A mode localization inspired vibration control method based on the axially functionally graded design for beam structures

Abstract

Vibration control plays a vital role in engineering structures, especially for low-frequency range, because designing structures with small dimensions makes it difficult to control large-wavelength vibrations. The present study seeks another road to realize low-frequency vibration control from the view of the real vibration responses. Similar to mode shapes, deflection modes are the main distributions of vibration amplitudes on structures in low frequency. Therefore, they are also essential vibration characteristics of structures. This paper proposes an effective passive vibration control method under both non-resonant and resonant excitations based on deflection mode theory and optimal algorithm. In fact, it is just like an axially functionally graded design for structures. The equations of motion for non-uniform beam structures are formulated by Hamilton’s principle. Firstly, a desired deflection mode is artificially designed, and the beam structure is discretely divided into subunits. Then, by adjusting the thickness or elastic modulus of each subunit to make the deflection mode of the beam coincide with that of the desired one. This process is completed by the genetic algorithm (GA). After that, by experimental and simulation analyses, the deflection mode of the optimally designed beam structures coincides with that of the desired one. Therefore, the present vibration control method is verified to be correct and effective.