Polynomial solutions to piezoelectric beams (II)—Analytical solutions to typical problems

Abstract

For the orthoropic piezoelectric plane problem, a series of piezoelectric beams is solved and the corresponding analytical solutions are obtained with the trial-and-error method on the basis of the general solution in the case of three distinct eigenvalues, in which all displacements, electrical potential, stresses and electrical displacements are expressed by three displacement functions in terms of harmonic polynomials. These problems are cantilever beam with cross force and point charge at free end, cantilever beam and simply-supported beam subjected to uniform loads on the upper and lower surfaces, and cantilever beam subjected to linear electrical potential.