A negative capacitance shunt is a basic, analog, active circuit electrically connected to a piezoelectric transducer to control the vibrations of flexural bodies. The shunt circuit consists of a resistor and a synthetic negative capacitor to introduce a real and imaginary impedance on a vibrating mechanical system. The electrical impedance of the negative capacitance shunt modifies the effective modulus of the piezoelectric transducer to reduce the stiffness and increase the damping, which causes a decrease in amplitude of the vibrating structure to which the elements are bonded. To gain an insight into the electromechanical coupling and power output, the shunt and the electrical properties of the piezoelectric transducer are modeled using circuit modeling software. The power output of the model is validated with experimental measurements of a shunt connected to a piezoelectric transducer pair bonded to a vibrating aluminum cantilever beam. The model is used to select the passive components of the negative capacitance shunt to increase the efficiency and quantify the voltage output limit of the op-amp. Nomenclature(The subscripts 'p' and 'b' denote patch and beam, respectively.)E b Elastic modulus C i Capacitor on branch i C T p Patch capacitance I Current k 31 Electromechanical coupling coefficient P Real or active power Q Reactive power R i Resistance on branch i |S| Apparent power V Voltage Y SU Shunt admittance Z = 1 Y Electrical impedance Z in The input impedance of a circuit ω Angular frequency, rad s −1

The use of both shunted piezoelectric elements and periodic arrays have been investigated independently as well as used in conjunction to modify the vibration of a system. Piezoelectric patches bonded to a cantilever beam which are shunted with an active circuit, specifically a negative capacitance shunt, can control broadband flexural vibrations of a structure. Also, periodic arrays integrated into a structure allow for modification of propagating waves through the mechanical "stop-bands". The performance of a combined shunted periodic piezoelectric patch array will be analyzed here by investigating the velocity amplitude of the beam upstream and downstream of the array section, and the number of control elements in the array. The negative capacitance shunts caused a global spatial average velocity reduction of 5 dB at the modal peaks from 500 to 5000 Hz. The reduction is shown to be greater in the downstream section of the beam. Also, by increasing the number of patches in the array the attenuation of the resonances increased nonlinearly. The results show that a negative capacitance periodic control array is an effective global vibration reduction system and has the ability to localize energy near the forcing of a structure.

Periodic arrays of hybrid-shunted piezoelectric actuators are used to suppress vibrations of an aluminum plate over broad frequency bands. Commonly, piezoelectric-shunted networks are used for individual mode control, through tuned, resonant resistive/inductive circuits, and for broadband vibration attenuation, through negative impedance converters. Periodically placed resonant shunts allow for broadband reduction resulting from the attenuation of propagating waves in frequency bands which are defined by the spatial periodicity of the array and by the shunting parameters considered on the circuit. Such attenuation typically occurs at medium–high frequencies, while negative impedance converter networks are effective in reducing the vibration amplitudes of the lower modes of the structure. In this article, the combination of periodic resonant shunts and negative impedance converter networks on the same aluminum panel is studied to verify the possibility of combining the advantages of the two concepts. Both numerical and experimental investigations demonstrate that broadband attenuation is achieved in the mid–high frequency regimes due to the presence of resistive/inductive networks, while the combination with negative impedance converter circuits is responsible for amplitude reduction of the full frequency spectrum. Numerical simulations and frequency response measurements on a plate demonstrate that an attenuation region of about 1000 Hz is achieved with a maximum 8 dB vibration reduction.

Piezoelectric materials allow for the manipulation of stiffness and damping properties of host structures by the application of electrical shunting networks. The use of piezoelectric patches for broadband control of vibration using a negative impedance shunt has been shown to be an effective active control solution. The wave-tuning and minimization of reactive input power shunt selection methodologies require the use a negative capacitance. This paper shows that the two theories are comparative and obtain the same shunt parameters. The results of the theoretical shunt selection and simulation are compared to experimental results of tip vibration suppression, spatial average vibration, and reactive input power minimization.

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