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.

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 studies the performance of the classical integral force feedback (IFF) controller for suppressing the forced response of a single degree of freedom (SDOF) system. An ℋ∞ optimization criterion is used to derive the optimal feedback gain of the IFF controller contributed as a complement for the state of the art. This optimal gain is calculated in the closed-form based on a SDOF system which is then applied to a two degrees of freedom system to study its adaptability. It is found that the ℋ∞ optimal gain can be easily transposed into multi-degrees of freedom applications without introducing too many errors. An equivalent mechanical model is also developed to enable a straightforward interpretation of the physics behind the IFF controller.

a b s t r a c tThis paper investigates the potential of using a nonlinear positive position feedback controller for vibration mitigation of a Duffing oscillator. The proposed controller is designed based on the principle of similarity which states that anti-vibration devices should be governed by the same equations as those of the host structure. Closed-form expressions for the H 1 optimal control parameters that minimise the maximal response of the structure are firstly derived for the linear positive position feedback controller and then extended to the nonlinear counterpart. The harmonic balance method is employed to approximate the analytical solutions. Both numerical simulations and experimental validations are performed to demonstrate the proposed control strategy.vibration absorbers can be designed as a mirror of the primary structures i.e. nonlinear vibration absorbers should possess the same nonlinearities as those in the primary systems. This design principle is also referred to as the principle of similarity. It was reported that nonlinear primary systems attached with nonlinear vibration absorbers designed based on the principle of similarity behave in a similar fashion as their linear counterpart. Although this concept is promising, it may become cumbersome and expensive to realise them in practice using passive means for complex nonlinear primary systems.On the other hand, in an active approach it is attempted to introduce the desired nonlinear control forces using sensors and actuators. This may yield a nonlinear anti-vibration system that is less complex. Various types of active controllers have been investigated for vibration attenuation of nonlinear systems [16][17][18][19][20][21][22][23][24][25]. Among them, linear positive position feedback (LPPF) and nonlinear positive position feedback (NPPF) controllers are found to be particularly effective if they are aimed to damp one particular structural vibration mode. This type of controller is implemented by feeding the structural position directly to a linear or nonlinear compensator, whose output is then fed through a fixed gain positively back to drive the actuator. In this context, they would be well suited for the applications where piezoelectric sensors and actuators are employed for vibration damping. This is because the voltage from the sensor is proportional to the strain of the attached structure, which can be directly measured to drive the strain-based piezoelectric actuators. Warminski et al. [21] compared the control performance of a LPPF controller with three other controllers, namely proportional position feedback, cubic position feedback and nonlinear saturation feedback, for suppression of nonlinear composite beam vibrations. It was found that the LPPF controller is only effective for weakly nonlinear systems and the nonlinear saturation controller was concluded to be superior for the nonlinear primary structure under consideration. The performance of the LPPF controller was also investigated in [22], but on a four-degree-of-freedo...