icdas

It is seen that the ST2 and ST3 modes differ in the two
systems. In the released girder in the ST2 mode the main
span cables vibrate clearly in two nodes, Figure 2.7c.
Moreover, in the ST3 mode at the released girder the
side span cables vibrate more than the corresponding
cables in the fixed girder. The frequencies are computed
by the analytical method (AM) and compared to FEM
results,
[00,0].

The tendency of the cable vibration that couples to the
lateral mode is also indicated, but the lateral
displacements are much more insignificant compared to
the vertical displacements, seen from the FEM graphic.

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Analytical method vs. FEM (calculation of natural frequencies)

The vibration of the main span cable and the side span cable with the following assumptions can illustrate the natural mode shapes and frequencies of a suspension bridge:

· No pylon flexural stiffness, i.e. the pylon tops are replaced by the

longitudinal moveable support joints.

· No flexural stiffness of the stiffening girder taking into account the

vertical modes.

· The small lateral translations of the cables due to the torsional modes

of the girder are omitted.

· The status supports of the stiffening girder do not refer to the equation

of the cable motion.

Based on these assumptions, the obtained torsional frequencies (lowest modes) are about 10 % lower than the values from the suspension bridge including all members and elements (by FEM design). Therefore the predicted critical wind velocity at flutter lowers, and the assumptions are on the safe side.

The six first SV, ASV, ST and AST frequencies are listed in Table 2.9.

Table 2.9 : Natural frequencies
Vertical modes (2D model)						Torsional modes (3D model)
	FEM		AM	Dev.		FEM		AM	Dev.
	mode	[rad/s]	[rad/s]	[%]		mode	[rad/s]	[rad/s]	[%]
SV1 ASV1 SV2 ASV2 SV3 ASV3	2 3 8 10 12 19	0.404 0.432 0.630 0.842 0.953 1.264	0.402 0.428 0.631 0.855 0.987 1.283	0.5 0.9 0.2 1.5 3.6 1.5	ST1 AST1 ST2 ST3 AST2 AST3	8 13 17 22 30 46	1.276 1.673 1.932 2.626 3.482 5.202	1.131 1.590 2.097 2.416 3.180 4.770	11.4 5.0 8.5 8.0 8.7 8.3

The vertical frequencies are computed by the 2D input where the flexural stiffness of the girder is neglected (depth-to-span ratios of 1/625). The mass per unit span of the bridge is located on the cable elements (one half of the girder plus one cable). The torsional frequencies are computed by the 3D input where the torsional stiffness of the girder converts to the thickness of the plate elements. The girder mass and the cable mass are located on the corresponding elements. These assumptions are made to go with the analytical assumptions.
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ICDAS • Hans Erik Nielsens Vej 3 • DK-3650 Ølstykke • E-mail: th@icdas.dk • Tel.: +45 29 90 92 96 • CVR no.: 34436169