Sommerfeld effect in an oscillator with a reciprocating mass

In this paper, the dynamics of a non-ideally driven single-degree-of-freedom vibrating system will be explored in detail. The objective is to describe Sommerfeld effect in a reciprocating system. As such, the concerned vibrating system comprises a reciprocating system with all components fully enclosed within a housing/foundation. The foundation is equipped with flexible mountings that are designed to contain and isolate any large amplitude vibrations. The assembly is devoid of any inertia forces arising due to rotational imbalances. As a result, all structural vibrations are caused due to a net unbalanced reciprocating mass only. As stated earlier, the mechanism is powered by a non-ideal drive. As a result, the non-ideal source-system interaction leads to the so-called Sommerfeld effect and the associated nonlinear jump phenomenon. For suitable component parameters, the nature of jump will be first investigated analytically. For a vibrating system, a non-ideal drive may inhibit smooth passages through resonance. Apart from sustainability issues, this may severely compromise a machine’s safety and reliability aspects. To that end, the power requirement conditions for smooth transition through resonance will be derived. It is to be noted that the analytical study will exclusively pertain to steady-state solutions. As such, to inspect the transient nature of the system dynamics, the non-ideal system will be modeled with the help of bond graphs. Additionally, the mechanism will also be assembled on MSC-Adams to confirm the responses obtained from the bond graph model. The simulated responses will then be used to verify the analytical predictions.