The Sommerfeld Effect in Rotation of a Flexible Rotor with a Limited-Power Motor

A mathematical model of a flexible rotor interacting with a limited-power motor is considered. The rotor is modeled by an Euler–Bernoulli beam with a uniformly distributed mass and a rigid unbalanced disk. The limited-power motor is characterized by a static characteristic. The equations describing joint transverse oscillations of the rotor and its rotation are presented. The solution of the problem is presented in the form of a Fredholm integral using the Green function with subsequent discretization by trapezoid method. The results obtained demonstrate the existence of the Sommerfeld effect in the first resonance region. The influence of the motor power on the rotor “sticking” upon passing the critical speed is analyzed.