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This paper extends the traditional plane wave expansion (PWE) method to calculate the band structure of the proposed simplified model of composite locally resonant phononic crystal (LRPC) plate. Explicit matrix formulations are developed for the calculation of band structure. In order to illustrate the accuracy of the results, the band structure calculated by PWE method is compared to that calculated by finite element (FE) method. In addition, in order to reveal the bandgap properties, band structures of the “spring–mass” simplified model of stubbed-on LRPC plate, “spring–torsional spring–mass” simplified model of stubbed-on LRPC plate and “spring–torsional spring–mass” simplified model of composite LRPC plate with and without the viscidity considered are presented and investigated in detail. [ABSTRACT FROM AUTHOR]

This paper couples the plane wave expansion (PWE) and finite element (FE) methods to calculate the band structures of the semi-infinite beam-like phononic crystals (PCs) with the infinite periodicity in z -direction and finiteness in x – y plane. Explicit matrix formulations are developed for the calculation of band structures. In order to illustrate the applicability and accuracy of the proposed coupled plane wave expansion and finite element (PWE/FE) method to beam-like PCs, several examples are displayed. At first, PWE/FE method is applied to calculate the band structures of the Pb/rubber beam-like PCs with circular and rectangular cross sections, respectively. Then, it is used to calculate the band structures of steel/epoxy and steel/aluminum beam-like PCs with the same geometric parameters. Last, the band structure of the three-component beam-like PC is also calculated by the proposed method. Moreover, all the results calculated by PWE/FE method are compared with those calculated by finite element (FE) method, and the corresponding results are in good agreement. [ABSTRACT FROM AUTHOR]

Bandgap properties of the locally resonant phononic crystal double panel structure made of a two-dimensional periodic array of a spring–mass resonator surrounded by n springs ( n equals to zero at the beginning of the study) connected between the upper and lower plates are investigated in this paper. The finite element method is applied to calculate the band structure, of which the accuracy is confirmed in comparison with the one calculated by the extended plane wave expansion (PWE) method and the transmission spectrum. Numerical results and further analysis demonstrate that two bands corresponding to the antisymmetric vibration mode open a wide band gap but is cut narrower by a band corresponding to the symmetric mode. One of the regulation rules shows that the lowest frequency on the symmetric mode band is proportional to the spring stiffness. Then, a new design idea of adding springs around the resonator in a unit cell ( n is not equal to zero now) is proposed in the need of widening the bandwidth and lowering the starting frequency. Results show that the bandwidth of the band gap increases from 50 Hz to nearly 200 Hz. By introducing the quality factor, the regulation rules with the comprehensive consideration of the whole structure quality limitation, the wide band gap and the low starting frequency are also discussed. [ABSTRACT FROM AUTHOR]