【作者】 黄飞；

【导师】 何锃；

【作者基本信息】 华中科技大学 ， 工程力学， 2007， 博士

【摘要】 具有周期性排列结构的复合材料被称为声子晶体,当声波或者弹性波在该结构中传播时,会形成一定的频率禁带,使得某些频率处于禁带范围内的声波或者弹性波不能在该结构中传播。对于这种周期性结构的研究具有广泛的应用价值,例如可以设计全新的减振降噪结构等。本文主要研究了以下三方面的内容:(1)采用平面波展开法对下述多种周期结构的声波(弹性波)禁带进行研究,包括1)正方形截面散射体的二维液相和固相周期结构中,考虑截面旋转时,结构中压力波(声波)和横向剪切波的传播特性和禁带的产生规律。2)在二维液相周期结构中引入了椭圆截面散射体这种新的结构形式,研究了椭圆截面长短半径的变化以及绕中心轴线旋转时,声波禁带的生成规律。3)在三维液相周期结构中引入了椭球散射体这种新的结构形式,研究了椭球半径变化时,声波禁带的生成规律。研究结果表明,组成周期性结构的各种材料的密度对声波频率禁带的影响最大,此外,在填充率保持一定的情况下,二维椭圆截面的半径和旋转角度、三维椭球散射体的半径都对声波禁带的产生有较大的影响。(2)提出了基于间接Trefftz法的波数法进行声场强度的预测。波数法将声场的动力学响应近似分解为两部分,一部分为一组精确满足齐次Helmholtz方程的通解(波函数),另一部分为外部激励产生的满足自由空间非齐次Helmholtz方程的特解。各个通解的系数可以通过采用加权余量公式,强迫该近似解在平均意义上满足边界条件来得到。通过对二维和三维非耦合稳态声场,二维耦合稳态声场和多层介质稳态声场的声压进行预测,证明了该方法的有效性,结果表明,波数法在计算的精度和收敛性方面要优于有限元和边界元方法。(3)应用波数法对有限周期性结构的声波禁带特性进行研究。通过对一维层状周期结构和二维正方形截面散射体周期结构的声压频率响应函数曲线来确定其不完全声波禁带。将波数法的结果与平面波展开法和有限元法的结果进行比较,验证该方法的有效性。更多还原

【Abstract】 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.更多还原