Numerical Solution for Response of Beams with Moving Mass

Akin, J.E.; Mofid, Massood

doi:10.1061/(asce)0733-9445(1989)115:1(120)

Cited by 201 publications

(72 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This has necessitated the quest for accurate evaluation of the vehicle-track interaction during the passage of the heavy subsystems. Nevertheless, it appears that most of the studies [Ismail (2011), Gbadeyan and Dada (2006), Wu et al (1987), Hsu (2009), Akin and Mofid (1989), Ali et al (2013), Shahed and Mohammad (2012), Sang-Jin (2013)] in this field focus on numerical simulations. Emphatically speaking, few studies concentrate on analytical developments.…”

Section: Introductionmentioning

confidence: 99%

Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

Omolofe

Oni

2015

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

This study concerns the dynamic characteristics of a prestressed isotropic, rectangular plate continuously supported by an elastic foundation and carrying accelerating mass M. Closed form solutions of the governing fourth order partial differential equations with variable and singular coefficients are presented. For the twodimensional plate problem, the solution techniques is based on the double Fourier Finite Sine integral transformation, the expansion of the Dirac Delta function in series form, a modification of Struble's asymptotic method and the use of Fresnel sine and Fresnel cosine integrals. Numerical analyses in plotted curves are presented. The analyses reveal interesting results on the effect of structural parameters such as foundation moduli, rotatory inertia correction factor and prestressing forces on the dynamic behaviour of isotropic rectangular plate under the actions of concentrated masses moving at variable velocity. In particular it is found that the critical velocity of the travelling load which brings about the occurrence of a resonance state increases as the values of these structural parameters increase.

show abstract

Section: Introductionmentioning

confidence: 99%

Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

Omolofe

Oni

2015

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

show abstract

“…13 the displacement at the free extremity of the beam and in Fig. 14 Results presented exactly match the expected ones presented in [12].…”

Section: Effect Of the Mass Of The Loadsupporting

confidence: 76%

Transverse Vibrations in Beams Supported by a Piece-Wise Homogeneous Visco-Elastic Foundation

Dimitrovová¹,

Frýba²

Civil-Comp Proceedings

View full text Add to dashboard Cite

Transversal vibrations induced by a load moving uniformly along an infinite beam resting on a piece-wise homogeneous visco-elastic foundation are studied. Special attention is paid to the additional vibrations, conventionally referred to as transition radiations, which arise as the point load traverses the place of foundation discontinuity. The governing equations of the problem are solved by the normalmode analysis. The solution is expressed in a form of infinite sum of orthogonal natural modes multiplied by the generalized coordinate of displacement. The natural frequencies are obtained numerically exploiting the concept of the global dynamic stiffness matrix. This ensures that the frequencies obtained are exact. The methodology has restrictions neither on velocity nor on damping. The approach looks simple, though, the numerical expression of the results is not straightforward. A general procedure for numerical implementation is presented and verified. To illustrate the utility of the methodology parametric optimization is presented and influence of the load mass is studied. The results obtained have direct application in analysis of railway track vibrations induced by high-speed trains when passing regions with significantly different foundation stiffness.

show abstract

“…(5), (6), and (14), it could be seen that the interaction force F T between the moving vehicle and the beam depended on the velocity and acceleration of the vehicle and the flexibility of the beam structure. The interaction force did indeed vary with time, which could be taken as an indicator of separation.…”

Section: Non-uniform Beam Traversed By a Simple Quarter-car Modelmentioning

confidence: 99%

“…Therefore, the numerical methods have been used frequently to solve various boundary conditions and complicated cases such as variable speed moving load, multiple span beam, damping within the beam, sprung mass, et cetera. Akin and Mofid 6 developed an analytical-numerical method to determine the behavior of beams carrying a moving mass. Esmailzadeh and Ghorashi 7 analyzed the Timoshenko beam traversed by a uniform partially distributed moving mass.…”

Section: Introductionmentioning

confidence: 99%

Vibration Interaction Analysis of Non-uniform Cross-Section Beam Structure under a Moving Vehicle

Asgari¹

2016

IJAV

View full text Add to dashboard Cite

One of an engineer's concern when designing bridges and structures under a moving load is the uniformity of stress distribution. The dynamic behavior of a vehicle on a flexible support is also of great importance. In this paper, an analysis of a variable cross-section beam subjected to a moving load (such as a concentrated mass), a simple quarter car (SQC) planar model, and a two-axle dynamic system with four degrees of freedom (4DOF) is carried out. The finite element method with cubic interpolation functions is used to model the structure based on the Euler-Bernoulli beam and a direct integration method is implemented to solve time dependent equations implicitly. The effects of variation of a cross-section and moving load parameters on the deflection, natural frequencies, and longitudinal stresses of the beam are investigated. The interaction between vehicle body vibration and the support structure is also considered. The obtained results indicate that using a beam of parabolically varying thickness with a constant weight can decrease the maximum deflection and stresses along the beam while increasing the natural frequencies of the beam. The effect of moving mass inertia at a high velocity of a moving vehicle is also investigated and the findings indicate that the effect of inertia is significant at high velocities.

show abstract

Numerical Solution for Response of Beams with Moving Mass

Cited by 201 publications

References 6 publications

Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

Transverse Vibrations in Beams Supported by a Piece-Wise Homogeneous Visco-Elastic Foundation

Vibration Interaction Analysis of Non-uniform Cross-Section Beam Structure under a Moving Vehicle

Contact Info

Product

Resources

About