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基于二维弹性理论,提出了Winkler-Paster-nak弹性地基上功能分级梁弯曲和自由振动的精确解。假设梁是正交各向异性,沿厚度方向材料性能指数变化。通过扩展状态变量为无穷三角级数,调节偏微分方程系统,最终采用状态空间法使这一问题得到解决。对几个参数的影响,如梯度指数、纵横比和功能梯度材料梁基本参数的力学性能进行研究。所提出的数值结果,为这类梁的分析提供了依据。
Based on the two-dimensional elastic theory, the exact solutions of bending and free vibration of functionally graded beams on Winkler-Paster-nak elastic foundation are proposed. The beam is assumed to be orthotropic and the material properties index changes along the thickness. By extending the state variable into an infinite triangular series, the system of partial differential equations is adjusted and finally the problem of using the state space method is solved. The influence of several parameters, such as gradient index, aspect ratio and the mechanical properties of the basic parameters of FGM beams were studied. The proposed numerical results provide the basis for the analysis of such beams.