Design of dynamic absorbers to control the flexural resonant vibration of structures characterized by multiple natural modes

Abstract

Dynamic Vibration Absorber (DVA) design methods based on one vibration mode have poor performance on controlling the resonant vibrations of complex flexible structures. A mathematical formulation for the DVA design which is suitable for suppressing the structural vibration characterized by multiple natural modes is proposed. An Excitation-Dependent Representative Basis (EDRB) for the structural vibration response characterized by multiple natural modes is derived via the dimensional reduction method proposed in modal space, based on which the DVA design method for one vibration mode can be directly used for the case when the vibration of structures is characterized by multiple natural modes. A new relationship between the optimal design of DVAs on a single-degree-of-freedom system and that on a single-mode system is also established, which enables the fixed-points theory or min-max optimization method to be directly applied on the DVA design for complex flexible structures with the derived EDRB. Numerical simulation on a simply-supported square plate is firstly conducted to verify the proposed method. Results show that the proposed method has better performance on vibration suppression than the existing method when the structural vibration is characterized by natural modes associated with the same natural frequency. The application on a complex fairing structure is presented to prove that the proposed method can effectively control the resonant vibrations of complex flexible structures with only one optimized DVA.