Research Article

Numerical Study on Propagative Waves in a Periodically Supported Rail Using Periodic Structure Theory

Table 3

Cross-sectional modes of propagative waves at the lower-bounding frequencies.

Stop bandSection group #1Section group #2
In-planeOut-of-planeIn-planeOut-of-plane

Wave A1st∼3rd--Torsion about the vertical axis1stHorizontal translation--
4th∼6thRotation of the foot--Small rotation about the longitudinal axis
2ndRotation of the foot--
Horizontal translation of the head
Bending of the web
Bending of the web3rdSame as previously mentioned (with larger amplitudes)--
Out-of-phase bending of the foot ends4th∼6th--Torsions of the head and web about the vertical axis
The horizontal translation of the head diminishes with the increasing frequencyTorsion of the foot about the horizontal axis; the higher-order stop band has the larger amplitude

Wave B1st--Rotation about the horizontal axis1stVertical translation--
Negligible foot flapping
2nd∼4th--S-shape deformations2nd∼4thWith the increasing frequency, the foot flapping becomes dominant, and the vertical translation of the head diminishes--
5thVertical deformation of the web--5th--S-shape deformations
Significant foot flapping

Wave C1st--Torsion about the vertical axis1stRotation of the cross section--
Small bending of the web
2nd--Torsion of the foot about the vertical axis2ndBending of the web--
Rotation of the foot
3rd∼4th--Torsion of the head about the vertical axis3rd∼4thHigh-order bending of the web--
Torsion of the foot about the horizontal axisOut-of-phase bending of the foot ends
Horizontal translation of the head
The center of the foot is immobile

D1st∼3rd--Torsion about the vertical axis; the higher-order stop band has the larger amplitude1st∼2ndBending of the web--
3rdBending of the web--
Rotations of the head and the foot
Horizontal translation of the foot

E1stTension and compression of the web--1st--Longitudinal translation
Foot flapping
Small bending of the cross section
2nd--Longitudinal translation2ndTension and compression of the web--
Bending of the cross sectionFoot flapping
The center of the foot is immobile

F1st∼2nd--Torsion about the vertical axis1st∼2ndHigh-order bending of the web--
Out-of-phase bending of the foot ends
Rotation of the head
The center of the head is immobile

G1st--S-shape deformations1stTension and compression of the web--
Foot flapping