A nonlinear piezoelectric shunt absorber with 2:1 internal resonance: experimental proof of concept

Abstract

An experimental proof of concept of a new semi-passive nonlinear piezoelectric shunt absorber, introduced theoretically in a companion article, is presented in this work. This absorber is obtained by connecting, through a piezoelectric transducer, an elastic structure to a resonant circuit that includes a quadratic nonlinearity. This nonlinearity is obtained by including in the circuit a voltage source proportional to the square of the voltage across the piezoelectric transducer, thanks to an analog multiplier circuit. Then, by tuning the electric resonance of the circuit to half the value of one of the resonances of the elastic structure, a two-to-one internal resonance is at hand. As a result, a strong energy transfer occurs from the mechanical mode to be attenuated to the electrical mode of the shunt, leading to two essential features: a nonlinear antiresonance in place of the mechanical resonance and an amplitude saturation. Namely, the amplitude of the elastic structure oscillations at the antiresonance becomes, above a given threshold, independent of the forcing level, contrary to a classical linear resonant shunt. This paper presents the experimental setup, the designed nonlinear shunt circuit and the main experimental results.

Subharmonic centrifugal pendulum vibration absorbers allowing a rotational mobility

“…Moreover, Eq. (36) shows that the subharmonic response of mode 1 is hardening but can be hardened even more or softened a little using 𝑐 𝑝 . Hence, 𝑐 𝑝 can be seen as the non-linear tuning parameter, and 𝑐 𝑝 < 0 and 𝑐 𝑝 > 0 correspond to hardened and softened tunings, respectively.…”

A nonlinear tunable piezoelectric resonant shunt using a bilinear component: theory and experiment

“…This behaviour is a characteristic of a non-symmetric nonlinearity (see the curve V nl = f (V ) in Fig. 1(b)) and suggests to investigate a 2:1 internal resonance, by tuning the electric oscillator at half the mechanical frequency (ω e ≃ ωi /2) and testing a transfer of energy from the mechanical oscillator to the electrical one, as already done using quadratic nonlinear terms in [19,20,22]. This is investigated in section 3.2.…”

“…1(a). Following [2,19,20], the displacement u(x, t) at position x in the structure and time t is truncated on one linear mode such that:…”

“…Due to the nonlinearities generated by the nonsmooth term, this tuning is expected to activate a nonlinear modal coupling through a 2:1 internal resonance. As discussed in [19,20], if quadratic nonlinear terms are present in V nl (t), the 2:1 internal resonance leads to create an antiresonance at which the amplitude of the host structure becomes independent of the forcing level, a so-called saturation phenomenon. In this section, we investigate the behavior of our system (which includes a nonsmooth nonlinearity and not a quadratic one) in the same internal resonance condition.…”

“…Another example is the so-called nonlinear tuned vibration absorber "NLTVA" introduced in [16] and realized with PE shunt theoretically [17] and experimentally [18]. Recently, a new semi-passive absorber, introduced in [19] and realized experimentally in [20], exploited a two-toone (2:1) internal resonance and a saturation phenomenon by adding a quadratic nonlinear component in a classical RL-shunt. This concept was improved to correct an unwanted detuning by adding a cubic component, as shown theoretically in [21] and experimentally in [22].…”