The dynamic behavior of a cantilever beam coupled to a non-ideal unbalanced motor through numerical and experimental analysis

An excitation force that is not influenced by the system state is said to be an ideal energy source. In real situations, a direct and feedback coupling between the excitation source and the system must always exist at a certain level. This manifestation of the law of conservation of energy is known as the Sommerfeld effect. In the case of obtaining a mathematical model for such a system, additional equations are usually necessary to describe the vibration sources with limited power and its coupling with the mechanical system. In this work, a cantilever beam and a non-ideal DC motor fixed to its free end are analyzed. The motor has an unbalanced mass that provides excitation to the system which is proportional to the current applied to the motor. During the coast up operation of the motor, if the drive power is increased slowly, making the excitation frequency pass through the first natural frequency of the beam, the DC motor speed will remain the same until it suddenly jumps to a much higher value (simultaneously its amplitude jumps to a much lower value) upon exceeding a critical input power. It was found that the Sommerfeld effect depends on some system parameters and the motor operational procedures. These parameters are explored to avoid the resonance capture in the Sommerfeld effect. Numerical simulations and experimental tests are used to help gather insight of this dynamic behavior.