Spectral Element Analysis of Non-stationary Wind …
467
s 44 = k(cos(k L) sinh(k L) − sin(k L) cosh(k L))
(15)
Using SEM for beam elements, very accurate results are obtained [22–24]. As in
FEM [25], local matrices form a global matrix.
3 Numerical Analysis
Experiments were performed in situ, during the maintenance period of the transmission line. The conductor was aluminium conductor steel reinforced type (ACSR),
and according to technical data sheet, it had weight per unit length m = 0.707 kg/m
and nominal diameter D = 22 mm. The span length of the conductor is 213 m. The
elasticity module was E = 74 GPa and density ρ = 2700 kg/m
3 .
3.1 Natural Vibrations
On the basis of the formulas presented in (11–15), it is possible to obtain the frequency
response function (FRF) of the overhead transmission conductor. For the numerical
tests, it is assumed a pinned–pinned boundary condition.
Once, the structure is excited with a unitary force we can expect that the resonance
picks are close to the natural frequency of the system. Figure 2a, b shows the FRF
for simulations measured at point L 1 = 33 m from the node. For the purpose of the
numerical simulation, it is assumed the circular area of the conductor A = 262 mm
2
and tension force of T = 100 kN. The zoom image at 0–20 Hz frequency band to
better visualization of the firsts resonance pick is shown in Fig. 2b. Time history
natural vibration is shown in Fig. 2c.
3.2 Wind Vibrations
In the spectral analysis, the wind force acting on the overhead transmission line is
determined by the expression:
F =
1
2
ρV
2 A ref C
(16)
where ρ = 1.25 kg/m
3 , V is the wind speed, A ref is the reference area of the
transmission line (diameter x length), C is the aerodynamic coefficient, equal to
2, according to Eurocode 1: Wind actions on structures, EN 1991-1-4 [26]. The
wind speed signal, numerically generated with maximal amplitudes measured in the
laboratory tests performed in the wind tunnel, is shown in Fig. 3.
467
s 44 = k(cos(k L) sinh(k L) − sin(k L) cosh(k L))
(15)
Using SEM for beam elements, very accurate results are obtained [22–24]. As in
FEM [25], local matrices form a global matrix.
3 Numerical Analysis
Experiments were performed in situ, during the maintenance period of the transmission line. The conductor was aluminium conductor steel reinforced type (ACSR),
and according to technical data sheet, it had weight per unit length m = 0.707 kg/m
and nominal diameter D = 22 mm. The span length of the conductor is 213 m. The
elasticity module was E = 74 GPa and density ρ = 2700 kg/m
3 .
3.1 Natural Vibrations
On the basis of the formulas presented in (11–15), it is possible to obtain the frequency
response function (FRF) of the overhead transmission conductor. For the numerical
tests, it is assumed a pinned–pinned boundary condition.
Once, the structure is excited with a unitary force we can expect that the resonance
picks are close to the natural frequency of the system. Figure 2a, b shows the FRF
for simulations measured at point L 1 = 33 m from the node. For the purpose of the
numerical simulation, it is assumed the circular area of the conductor A = 262 mm
2
and tension force of T = 100 kN. The zoom image at 0–20 Hz frequency band to
better visualization of the firsts resonance pick is shown in Fig. 2b. Time history
natural vibration is shown in Fig. 2c.
3.2 Wind Vibrations
In the spectral analysis, the wind force acting on the overhead transmission line is
determined by the expression:
F =
1
2
ρV
2 A ref C
(16)
where ρ = 1.25 kg/m
3 , V is the wind speed, A ref is the reference area of the
transmission line (diameter x length), C is the aerodynamic coefficient, equal to
2, according to Eurocode 1: Wind actions on structures, EN 1991-1-4 [26]. The
wind speed signal, numerically generated with maximal amplitudes measured in the
laboratory tests performed in the wind tunnel, is shown in Fig. 3.