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Several solutions for multimodal vibration damping of thin mechanical structures based on piezoelectric coupling have been developed over the years. Among them, piezoelectric network damping consists in using piezoelectric transducers to couple a structure to an electrical network, where the transferred electrical energy can be dissipated. In particular, the effectiveness of coupling rods, beams and plates to their analogous electrical networks has been proven. This work is the first step going towards more complex structures. After defining and experimentally validating a fully passive electrical analogous network of a simply-supported plate, the study is extended to the damping of a non-periodic plate. The non-periodicities here studied include the addition of a local mass and a variable thickness. Numerical simulations and experiments show that in these cases, a broadband damping is achieved once the piezoelectric transducers are coupled to an adequate analogous network. A finite element model of the structure coupled to a 2D non-periodic electrical network is concurrently developed and validated, which is another contribution of the present work.

In this paper, the method of electric analog synthesis is applied to design a piezo-electro-mechanical arch able to show the capacity of multimodal damping. An electric-analog circuit is designed by using a finite number of lumped elements representing the equivalent of a curved beam. Spatial and frequency coherence conditions are proven to be verified for the modes to be damped: in fact, lumped-element circuit can damp only a finite number of vibration modes. Analogous boundary conditions are ensured, so that natural frequencies and mode shapes of both the curved beam and the analog circuit are equal. The instance considered here is the vibration mitigation of a piezo-electro-mechanical arch. Having a view towards prototypical applications, all simulations consider values of physically feasible passive circuital elements. It is believed that the present results may represent a step towards the design of multi-physics metamaterials based on micro-structures exploiting the principle of multimodal damping.

Piezoelectric shunt damping offers a passive solution to mitigate mechanical vibrations: the electromechanical coupling induced by piezoelectric patches bound to the vibrating structure allows the transfer of vibration energy to an electrical circuit, where it can be dissipated in a resistive component. Among the existing passive piezoelectric shunt circuits, the resonant shunt leads to significant vibration damping if it is tuned with enough precision. However, temperature may have a strong influence on electrical parameters such as the piezoelectric capacitance and the circuit inductance. As a consequence, a temperature variation can lead to a deterioration of vibration damping performance. This paper describes how inductive components can be chosen to minimize the mistuning of the resonant shunt when temperature evolves. More specifically, inductors are made of magnetic cores whose magnetic permeability varies with temperature, which counterbalances the variations with temperature of the mechanical resonance frequency and of the piezoelectric capacitance. Experiments show the benefits of adequately choosing the magnetic material of the inductor for vibration damping of a cantilever beam. The concept of a fully passive shunt adapting to temperature variations is hence validated.

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