线性电势和磁势边条下磁电弹性梁的解析解

The Analytical Solution for Magneto-electro-elastic Beams under Linear Electric and Magnetic Potential

对一系列的磁电弹性梁按正交磁电弹性平面问题进行了研究.首先推导了4个特征根互异情况下,所有物理量均用4个拟调和位移函数表达的通解,进而用试凑法推导出相应系列问题的精确解或解析解.这些问题有:矩形磁电弹性梁承受刚体位移、均匀电势和均匀磁势,两端自由梁承受均布电势和磁势,及悬臂梁承受线性电势和磁势等.利用叠加原理,可将本文所得到的精确解或解析解应用于有更复杂的荷载和边界条件问题的研究,此外,本文所得解可为验证各种数值计算方法提供参考依据.

For the orthotropic magneto-electro-elastic plane problem, a series of magneto-electro-elastic beams is solved and the corresponding exact or analytical solutions are obtained with the trial-and-error method on the basis of the general solution in the case of four distinct eigenvalues, in which all physical quantities are expressed by four displacement functions in terms of harmonic polynomials. These are magneto-electro-elastic rectangular beam with rigid body displacements, identical electric and magnetic potential, beams with two free ends under uniform electric potential and magnetic potential, and cantilever beam under linear electric potential and magnetic potential. The exact and analytical solutions obtained in this paper are also helpful for study of other problems relating to more complicated loads and boundary conditions by the superposition principle. Moreover, these solutions can serve as benchmarks for numerical methods such as the finite element method, the boundary element method, etc.