A new approach to suppressing the Sommerfeld effect in vibrating structures

The Sommerfeld effect is a non-linear phenomenon which occurs due to the interaction between non-ideal sources of energy and a mechanical system operating in the non-stationary regime. In certain conditions, this leads to high-amplitude vibrations that may be potentially harmful to the health of the structure. Although the Sommerfeld effect is relatively well studied, control strategies specifically designed for it still lack in the literature. Therefore, this work proposes a new approach to suppressing these undesired effects, based on fuzzy Takagi-Sugeno Modeling, in a three-degree-of-freedom shear building considering the equations of motion with and without a non-linear stiffness. The results show that the vibrations can be efficiently controlled and even chaotic patterns of motion are suppressed. Practical applications involving the controller for future work are also discussed in detail.