profile with acceleration and deceleration. We compared the transverse vibration results by the simulation and experiment. The observed response by the Eulerian description were analyzed.

Robust Design Optimization of a Fighter Wing Using an Uncertainty Model Constructed by Neural Network (신경망으로 구축된 불확실성 모델을 이용한 전투기 날개의 강건 최적 설계)

  • Kim, Ju-Hyun;Kim, Byung-Kon;Jun, Sang-Ook;Jeon, Yong-Hee;Lee, Dong-Ho
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.36 no.2
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    • pp.99-104
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    • 2008
  • This study performed robust design optimization of fighter wing planform, considering uncertainty based on neural network model. To construct uncertainty model, aerodynamic performance and their sensitivity were evaluated by 3-dimensional Euler equations and adjoint variable method at experimental points selected from central composite design. In addition, because a neural network model has the advantage of capturing non-linear characteristic, it was possible to predict sensitivity of the aerodynamic performance efficiently and accurately . From the results of robust design optimization, it could be confirmed that the robustness of the objective function and constraints were improved if the variation of uncertainty and sigma level were increased.

Performance Simulation of a Turboprop Engine for Basic Trainer

  • Kong, Changduk;Ki, Jayoung;Chung, Sukchoo
    • Journal of Mechanical Science and Technology
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    • v.16 no.6
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    • pp.839-850
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    • 2002
  • A performance simulation program for the turboprop engine (PT6A-62), which is the power plant of the first Korean indigenous basic trainer KT-1, was developed for performance prediction, development of an EHMS (Engine Health Monitoring System) and the flight simulator. Characteristics of components including compressors, turbines, power turbines and the constant speed propeller were required for the steady state and transient performance analysis with on and off design point analysis. In most cases, these were substituted for what scaled from similar engine components'characteristics with the scaling law. The developed program was evaluated with the performance data provided by the engine manufacturer and with analysis results of GASTURB program, which is well known for the performance simulation of gas turbines. Performance parameters such as mass flow rate, compressor pressure ratio, fuel flow rate, specific fuel consumption and turbine inlet temperature were discussed to evaluate validity of the developed program at various cases. The first case was the sea level static standard condition and other cases were considered with various altitudes, flight velocities and part loads with the range between idle and 105% rotational speed of the gas generator. In the transient analysis, the Continuity of Mass Flow Method was utilized under the condition that mass stored between components is ignored and the flow compatibility is satisfied, and the Modified Euler Method was used for integration of the surplus torque. The transient performance analysis for various fuel schedules was performed. When the fuel step increase was considered, the overshoot of the turbine inlet temperature occurred. However, in case of ramp increase of the fuel longer than step increase of the fuel, the overshoot of the turbine inlet temperature was effectively reduced.

Axial load detection in compressed steel beams using FBG-DSM sensors

  • Bonopera, Marco;Chang, Kuo-Chun;Chen, Chun-Chung;Lee, Zheng-Kuan;Tullini, Nerio
    • Smart Structures and Systems
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    • v.21 no.1
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    • pp.53-64
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    • 2018
  • Nondestructive testing methods are required to assess the condition of civil structures and formulate their maintenance programs. Axial force identification is required for several structural members of truss bridges, pipe racks, and space roof trusses. An accurate evaluation of in situ axial forces supports the safety assessment of the entire truss. A considerable redistribution of internal forces may indicate structural damage. In this paper, a novel compressive force identification method for prismatic members implemented using static deflections is applied to steel beams. The procedure uses the Euler-Bernoulli beam model and estimates the compressive load by using the measured displacement along the beam's length. Knowledge of flexural rigidity of the member under investigation is required. In this study, the deflected shape of a compressed steel beam is subjected to an additional vertical load that was short-term measured in several laboratory tests by using fiber Bragg grating-differential settlement measurement (FBG-DSM) sensors at specific cross sections along the beam's length. The accuracy of midspan deflections offered by the FBG-DSM sensors provided excellent force estimations. Compressive load detection accuracy can be improved if substantial second-order effects are induced in the tests. In conclusion, the proposed method can be successfully applied to steel beams with low slenderness under real conditions.

Free vibration analysis of a piezoelectric nanobeam using nonlocal elasticity theory

  • Kaghazian, Abbas;Hajnayeb, Ali;Foruzande, Hamidreza
    • Structural Engineering and Mechanics
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    • v.61 no.5
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    • pp.617-624
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    • 2017
  • Piezoelectric nanobeams are used in several nano electromechanical systems. The first step in designing these systems is conducting a vibration analysis. In this research, the free vibration of a piezoelectric nanobeam is analyzed by using the nonlocal elasticity theory. The nanobeam is modeled based on Euler-Bernoulli beam theory. Hamilton's principle is used to derive the equations of motion and also the boundary conditions of the system. The obtained equations of motion are solved by using both Galerkin and the Differential Quadrature (DQ) methods. The clamped-clamped and cantilever boundary conditions are analyzed and the effects of the applied voltage and nonlocal parameter on the natural frequencies and mode shapes are studied. The results show the success of Galerkin method in determining the natural frequencies. The results also show the influence of the nonlocal parameter on the natural frequencies. Increasing a positive voltage decreases the natural frequencies, while increasing a negative voltage increases them. It is also concluded that for the clamped parts of the beam and also other parts that encounter higher values of stress during free vibrations of the beam, anti-nodes in voltage mode shapes are observed. On the contrary, in the parts of the beam that the values of the induced stress are low, the values of the amplitude of the voltage mode shape are not significant. The obtained results and especially the mode shapes can be used in future studies on the forced vibrations of piezoelectric nanobeams based on Galerkin method.

Total Dynamic Analysis of Deep-Seabed Integrated Mining System (심해저 광물자원 채광시스템의 통합거동 해석)

  • Kim, Hyung-Woo;Hong, Sup;Choi, Jong-Su;Yeu, Tae-Kyeong
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2006.11a
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    • pp.311-314
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    • 2006
  • This paper concerns about total dynamic analysis of integrated mining system. This system consists of vertical steel pipe, intermediate buffer station, flexible pipe and self-propelled miner. The self-propelled miner and buffer are assumed as rigid-body of 6-dof. Discrete models of vertical steel pipe and flexible pipe are adopted, which are obtained by means of lumped-parameter method. The motion of mining vessel is not considered. Instead, the motion of mining vessel is taken into account in form of various boundary conditions (e.g. forced excitation in slow motion and/or fast oscillation and so on). A terramechanics model of extremely soft cohesive soil is applied to the self-propelled miner. The hydrodynamic forces and moments are included in the dynamic models of vehicle and lifting pipe system. Hinged and fixed constraints are used to define the connections between sub-systems (vertical steel pipe, buffer, flexible pipe, miner). Equations of motion of the coupled model are derived with respect to the each local coordinates system. Four Euler parameters are used to express the orientations of the sub-systems. To solve the equations of motion of the total dynamic model, an incremental-iterative formulation is employed. Newmark-b method is used for time-domain integration. The total dynamic responses of integrated mining system are investigated.

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Mechanical analysis of cutout piezoelectric nonlocal nanobeam including surface energy effects

  • Eltaher, Mohamed A.;Omar, Fatema-Alzahraa;Abdalla, Waleed S.;Kabeel, Abdallah M.;Alshorbagy, Amal E.
    • Structural Engineering and Mechanics
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    • v.76 no.1
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    • pp.141-151
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    • 2020
  • This manuscript tends to investigate influences of nanoscale and surface energy on a static bending and free vibration of piezoelectric perforated nanobeam structural element, for the first time. Nonlocal differential elasticity theory of Eringen is manipulated to depict the long-range atoms interactions, by imposing length scale parameter. Surface energy dominated in nanoscale structure, is included in the proposed model by using Gurtin-Murdoch model. The coupling effect between nonlocal elasticity and surface energy is included in the proposed model. Constitutive and governing equations of nonlocal-surface perforated Euler-Bernoulli nanobeam are derived by Hamilton's principle. The distribution of electric potential for the piezoelectric nanobeam model is assumed to vary as a combination of a cosine and linear variation, which satisfies the Maxwell's equation. The proposed model is solved numerically by using the finite-element method (FEM). The present model is validated by comparing the obtained results with previously published works. The detailed parametric study is presented to examine effects of the number of holes, perforation size, nonlocal parameter, surface energy, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric perforated nanobeams. It is found that the effect of surface stresses becomes more significant as the thickness decreases in the range of nanometers. The effect of number of holes becomes significant in the region 0.2 ≤ α ≤ 0.8. The current model can be used in design of perforated nano-electro-mechanical systems (PNEMS).