理想结合两层无限大弹性板中波的传播

针对理想结合的两层无限大弹性板，研究了Lamb波的传播特性.从基本特征方程式出发，理论上导出了两组非耦合的求解截止频率的方程式；利用泰勒展开技术，给出了长波区域弯曲振动模式和伸缩振动模式的弥散曲线渐近表达式；利用行列式运算规则，得到了弥散曲线在短波区域的渐近行为.数值计算表明，两层无限大弹性板频谱曲线图上存在且只有两个分支通过原点；在相速度谱曲线上，长波区域存在且只有一个极限相速度，在短波区域有两条分支分别趋近于两种板的Rayleigh波波速.

Wave propagation in perfectly bonded two-layered infinite elastic plate

Aimed at a perfectly bounded two-layered infinite elastic plate, the wave propagation characteristics of Lamb wave were investigated. Based on the basic characteristic equation, two uncoupled equations for cutoff frequencies were obtained theoretically. By means of the Taylor expansion technique, the asymptotic expressions of the dispersion curves at the long wavelength region were derived for flexural and longitudinal vibration modes. By utilizing the determinant calculation rules, the asymptotic behaviors of the dispersion curves at the short wavelength region were studied. Numerical results show that two and only two branches in the frequency spectra of two-layered infinite elastic plate start from the original point. One and only one limitation value of the phase velocity in the phase velocity spectra exists at the long wavelength region, and two phase velocities among the branches approach to the Rayleigh waves velocities of the two plates at the short wavelength region.