• Title/Summary/Keyword: Spring-Beam Model

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Vibration analysis of sandwich beam with nanocomposite facesheets considering structural damping effects

  • Cheraghbak, Ali;Dehkordi, M. Botshekanan;Golestanian, H.
    • Steel and Composite Structures
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    • v.32 no.6
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    • pp.795-806
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    • 2019
  • In this paper, free vibration of sandwich beam with flexible core resting on orthotropic Pasternak is investigated. The top and bottom layers are reinforced by carbon nanotubes (CNTs). This sandwich structural is modeled by Euler and Frostig theories. The effect of agglomeration using Mori-Tanaka model is considered. The Eringen's theory is applied for size effect. The structural damping is investigated by Kelvin-voigt model. The motion equations are calculated by Hamilton's principle and energy method. Using analytical method, the frequency of the structure is obtained. The effect of agglomeration and CNTs volume percent for different parameter such as damping of structure, thickens and spring constant of elastic medium are presented on the frequency of the composite structure. Results show that with increasing CNTs agglomeration, frequency is decreased.

Modelling the dynamic response of railway track to wheel/rail impact loading

  • Cai, Z.;Raymond, G.P.
    • Structural Engineering and Mechanics
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    • v.2 no.1
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    • pp.95-112
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    • 1994
  • This paper describes the formulation and application of a dynamic model for a conventional rail track subjected to arbitary loading functions that simulate wheel/rail impact forces. The rail track is idealized as a periodic elastically coupled beam system resting on a Winkler foundation. Modal parameters of the track structure are first obtained from the natural vibration characteristics of the beam system, which is discretized into a periodic assembly of a specially-constructed track element and a single beam element characterized by their exact dynamic stiffness matrices. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the rail support components is introduced to reduce the degrees of freedom of the track element. The forced vibration equations of motion of the track subjected to a series of loading functions are then formulated by using beam bending theories and are reduced to second order ordinary differential equations through the use of mode summation with non-proportional modal damping. Numerical examples for the dynamic responses of a typical track are presented, and the solutions resulting from different rail/tie beam theories are compared.

Vibration Characteristics of the PWR Fuel Rod Supported by New Doublet Spacer Grids (새이중판 지지격자로 지지된 경수로용 연료봉의 진동특성)

  • 최명환;강흥석;윤경호;김형규;송기남
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.05a
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    • pp.905-910
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    • 2003
  • One of the methods that are used to compare and verify the supporting performance of the spacer grids developed is the vibration characteristic test. A modal test in this paper is performed for a dummy rod 3,847mm tall supported by eight New Doublet (ND) spacer grids. For the vibration test in air, nine accelerometers, one displacement sensor and one shaker are used for acquiring signals, and an I-DEAS TDAS software is employed for analyzing the signals. Also, a finite element (FE) analysis is performed by a beam-spring simple model and a contact model simulating the contact phenomenon between the rod and the fm spring. And then, the result of the FE analysis is compared with that of the modal test. The natural frequencies as well as the mode shapes calculated by the proposed contact models have a greater similarity to the test results than those by the previous beam-spring model. In addition, for grasping whether or not the modal parameters are influenced by where shaking spot is, two kinds of tests are performed; one is for the shaker attached at the fourth span (center), the other is for the shaker at the fifth span that is one span nearer to the bottom of the rod. The latter shows higher MAC than the former. Finally, the vibration displacements are measured in the range of 0.112-0.214mm for the excitation force of 0.25-0.75 N.

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Nonlinear forced vibration of imperfect FG beams with hygro-thermal factor

  • Y.J. He;G.L She
    • Structural Engineering and Mechanics
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    • v.92 no.2
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    • pp.163-172
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    • 2024
  • This paper intends to analyze the nonlinear forced vibrations of functionally graded material (FGM) beams with initial geometrical defects in hygro-thermal ambiences. For this purpose, we assume that the correlation properties of the material alter along the thickness direction in succession and the surface of the beam is subjected to humid and thermal loads. Based on the Euler Bernoulli beam theory and geometrical non-linearity, we use the Hamiltonian principle to formulate a theoretical model with consideration of the hygrothermal effects. Galerkin's technique has been proposed for the control equations of discrete systems. The non-linear primary resonances are acquired by applying the modified Lindstedt-Poincare method (MLP). Verify the reliability of the data obtained through comparison with literature. The non-linear resonance response is reflected by amplitude-frequency response curves. The numerical results indicate that the resonances of FGM beams include three non-linear characteristics, namely hard springs, soft springs and soft-hard spring types. The response modalities of the structure may transform between those non-linear characteristics when material properties, spring coefficients, geometric defect values, temperature-humidity loads and even the external stimulus generate variations.

An energy-based vibration model for beam bridges with multiple constraints

  • Huang, Shiping;Zhang, Huijian;Chen, Piaohua;Zhu, Yazhi;Zuazua, Enrique
    • Structural Engineering and Mechanics
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    • v.82 no.1
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    • pp.41-53
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    • 2022
  • We developed an accurate and simple vibration model to calculate the natural frequencies and their corresponding vibration modes for multi-span beam bridges with non-uniform cross-sections. A closed set of characteristic functions of a single-span beam was used to construct the vibration modes of the multi-span bridges, which were considered single-span beams with multiple constraints. To simplify the boundary conditions, the restraints were converted into spring constraints. Then the functional of the total energy has the same form as the penalty method. Compared to the conventional penalty method, the penalty coefficients in the proposed approach can be calculated directly, which can avoid the iteration process and convergence problem. The natural frequencies and corresponding vibration modes were obtained via the minimum total potential energy principle. By using the symmetry of the eigenfunctions or structure, the matrix size can be further reduced, which increases the computational efficiency of the proposed model. The accuracy and efficiency of the proposed approach were validated by the finite element method.

Prediction of Residual Deformation and Stress Distribution for a Thermo-Elastic-Plastic Beam Using a Simplified Numerical Analysis (간이 수치해석에 의한 열탄소성보의 잔류변형 및 응력분포의 예측)

  • S.H. Jun;K. Choi
    • Journal of the Society of Naval Architects of Korea
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    • v.33 no.3
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    • pp.22-34
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    • 1996
  • Regarding the plate bending process by line heating method, in this study a simplified numerical analysis is performed for a beam model to predict its residual deformation and stress distribution. Using the modified strip theory and beam finite element method, a PC-based simulation program is developed for a thermo-elastic-plastic beam. The plate bending problem can be approximately replaced by a beam model using distributed springs to account for the effect of adjacent strips. The spring constants are chosen as the best fit with experiments. In this paper, it is assumed that the temperature distribution is already given and the temperature-dependent material properties are considered. To verify the simulation program, the results using present numerical algorithm are compared with other published experimental results and similar numerical studies. The comparison shows good agreement. The present PC-based computer program also shows good efficiency in computing time.

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Effects of deformation of elastic constraints on free vibration characteristics of cantilever Bernoulli-Euler beams

  • Wang, Tong;He, Tao;Li, Hongjing
    • Structural Engineering and Mechanics
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    • v.59 no.6
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    • pp.1139-1153
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    • 2016
  • Elastic constraints are usually simplified as "spring forces" exerted on beam ends without considering the "spring deformation". The partial differential equation governing the free vibrations of a cantilever Bernoulli-Euler beam considering the deformation of elastic constraints is firstly established, and is nondimensionalized to obtain two dimensionless factors, $k_v$ and $k_r$, describing the effects of elastically vertical and rotational end constraints, respectively. Then the frequency equation for the above Bernoulli-Euler beam model is derived using the method of separation of variables. A numerical analysis method is proposed to solve the transcendental frequency equation for the continuous change of the frequency with $k_v$ and $k_r$. Then the mode shape functions are given. Finally, effects of $k_v$ and $k_r$ on free vibration characteristics of the beam with different slenderness ratios are calculated and analyzed. The results indicate that the effects of $k_v$ are larger on higher-order free vibration characteristics than on lower-order ones, and the impact strength decreases with slenderness ratio. Under a relatively larger slenderness ratio, the effects of $k_v$ can be neglected for the fundamental frequency characteristics, while cannot for higher-order ones. However, the effects of $k_r$ are large on both higher- and lower-order free vibration characteristics, and cannot be neglected no matter the slenderness ratio is large or small.

An efficient modeling method for open cracked beam structures (열린 균열이 있는 보의 효율적 모델링)

  • Kim, M.D.;Choi, S.H.;Hong, S.W.;Lee, C.W.
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.11b
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    • pp.725-730
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    • 2002
  • This paper presents an efficient modeling method for open cracked beam structures. An equivalent bending spring model is introduced to represent the structural weakening effect in the presence of open cracks. The proposed method adopts the exact dynamic element method (EDEM) to avoid the difficulty and numerical errors in association with re-meshing the structure. The proposed method is rigorously compared with a commercial finite element code. Experiments are also performed to validate the proposed modeling method. Finally, a diagnostic scheme for open cracked beam structures is proposed and demonstrated through a numerical example.

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Analytical and Experimental Study for Development of Composite Coil Springs (복합재 코일스프링 개발을 위한 수치해석 및 실험적 연구)

  • Oh, Sung Ha;Choi, Bok Lok
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.38 no.1
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    • pp.31-36
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    • 2014
  • This paper shows the feasibility of using carbon-fiber-reinforced polymer (CFRP) composite materials for manufacturing automotive coil springs. For achieving weight reduction by replacing steel with composite materials, it is essential to optimize the material parameters and design variables of the coil spring. First, the shear modulus of a CFRP beam model, which has $45^{\circ}$ ply angles for maximum torsional stiffness, was calculated and compared with the test results. The diameter of the composite spring was predicted to be 17.5 mm for ensuring a spring rate equal to that when using steel material. Finally, a finite element model of the composite coil spring with $45^{\circ}$ ply angles and 17.5 mm wire diameter was constructed and analyzed for obtaining the static spring rate, which was then compared with experimental results.

Calibration of Parameters for Predicting Hysteretic Behavior of Diagonally Reinforced Concrete Coupling Beams (반복하중을 받는 대각보강 콘크리트 연결보의 이력거동 예측을 위한 매개변수 결정방법)

  • Koh, Hyeyoung;Han, Sang Whan;Heo, Chang Dae;Lee, Chang Seok
    • Journal of the Earthquake Engineering Society of Korea
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    • v.21 no.6
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    • pp.303-310
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    • 2017
  • The coupled shear wall system with coupling beams is an efficient structural system for high-rise buildings because it can provide excellent ductility and energy dissipation to the buildings. The objective of this study is to simulate the hysteretic behavior of diagonally reinforced concrete coupling beams including pinching and cyclic deteriorations in strength and stiffness using a numerical model. For this purpose, coupling beams are modeled with an elastic beam element and plastic spring element placed at the beam ends. Parameters for the analytical model was calibrated based on the test results of 6 specimens for diagonally reinforced concrete coupling beams. The analytical model with calibrated model parameters is verified by comparing the hysteretic curves obtained from analysis and experimental tests.