This is a theoretical, numerical, and experimental study on the vibration attenuation capability of the dynamic response of a building-like structure using a dynamic vibration absorber in cantilever flexible beam configuration, taking into account gravitational effects associated with its mass. The dynamic model of the primary vibrating structure with the passive vibration control device is obtained using the Euler–Lagrange formulation considering the flexible vibration absorber as a generalized system of one degree of freedom. The application of the Hilbert transform to the frequency response function to determine the tuning conditions between this nonlinear flexible beam vibration absorber and the primary system is also proposed. In this fashion, Hilbert transform analysis is then carried out to show that nonlinearities present in the dynamic model do not significantly contribute to the performance of the implemented absorber. Therefore, it is valid to linearize the equations of motion to obtain the tuning condition in which the flexible vibration absorber can attenuate undesirable harmonic vibrations that are disturbing to the building-like flexible structure. Thus, the present study shows that the Hilbert transform can be applied to obtain tuning conditions for other configurations of dynamic vibration absorbers in nonlinear vibrating systems. Simulation and experimental results are included to demonstrate the efficient performance of the presented vibration absorption scheme.

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