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研究了导波在任意梯度分布功能梯度板的频散特性.假设板的上、下表面满足应力自由边界条件,且材料参数沿板厚方向按同一函数规律变化.将功能梯度板分成若干子层,并假设各子层的材料常数均相同,以此构造带状单元.运用哈密尔顿原理,推导出导波在板中传播的特征值问题.通过求解该特征值问题,得到导波的频散特性.最后通过算例验证了本文提出方法的正确性,同时也讨论了材料参数沿板厚方向为余弦函数分布时,不同梯度参数及分层数对频散特性的影响.本文提出的方法不仅能得到导波的实频散特性,还能获得复频散特性.
The dispersion characteristics of the guided wave in a functionally graded plate with arbitrary gradient distribution are studied. Assuming that the upper and lower surfaces of the plate satisfy the stress free boundary condition and the material parameters change along the same function law along the plate thickness, the function gradient plate is divided into several sublayers , And assuming that the material constants of all the sublayers are the same, we construct the banded elements. Using the Hamiltonian principle, we derive the eigenvalue problem that the guided wave propagates in the plate. By solving this eigenvalue problem, the dispersion characteristics of the guided wave Finally, an example is given to verify the correctness of the proposed method, and the influence of different gradient parameters and number of layers on the dispersion characteristics when the material parameters are distributed along the thickness direction is discussed. The proposed method not only Get the real dispersion characteristics of guided waves, but also get complex dispersion characteristics.