FINITE ELEMENT MODELLING OF INFINITE EULER BEAMS ON KELVIN FOUNDATIONS EXPOSED TO MOVING LOADS IN CONVECTED CO-ORDINATES
✍ Scribed by L. ANDERSEN; S.R.K. NIELSEN; P.H. KIRKEGAARD
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 443 KB
- Volume
- 241
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
The paper deals with the "nite element method (FEM) solution of the problem with loads moving uniformly along an in"nite Euler beam supported by a linear elastic Kelvin foundation with linear viscous damping. Initially, the problem is formulated in a moving co-ordinate system following the load using a Galilean co-ordinate transformation and subsequently the analytical solution to the homogeneous beam problem is shown. To be used in more complicated cases where no analytical solutions can be found, a numerical approach of the same problem is then suggested based on the FEM. Absorbing boundary conditions to be applied at the ends of the modelled part of the in"nite beam are derived. The quality of the numerical results for single-frequency, harmonic excitation is tested by comparison with the indicated analytical solution. Finally, the robustness of the boundary condition is tested for a Ricker pulse excitation in the time domain.
2001 Academic Press
Hence, in the convected co-ordinate description, the equation of motion for an Euler beam supported by a Kelvin foundation is found to be
Here use has been made of the fact that the displacement "eld is identical in "xed and moving co-ordinates, i.e., u(x, t)"u(X, t), as long as x and X describe the same material point, which will be the case when equation (3) is applied.
3. DISPLACEMENT FIELD FOR HARMONIC EXCITATION
The load is assumed to vary harmonically with time at the circular frequency , thereby giving rise to harmonic bending waves in the beam that may or may not propagate as