CA18232 – MATHEMATICAL MODELS FOR INTERACTING DYNAMIC NETWORKS -PART 3 SOMMERFEL D EFFECT IN DYNAMIC NONLINEAR SYSTEMS

Abstract

Sommerfeld effect is a universal phenomenon which appears as a result of the law of energy conservation. Arnold Sommerfeld discovered this phenomenon in 1902, while making an experiment with a cantilever beam connected with an energy source at its free end. He detected the change of energy between the source and the beam. He observed that the motor has a speed which remains the same until it suddenly jumps to a much higher value when the driving frequency is closer to the natural frequency of the beam and the drive power increases further. Its amplitude jumps to a much lower value upon exceeding a critical input power. Sommerfeld observed that the structural response of the system to which an electrical motor is connected may act like energy sink under certain conditions so that a part. The Sommerfeld effect results from the balance of the energy and it is due to the coupling between the excitation mechanism and the vibrational loads. When a dynamical system is coupled to a power source, it acts like a energy sink for which a part of the source energy is spend to deform the system rather than increasing the drive speed.