无限大功能梯度板中弹性导波频散特性的研究

STUDY ON DISPERSION CHARACTERISTICS OF ELASTIC GUIDED WAVES IN AN INFINITE FUNCTIONALLY GRADED PLATE

建立了无限大功能梯度板的理论模型,得到了直角坐标系下功能梯度板的几何方程。采用Rayleigh-Ritz法(RRM),引入Legendre正交多项式作为位移试函数,基于Hamilton原理获得了功能梯度板中弹性导波的频散方程。数值计算各向异性材料组成的无限大功能梯度板中相速度和群速度频散曲线,分析了不同体积分数指数N、不同入射角θ对功能梯度板中导波传播的影响。研究结果表明,当采用高阶节点数计算时,Rayleigh-Ritz法在分析导波问题上具有很好的收敛性和准确性。

In order to investigate the dispersion characteristics of elastic guided waves in an infinite functionally graded plate,this article built the theoretical analysis model for elastic guided waves of a functionally graded plate,and established the geometric equation under Cartesian coordinate system.In this paper,the Legendre orthogonal polynomial is introduced as trial functions of displacement.According to the Hamilton principle,Raleigh-Ritz Method(RRM)is applied to obtain the dispersion equation of elastic guided waves in a functionally graded plate.It is found that Raleigh-Ritz method has a great convergence and accuracy in solving guided wave propagation problems when using high-order node numbers for calculation.Raleigh-Ritz Method is not limited to homogenous plates.Phase velocity and group velocity dispersion curves of an infinite functionally graded plate composed of anisotropic materials are given,and the influences of different volume fraction indexes N and incident angleθon dispersive behavior for guided wave propagation are analyzed.