Amplitude Build-Up during Acceleration of Oscillatory Systems Possessing Several Degrees or Freedom

Rotational systems consisting of impellers, motors, and couplings possess a number of natural frequencies and are, if the damping is small, very sensitive to harmonic torque components of even small magnitudes, should the frequencies of these components coincide with any of the natural frequencies. Certain types of electric motors will deliver harmonic torque components having frequencies that vary with the motor speed. During acceleration periods these torques will excite the oscillatory system, usually on several of its natural frequencies, and amplitude build-up with accompanying dangerous stresses may occur. This paper contains an analysis of this general problem and proposes an approximate semigraphical solution of the differential equation pertaining thereto.