A closed-form solution of beam on viscoelastic subgrade subjected to moving loads

A closed-form solution of beam on viscoelastic subgrade subjected to moving loads is proposed in this paper. The Green's function of the beam is obtained by means of Fourier transform. Theory of linear partial differential equation is used to express the deflection of the beam in terms of the Green's function. Beam's deflection is represented as a generalized integral using inverse Fourier transform. To evaluate this generalized integral analytically, poles of the integrand are identified using the theory of algebraic equation. Every pole and its order are isolated and given in a closed form. The theorem of residue is then applied to represent the generalized integral in the form of contour integral in the complex plane. Closed-form deflection and numerical computation of distinct cases are provided as an illustration of the proposed solution.

[1]  Louis Jezequel.  Response of Periodic Systems to a Moving Load , 1981 .

[2]  Charles R. Steele,et al.  The Finite Beam With a Moving Load , 1967 .

[3]  Hideo Saito,et al.  Steady-State Vibrations of a Beam on a Pasternak Foundation for Moving Loads , 1980 .

[4]  Shirish P. Patil.  Response of Infinite Railroad Track to Vibrating Mass , 1988 .

[5]  Jan Drewes Achenbach,et al.  Dynamic Response of Beam on Viscoelastic Subgrade , 1965 .

[6]  Charles R. Steele,et al.  The Timoshenko Beam With a Moving Load , 1968 .

[7]  E. J. Yoder.  Principles of Pavement Design , 1959 .

[8]  A. L. Florence.  Traveling Force on a Timoshenko Beam , 1965 .

[9]  George G. Adams,et al.  Steady Solutions for Moving Loads on Elastic Beams With One-Sided Constraints , 1975 .

[10]  Betsy S. Greenberg,et al.  DYNAMIC RESPONSE OF LINEAR SYSTEMS TO MOVING STOCHASTIC SOURCES , 2000 .

[11]  Heow Pueh Lee,et al.  Dynamic Response of a Beam With Intermediate Point Constraints Subject to a Moving Load , 1994 .

[12]  L Fryba,et al.  VIBRATION OF SOLIDS AND STRUCTURES UNDER MOVING LOADS (3RD EDITION) , 1999 .

[13]  David Cebon,et al.  Importance of Speed and Frequency in Flexible Pavement Response , 1994 .

[14]  D. Xuejun,et al.  Dynamic analysis to infinite beam under a moving line load with uniform velocity , 1998 .

[15]  George G. Adams,et al.  A Steadily Moving Load on an Elastic Beam Resting on a Tensionless Winkler Foundation , 1979 .

[16]  Satya N. Atluri,et al.  DYNAMIC RESPONSE OF FINITE SIZED ELASTIC RUNWAYS SUBJECTED TO MOVING LOADS: A COUPLED BEM/FEM APPROACH , 1995 .

[17]  Samuel D. Conte,et al.  Elementary Numerical Analysis: An Algorithmic Approach , 1975 .