A concept of "hot modes" of aero-engines rotor was put forward to adapt to the design of rotor dynamics for variable speed operation of aero-engines. The "hot modes" were explained with two different models

and a procedure of rotor dynamics design under "hot modes" was developed. The ratios of critical speeds of rotor with elastic supports to those of the rotor with rigid supports were taken as design parameters for dynamic optimization of the rotor

which involved the influences of stiffness

mass of the rotor. Result shows that

when all "hot modes" are under the first mode of rotor with rigid supports

the critical speeds of the rotor should be lower than the first critical speed of the rotor with rigid supports. If the first "hot modes" under the first mode of rotor with rigid supports

and the second "hot modes" is between the first and the second modes of rotor with rigid supports

the second critical speed should be equal to the root mean square of the first and the second critical speeds of the rotor with rigid supports. Additionally

it is suggested that the residual imbalance should be kept orthogonal to the modes of the rotor with rigid supports.