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.

The online frequency estimation of forced harmonic vibrations on a building-like structure, using a nonlinear flexible vibration absorber in a cantilever beam configuration, is addressed in this article. Algebraic formulae to compute online the harmonic excitation frequency on the nonlinear vibrating mechanical system using solely available measurement signals of position, velocity, or acceleration are presented. Fast algebraic frequency estimation can, thus, be implemented to tune online a semi-active dynamic vibration absorber to obtain a high attenuation level of undesirable vibrations affecting the main mechanical system. A semi-active vibration absorber can be tuned for application where variations of the excitation frequency can be expected. Adaptive vibration absorption for forced harmonic vibration suppression for operational scenarios with variable excitation frequency can be then performed. Analytical, numerical, and experimental results to demonstrate the effectiveness and efficiency of the operating frequency estimation, as well as the acceptable attenuation level achieved by the tunable flexible vibration absorber, are presented. The algebraic parametric estimation approach can be extended to add capabilities of variable frequency vibration suppression for several configurations of dynamic vibration absorbers.

A solution of the vibration attention problem on a flexible structure from a dynamic vibration absorption perspective is experimentally and numerically studied in this article. Linear and nonlinear dynamic vibration absorbers are properly implemented on a primary structure of n degrees of freedom through a modal decomposition analysis and using the tuning condition when the primary system has one single degree of freedom. A time-domain algebraic identification scheme for on-line modal parameter estimation of flexible structures is presented. A fast frequency estimation of harmonic excitation force is also obtained. A Hilbert transform analysis of the frequency response function for the case of nonlinear dynamic vibration absorption is introduced. In this way, influence of this particular passive nonlinear control device on system dynamic response can be determined. The proposed approach is validated on an harmonically perturbed building-like structure, which is discretized in a finite number of degrees of freedom. The flexible structure is subjected to resonant operational conditions, and coupled to a pendulum vibration absorber configured as a tuned mass damper as well as an autoparametric system.