Theoretical study of Sommerfeld effect in flexible rotor shaft on structural model with two degrees of freedom

Resumo

This paper address nonlinear dynamical analysis of a foundation structure for a flexible rotor machine.
The residual unbalance will always be present in rotating equipment systems. This aspect is often not considered
during the design steps, although all real motors are non-ideal power sources. Thus, the interest in further studying
the machine-foundation and soil-foundation interactions.
Our mathematical model considers this system as non-ideal, subjected to the Sommerfeld effect, which may
manifest close to the low power machine’s resonance, with possible jumps from lower to higher frequency rotation
regimes without intermediate stable solutions. The model proposed is defined by two degrees of freedom, vertical

and horizontal translations, and an additional one associated with the rotation of the rotor shaft (intrinsic to the so-
called non-ideal systems).

The mathematical model that describes the system’s motion is derived via Lagrange equations. The solution of
this system of differential equations can in principle be solved analytically, but this can be difficult or even
impossible in some cases, particularly when these equations are nonlinear, such as the proposed model. The
numerical solution adopted here will be implemented in the Matlab®. This paper aims to analyze a little studied
problem of practical importance.