• 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.

• Steel and Composite Structures
• /
• v.42 no.5
• /
• pp.649-655
• /
• 2022

In presented paper, moving load problem of simply supported axially functionally graded (AFG) beam is investigated under temperature rising based on the first shear beam theory. The material properties of beam vary along the axial direction. Material properties of the beam are considered as temperature-dependent. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the moving load problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of material graduation, temperature rising and velocity of moving load on the dynamic responses ofAFG beam are presented and discussed.

• 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.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
• /
• 1998.04a
• /
• pp.277-285
• /
• 1998

This paper presents the deformation characteristics of the moving pressure plate in a balanced type vane pump that widely used automotive power steering systems. Moving pressure plate can control the clearance between rotor and plate in accordance with load pressure variation; it always guarantees that pump to have optimal volumetric efficiency. In this paper, firstly, we calculate the acting force on the pressure plate, which is used to determine the angular position and load condition for analyzing the deformation of pressure plate. Secondary, finite element method is used for the deformation analysis. As results of acting force analysis, it is found that maximum difference of forces occurs at angular position 28$\circ$ from the small arc center of cam ring and load pressure is a dominant factor to affect acting force variation. The deformation of pressure plate increases as load pressure increases. At high load pressure, the deformation of pressure plate becomes larger than the initial clearance between rotor and plate. Therefore, it is required to design the plate for controlling the deformation.

• Journal of Industrial Technology
• /
• v.19
• /
• pp.313-320
• /
• 1999

Steel railway bridge gets vibration from moving load ; additionally, this kind of moving load is going to be a sufficient reason, which causes fatigue damage to steel railway bridge. Fatigue damage and stress curve were raised by moving load depends on span length in steel railway bridge. In other words, stress curve appears index regarding every axial load in short span, but self weight lets stress curve's change decrease in proportion to increasing span length. Thereby, we have studied that how the steel railway bridge appear fatigue damage in proportion to span length of steel railway bridge. Dynamic strain was measured in 4 steel plate-girder railway bridge during the trains was passing, which is located on the line of Kyoung-chun railway. And time history response analysis has been done in order to ensure actual survey. The results of this study show the decreased of the fatigue damage in steel railway bridge according to length of span. This paper ends is bases research of fatigue design in steel railway bridges according to span length.

• Steel and Composite Structures
• /
• v.46 no.2
• /
• pp.253-261
• /
• 2023

The goal of this paper is to investigate dynamic responses of simply-supported laminated micro beams under moving load. In the considered micro-scale problem, the modified coupled stress theory which includes the length scale parameter is used. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the moving load problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of stacking sequence of laminas, fibre orientation angles and the length scale parameter on the dynamic responses of laminated micro beams are examined and discussed.

• Earthquakes and Structures
• /
• v.5 no.5
• /
• pp.589-605
• /
• 2013

The effect of dead loads on dynamic responses of a uniform elastic beam subjected to moving loads is examined by means of a governing equation which takes into account initial bending stresses due to dead loads. First, the governing equation of beams which includes the effect of dead loads is briefly presented from the author's paper (1990, 1991, 2010). The effect of dead loads is considered by a strain energy produced by conservative initial stresses caused by the dead loads. Second, the effect of dead loads on dynamical responses produced by moving loads in simply supported beams is confirmed by the results of numerical computations using the Galerkin method and Wilson-${\theta}$ method. It is shown that the dynamical responses by moving loads are decreased remarkably on a heavyweight beam when the effect of dead loads is included. Third, an approximate solution of dynamic deflections including the effect of dead loads for a uniform beam subjected to moving loads is presented in a closed-form for the case without the additional mass due to moving loads. The proposed solution shows a good agreement with results of numerical computations with the Galerkin method and Wilson-${\theta}$ method. Finally it is clarified that the effect of dead loads on elastic uniform beams subjected to moving loads acts on the restraint of the transverse vibration for the both cases without and with the additional mass due to moving loads.

• 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.

• 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.