• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1996.04a
• /
• pp.111-118
• /
• 1996

Dynamic load models which show the practical behavior of truss bridge subjected to moving train load are presented. Three basically approaches are available for evaluating structural response to dynamic effects : moving force, moving mass, and influence moving force and mass. Simple warren truss bridge model is selected in this research, and idealized lumped mass system, modelled as a planar structure. In the process of dynamic analysis, the uncoupled equation of motion is derived from simultaneous equation of the motion of truss bridge and moving train load. The solution of the uncoupled equations of motion is solved by Newmark-$\beta$ method. The results show that dynamic response of moving mass and static analysis considering the impact factor specified in the present railway bridge code was nearly the same. Generally, the dynamic response of moving force is somewhat greater than that of moving mass. The dynamic load models which are presented by this study are obtained relatively adequate load model when apply to a truss bridge.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.21 no.3
• /
• pp.271-279
• /
• 2011

In this study, the dynamic analysis of a beam is analyzed by using the finite element method when the beam has moving mass and axial load. To consider the contact force between the moving mass and beam, coupled nonlinear equations of contact dynamics are derived, and then the weak form for the finite element method is established. The finite element computer programs based on the Lagrange multiplier method are developed to compute the contact force. Furthermore, a variety of simulations are performed for various design parameters such as moving mass velocity, compressive axial load and tension load. Finally, relations between the dynamic response and contact force are also discussed.

• Interaction and multiscale mechanics
• /
• v.5 no.2
• /
• pp.105-114
• /
• 2012

The study of rigid roadway pavement under dynamic traffic loads with variable velocity is investigated in this paper. Rigid roadway pavement is modeled as a rectangular damped orthotropic plate supported by elastic Pasternak foundation. The boundary supports of the plate are the steel dowels and tie bars which provide elastic vertical support and rotational restraint. The natural frequencies of the system and the mode shapes are solved using two transcendental equations, obtained from the solution of two auxiliary Levy's type problems, known as the Modified Bolotin Method. The dynamic moving traffic load is expressed as a concentrated load of harmonically varying magnitude, moving straight along the plate with a variable velocity. The dynamic response of the plate is obtained on the basis of orthogonality properties of eigenfunctions. Numerical example results show that the velocity and the angular frequency of the loads affected the maximum dynamic deflection of the rigid roadway pavement. It is also shown that a critical speed of the load exists. If the moving traffic load travels at critical speed, the rectangular plate becomes infinite in amplitude.

• Structural Engineering and Mechanics
• /
• v.52 no.1
• /
• pp.173-203
• /
• 2014

The cross-section warping due to the passage of high-speed trains can be a relevant issue to consider in the dynamic analysis of bridges due to (i) the usual layout of railway systems, resulting in eccentric moving loads; and (ii) the use of cross-sections prone to warping deformations. A thin-walled beam formulation for the dynamic analysis of bridges including the cross section warping is presented in this paper. Towards a numerical implementation of the beam formulation, a finite element with seven degrees of freedom is proposed. In order to easily consider the compatibility between elements, and since the coupling between flexural and torsional effects occurs in non-symmetric cross-sections due to dynamic effects, a single axis is considered for the element. The coupled flexural-torsional free vibration of thin-walled beams is analysed through the presented beam model, comparing the results with analytical solutions presented in the literature. The dynamic analysis due to an eccentric moving load, which results in a coupled flexural-torsional vibration, is considered in the literature by analytical solutions, being therefore of a limited applicability in practice engineering. In this paper, the dynamic response due to an eccentric moving load is obtained from the proposed finite element beam model that includes warping by a modal analysis.

• Coupled systems mechanics
• /
• v.3 no.3
• /
• pp.247-265
• /
• 2014

This article discusses the dynamic response of Bernoulli-Euler straight beam with angular elastic supports subjected to moving load with variable velocity. A new engineering approach for determination of the dynamic effect from the moving load on the stressed and strained state of the beam has been developed. A dynamic coefficient, a ratio of the dynamic to the static deflection of the beam, has been defined on the base of an infinite geometrical absolutely summable series. Generalization of the R. Willis' equation has been carried out: generalized boundary conditions have been introduced; the generalized elastic curve's equation on the base of infinite trigonometric series method has been obtained; the forces of inertia from normal and Coriolis accelerations and reduced beam mass have been taken into account. The influence of the boundary conditions and kinematic characteristics of the moving load on the dynamic coefficient has been investigated. As a result, the dynamic stressed and strained state has been obtained as a multiplication of the static one with the dynamic coefficient. The developed approach has been compared with a finite element one for a concrete engineering case and thus its authenticity has been proved.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.23 no.11 s.170
• /
• pp.2058-2066
• /
• 1999

The present paper proposes a new dynamic analysis method for multi-span Timoshenko beam structures supported by joints with damping subject to moving loads. An exact dynamic element matrix method is adopted to model Timoshenko beam structures. A generalized modal analysis method is applied to derive response formulae for beam structures subject to moving loads. The proposed method offers an exact and closed form solution. Two numerical examples are provided for validating and illustrating the proposed method. In the first numerical example, a single span beam with multiple moving loads is considered. A dynamic analysis on a multi-span beam under a moving load is considered as the second example, in which the flexibility and damping of supporting joints are taken into account. The numerical study proves that the proposed method is useful for the vibration analysis of multi-span beam-hype structures by moving loads.

• Composites Research
• /
• v.16 no.6
• /
• pp.23-32
• /
• 2003

Applications of advanced composite material in construction field are tending upwards and development of all composite material bridges is making progress rapidly in home and abroad due to their high strength to weight ratio. This paper formulated the dynamic responses of the laminated composite structures subjected to moving load and analyzed the various dynamic behaviors using the finite element method. The nondimensionalized natural frequencies of a simply supported square-laminated composite plate are considered for verifications. Mode superposition and Newmark direct integration method are applied for moving load analysis. For structural models, dynamic magnification factor calculated for various velocities of the moving load and displacements characteristics of laminated composite structures due to the moving load are investigated theoretically Numerical results are presented to study the effects of lamination scheme, stacking sequence, and fiber angle for laminated composite structures during moving load. The various results on moving load and lamination through numerical analysis will present an important basic data for development and grasp the behavior of all composite material bridges.

• Structural Engineering and Mechanics
• /
• v.91 no.6
• /
• pp.567-581
• /
• 2024

In this paper, an effort is made to present a detailed analysis of dynamic behavior of functionally graded carbon nanotube-reinforced pipes under the influence of an accelerating moving load. Again, the material properties of the nanocomposite pipe will be determined by following the rule of mixtures, considering a specific distribution and volume fraction of CNTs within the pipe. In the present study, temperature-dependent material properties have been considered. The Navier-Stokes equations are used to determine the radial force developed by the viscous fluid. The structural analysis has been carried out based on Reddy's higher-order shear deformation shell theory. The equations of motion are derived using Hamilton's principle. The resulting differential equations are solved using the Differential Quadrature and Integral Quadrature methods, while the dynamic responses are computed with the use of Newmark's time integration scheme. These are many parameters, ranging from those connected with boundary conditions to nanotube geometrical characteristics, velocity, and acceleration of the moving load, and, last but not least, volume fraction and distribution pattern of CNTs. The results indicate that any increase in the volume fraction of CNTs will lead to a decrease in the transient deflection of the structure. It is also observed that maximum displacement occurs with an increase in the load speed, slightly delayed compared to decelerating motion.

• Coupled systems mechanics
• /
• v.12 no.1
• /
• pp.83-102
• /
• 2023

First introduced in 2016, the dynamic foundation model is an interesting topic in which the foundation is described close to reality by taking into account the influence of the foundation mass in the calculation of oscillation and is an important parameter that should be considered. In this paper, a follow-up investigation is conducted with the object of the Mindlin plate on a nonlinear dynamic foundation under moving loads. The base model includes nonlinear elastic springs, linear Pasternak parameters, viscous damping, and foundation mass. The problem is formulated by the finite element analysis and solved by the Newmark-β method. The displacement results at the center of the plate are analyzed and discussed with the change of various parameters including the nonlinear stiffness, the foundation mass, and the load velocity. The dynamic response of the plate sufficiently depends on the foundation mass.

• Steel and Composite Structures
• /
• v.11 no.1
• /
• pp.59-76
• /
• 2011

Dynamic analysis of an embedded single-walled carbon nanotube (SWCNT) traversed by a moving nanoparticle, which is modeled as a moving load, is investigated in this study based on the nonlocal Timoshenko beam theory, including transverse shear deformation and rotary inertia. The governing equations and boundary conditions are derived by using the principle of virtual displacement. The Galerkin method and the direct integration method of Newmark are employed to find the dynamic response of the SWCNT. A detailed parametric study is conducted to study the influences of the nonlocal parameter, aspect ratio of the SWCNT, elastic medium constant and the moving load velocity on the dynamic responses of SWCNT. For comparison purpose, free vibration frequencies of the SWCNT are obtained and compared with a previously published study. Good agreement is observed. The results show that the above mentioned effects play an important role on the dynamic behaviour of the SWCNT.