Quasi-one-dimensional phononic crystals studied using the improved lumped-mass method: Application to locally resonant beams with flexural wave band gap
The width of band gap is calculated with lumped mass method in order to study the wave propagation of longitudinal and transverse elastic wave of one-dimensional phononic crystal. The starting and terminating frequency is analyzed by changing the filling rate, the density difference of two materials, cross-section height ratio, and the Young's modulus of the scatter.
The elastic wave band structures of the one dimensional rod phononic crystal are studied by the lumped-mass method. For the infinite periodic structure, the accuracy of numerical results is influenced by the number of discrete mass. The initial and stop frequecy of the first bandgap need different number of discrete mass to achieve calculation accuracy when two materials composed phononic crystal at different volume ratios. For the finite structure, the different arrangements make different width of the attenuation area at periodic load. The width of the bangap exhibits largely when the external load acts on the matrial with lower denstiy and elastic modulus in front of the higher density and elastic mudulus material.
In this paper, a one-dimensional bi-stage phononic band gap (PBG) structure based on double local resonant effects is presented to reduce the torsional vibration for the first time. A unit cell of the bi-stage PBG structure is composed of two harmonic LR oscillators in the radial direction, distributed periodically along the shaft. A new method, combining the transfer matrix method and the lumped-mass method is proposed to study the torsional vibration band gaps of the double PBG-like shaft theoretically and proved by the finite element method. The results show that the mid-gap frequency of the bi-stage PBG structure shaft is lower than that in the one-stage PBG shaft and the relative width of the band gaps reaches 1.3 with the average attenuation of the vibration amplitude about 40dB.
Lumped-mass method on calculation of elastic band gaps of one-dimensional phononic crystals