Tuning of a vibration absorber with shunted piezoelectric transducers

Abstract

In order to reduce structural vibrations in narrow frequency bands, tuned mass absorbers can be an appropriate measure. A quite similar approach which makes use of applied piezoelectric elements, instead of additional oscillating masses, are the well-known resonant shunts, consisting of resistances, inductances, and possibly negative capacitances connected to the piezoelectric element. This paper presents a combined approach, which is based on a conventional tuned mass absorber, but whose characteristics can be strongly influenced by applying shunted piezoceramics. Simulations and experimental analyses are shown to be very effective in predicting the behavior of such electromechanical systems. The vibration level of the absorber can be strongly attenuated by applying different combinations of resistant, resonant, and negative capacitance shunt circuits. The damping characteristics of the absorber can be changed by applying a purely resistive or resonant resistant shunt. Additionally, the tuning frequency of the absorber can be adapted to the excitation frequency, using a negative capacitance shunt circuit, which requires only the energy to supply the electric components.

An approach to determination of shunt circuits parameters for damping vibrations

“…Many authors [2][3][4][5][6][7][8][9][10][11][12][13][14] determined the parameters of an external electric circuit required for damping the specified vibration mode based on transfer functions of various kinds. It would be of considerable importance to compare the results obtained with the help of the transfer function with the results of solving the problem of natural vibrations of the structure in the proposed mathematical formulation.…”

“…where elements, respectively, and R q ; L p ; C r are the values of the inductance, resistance and capacitance of the corresponding circuit elements. For the problem of natural vibrations under zero-value boundary conditions (5,6,7), eigensolutions are sought in the following form: uðx; tÞ ¼ " uðxÞe iωt ; φðx; tÞ ¼ " φðxÞe iωt ; (14) where ω ¼ ω Re þ iω Im gives the complex natural vibration frequency, wherein ω Re corresponds to the circular natural vibration frequency, ω Im is the rate of its damping (the damping ratio of vibrations) and " uðxÞ; " φðxÞ are the natural vibration forms. Taking into account the form of solution (14), the variational equation for the problem of the natural vibrations of an electro-viscoelastic body with external electric circuits in the case of an absence of external loads takes the following form:…”

“…The analysis of literature [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] shows that, in terms of optimal damping this approach still remains the most popular one in the analysis of dynamic behaviour of systems with shunted piezoelectrics. Apart from that, there are some techniques to obtain optimal parameters of the external circuit within this approach, such as optimization by H 2 -or H ∞norms of transfer function [4,13,20,21], optimisation by equality of transfer function magnitudes [2,3,6], and optimisation by transfer function pole placement [5,6,14]. All of these lead to different optimal values of circuit parameters for the same structure, depending on choice of transfer function and optimisation criterion [2,6,13].…”

A search for optimal parameters of resonance circuits ensuring damping of electroelastic structure vibrations based on the solution of natural vibration problem

“…The analysis of the literature showed that in terms of efficiency of finding the appropriate parameters for external circuits providing passive vibration damping, this approach is still most popular when analyzing the dynamic behavior of electroelastic systems with external electric circuits. In this case, the optimal values of the external circuit parameters estimated on the basis of the transfer functions can be obtained by different ways, for example, by optimizing the transfer functions with respect to 2  -or  -norms [8,17], assuming the equality of amplitudes of transfer functions at the characteristic intersection points of curves [2,6,10], using the technique for placing the poles of the transfer function ( pole placement technique) [9][10]18], etc. The result of all these peculiarities is that, depending on the ways of constructing the transfer function and selecting the optimization criterion, the optimal parameters of the external circuit parameters can take different values [2,10,17].…”

Passive, Adaptive, Active Vibration Control, and Integrated Approaches

“…By using active circuits to realize negative capacitances, a broad adaptation frequency range can be realized. However, the active circuits have to be designed with respect to the high voltages that occur at the piezoelectric elements, which still remain a challenge [19].…”