【摘要】 将一维声子晶体的原胞简化为有限多个自由度的弹簧振子结构,在辛对偶变量体系下探讨晶格振动,引入辛数学方法确定波矢与本证值的色散关系。通过本证值计数法计算特征频率,从而得到禁带区间。与传统集中质量法相比,该算法的计算结果与之吻合很好,且提高了计算精度和计算效率,更重要的是在低频处收敛性更好。更多还原

【Abstract】 The unit cell of one-dimensional phononic crystal was reduced to a spring-mass structure with limited number of degrees of freedom.The lattice vibrations were investigated in agreement with the dual variables system,and the dispersion relation was obtained by the symplectic mathematical method.Furthermore,the eigenfrequency was given by using the Wittrick-Williams algorithm,thus the band gap was obtained.Comparing the results calculated by the present method with those by the traditional lumped-mass method,it is obvious that there is a good agreement.However,the former is capable of improving the calculation accuracy and computational efficiency,and more importantly,is of better convergence.更多还原