The tuning of a simplified current blocking shunt circuit able to mitigate the vibration amplitude of multiple structural resonances is addressed in this article. The proposed strategy exploits the two-port network formalism in combination with physically motivated approximations to tune sequentially the electrical elements of the different branches of the shunt circuit. The resulting tuning method does not resort to optimization algorithms and requires only the knowledge of quantities that are easy to measure experimentally. It is demonstrated both numerically and experimentally using a piezoelectric beam.

This study presents the practical realization of a digital vibration absorber that, owing to the flexibility provided by the digital unit, synthesizes linear and nonlinear shunt circuits. The absorber, composed of a microprocessor and a current source, is connected to the host structure with piezoelectric patches. The performance of both circuits is compared experimentally for a nonlinear host structure. The superiority of a properly-tuned nonlinear absorber over its linear counterpart is validated, but the limits of the nonlinear absorber are also explored. Moreover, the accuracy of the tuning procedure and formulas is assessed through experimental parametric studies.

In this paper, an active tuned inerter damper (ATID) is proposed and theoretically analysed. The proposed device is composed of a pair of collocated reactive actuator and force sensor. It is functioned by feeding back the output of the force sensor, through both single and double integrators to drive the actuator in order to destructively interfere with the host structure vibrations. The equivalent mechanical components for the single integrator and the double integrator are identified to correspond to a dashpot and an inerter, respectively. The H 1 optimisation criterion is used for tuning the ATID, and closed-form expressions for the feedback gains are derived.

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This paper presents a tuning methodology for multiple nonlinear vibration absorbers that mitigate several nonlinear resonances simultaneously. Specifically, the objective is to maintain equal peaks in the frequency response for all controlled resonances in an as large as possible range of forcing amplitudes. Relying on an all-equal-peak design for linear regimes of motion and adopting a principle of similarity for nonlinear regimes, a semi-analytical expression of the absorber coefficients is derived using first-order harmonic balance and a series expansion of the harmonic coefficients. The proposed methodology is demonstrated numerically using two spring-mass systems.