Table 1 Variables used in the model.
Variables | |||
|---|---|---|---|
x | Axial coordinate of the bridge | N | Number of coils |
T | Time | A | Electromagnet area |
EIB | Bending rigidity | μ0 | Magnetic permeability of the vacuum |
ρB | Density of the bridge | u0 | Initial voltage |
f(x,t) | Electromagnetic forces, which depend on the vehicle location | i0 | Initial current |
λB | Spatial wavelength of the first mode | FE0 | Initial electromagnetic force |
FEi (t) | Electromagnetic forces (x = 0.5LB) | kp | Gap feedback coefficient |
Ω | Spatial circular frequency of the guideway irregularity | kd | Gap first feedback derivative |
S(Ω) | PSD (mm2∙m) | kep | Equivalent magnetic dynamic stiffness |
A ~ G | Spectral characteristic parameters | ked | Equivalent magnetic dynamic damping |
α2 | Interference intensity of the Gaussian white noise | ρ | Canonical transformation variate |
β | center frequency | ξB | Damping ratio of the bridge |
σ2 | Variance of the guideway irregularity, with ξ(x) = Rξ(0) | ωB | Self-frequency of the bridge |
Sξ(ω) | Spectral density of the shaping filter | R | Resistance |
mE | Mass of the maglev vehicle | −fv | Aerodynamic drop |
mB | Mass of the bridge | ξ1 (t) | Random irregularity |
yE | Vertical displacement of the electromagnets | σ(H) | Diffusion coefficient |
yB | Bridge vertical displacement | ρ | Canonical transformation variate |
LE | Magnet length | \(\delta\) | Measurement gap between the electromagnet and bridge |
+ fv | Aerodynamic lift | \({\delta }_{0}\) | Initial measurement gap |
B(t) | Unit Wiener process | H(t) | Slowly varying stochastic process |
m(H) | Drift coefficient | α1 | Canonical transformation variate |
