Analytical Solutions for Magneto-Electro-Elastic Beams Under Uniform or Linear Electric and Magnetic Potential

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 of 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 useful for study of other problems relating to more complicated loads and boundary conditions by the superposition principle.