Green's tensors and lattice sums for electrostatics and elastodynamics

We present expressions for the Green's tensors in terms of lattice sums for general two–dimensional arrays in both elastostatics and elastodynamics. We represent the lattice sums in rapidly convergent forms by Fourier transform methods. We compare the static lattice sums with recently published highly accurate values for square arrays. We also establish Rayleigh identities for elastostatic and elastodynamic problems, generalizing previous work in electrostatics and electromagnetism. The Rayleigh identities may be used in studies of phononic band gaps.

我们给出了在弹性静力学和弹性动力学中一般二维阵列的格林张量用晶格求和表示的表达式。我们通过傅里叶变换方法将晶格求和表示为快速收敛的形式。我们将静态晶格求和与最近发表的正方形阵列的高精度值进行了比较。我们还为弹性静力学和弹性动力学问题建立了瑞利恒等式，推广了先前在静电学和电磁学中的工作。瑞利恒等式可用于声子带隙的研究。