Study On Acoustic Characteristics And Computing Methods Of Periodic Structures

The composite material with periodic structure is called Phononic crystal. It can give rise to complete acoustic band gaps within which sound and vibration are forbidden. The motivation for these studies is their numerous engineering applications such as kinds of new equipments which can attenuate the noise and vibration.The main content of this dissertation are listed as follow:Firstly, the plane wave expansion method is used to calculate the acoustic(elastic) wave band gap of some specific periodic structures, for example (1)In the two dimensional liquid or solid periodic structure with square cross section, the characteristics of the band gap structures of the longitudinal wave or transverse wave are studied respectively as the cross section rotates. (2) The elliptic cross section is introduced in the two dimensional liquid periodic structure, and the influences of the elliptical radii and the rotation angel on acoustic wave band gaps are studied. (3)The ellipsoid cross section is introduced in the three dimensional liquid periodic structure, and the influences of the ellipsoid radii on acoustic wave band gap are studied.The results show that, the material density has more influence on the acoustic wave band gap structures than the other parameters, and the radii and rotation angle of the ellipse or ellipsoid have influence also if the filling fraction is unchanged.Secondly, a wave number method is proposed to deal with the acoustic problem. The method is based on an indirect Trefftz approach, in which the dynamic pressure response variable is approximated by a set of wave functions exactly satisfying the Helmholtz equation. The set of wave functions comprise the exact solutions of the homogeneous part of the governing equations and some particular solution functions, which arise from the external excitations. The weighting coefficients of the wave functions can be obtained by enforcing the pressure approximation to satisfy the boundary conditions and it is performed by applying the weighted residual formulation. The two and three dimensional uncoupled, the two dimensional coupled and the multilayer inhomogeneous acoustic problems are calculated. Comparing with FEM and BEM, the wave number method has better accuracy and convergence.Thirdly, the wave number method is used to calculate the acoustic wave band gap of periodic structure with finite size. From the acoustic pressure distribution and the pressure frequency response function of the one dimensional finite multilayer structure and the two dimensional finite periodic structure with square scatterers, the directional acoustic wave band gap structures are obtained. Comparing the results of the wave number method with the FEM and the plane wave expansion method, the prior method shows more efficiency than the other two.