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. 2025 Nov 27;25(23):7242. doi: 10.3390/s25237242
ϕn(z) nth principal mode
Sn Modal mass of the nth mode
m(z) Continuous mass along the z-axis
l Total length of the shaft
P(z) Distribution function of rotor unbalance
Ps Unbalance equivalent of the sth-order mode shape.
UK Isolated unbalance at point K
Up Continuous unbalance of the rotor system
qn nth-order modal component of the unbalanced distribution
ω(t) Angular velocity of the power turbine rotor
mr Mass of the r-th disk
er Eccentricity of the r-th disk
θur Initial unbalance azimuth of the r-th disk
a(t) Angular acceleration of the power turbine rotor
α(t) Phase term
κ(t) Rotational angle of the disk
ωws Rated operating speed of the rotor
O Order
f Frequency
nrs Rotating speed