Flexural wave band-gaps in phononic metamaterial beam with hybrid shunting circuits

Periodic arrays of hybrid-shunted piezoelectric patches are used to control the band-gaps of phononic metamaterial beams. Passive resistive-inductive （RL） shunting circuits can produce a narrow resonant band-gap （RG）, and active negative capacitive （NC） shunting circuits can broaden the Bragg band-gaps （BGs）. In this article, active NC shunting circuits and passive resonant RL shunting circuits are connected to the same piezoelectric patches in parallel, which are usually called hybrid shunting circuits, to control the location and the extent of the band-gaps. A super-wide coupled band-gap is generated when the coupling between RG and the BG occurs. The attenuation constant of the infinite periodic structure is predicted by the transfer matrix method, which is compared with the vibration transmittance of a finite periodic structure calculated by the finite element method. Numerical results show that the hybrid-shunting circuits can make the band-gaps wider by appropriately selecting the inductances, negative capacitances, and resistances.

An approach to determination of shunt circuits parameters for damping vibrations

This paper considers the problem of natural vibrations of a deformable structure containing elements made of piezomaterials.The piezoelectric elements are connected through electrodes to an external electric circuit,which consists of resistive,inductive and capacitive elements.Based on the solution of this problem,the parameters of external electric circuits are searched for to allow optimal passive control of the structural vibrations.The solution to the problem is complex natural vibration frequencies,the real part of which corresponds to the circular eigenfrequency of vibrations and the imaginary part corresponds to its damping rate(damping ratio).The analysis of behaviour of the imaginary parts of complex eigenfrequencies in the space of external circuit parameters allows one to damp given modes of structure vibrations.The effectiveness of the proposed approach is demonstrated using a cantilever-clamped plate and a shell structure in the form of a semi-cylinder connected to series resonant RL circuits.

Two Kinds Equal Frequency Circuits to Achieve Locally Resonant Band Gap of a Circular Plate Attached Alternately by Piezoelectric Unimorphs

A circular thin plate is proposed for vibration attenuation,which is attached alternately by annular piezoelectric unimorphs with resonant shunt circuits.Two kinds of equal frequency resonant shunt circuits are designed to achieve an integrated locally resonant（LR）band gap（BG） with a much smaller transmission factor：（1） the structure is arrayed periodically while the resonant shunt circuits are aperiodic;（2） the resonant shunt circuits are periodic while the structure is aperiodic.The transmission factor curve is calculated,which is validated by the finite element method.Dependences of the LR BG performance upon the geometric and electric parameters are also analyzed.