密度功能梯度压电悬臂梁的解析解

摘要

得到了用三个调和位移函数表达的材料特征值互不相同情况下平面压电介质通解,同时推导出压电平面有体力问题的特别解.然后,利用试凑法和叠加法研究了一系列压电梁问题解析解,包括:压电悬臂梁体力分别随z或x呈指数函数或多项式形式变化,并通过数值计算结果分析了压电材料的不均匀性的影响.%The general solution of the two-dimensional piezoelectric media expressed with three harmonic displacement functions was first given in the case of distinct eigenvalues. Then, the expressions of specific solutions of piezoelectric plane problems with body force were derived. Finally, a series of beam problems was solved by the trial-and-error method, including cantilever beam with body forces varying exponentially only in the z direction or depending only on x coordinate and expressed by x polynomial. Numerical examples were given and discussed to show the significant influence of material inhomogeneity, and adopting certain value of in-homogeneity parameters λ, Cn can optimize the mechanical-electric responses.