Analytical Solutions to Density Functionally Graded Piezoelectric Cantilever Beams

In this paper, the general solution of the two-dimensional piezoelectric media expressed with three harmonic displacement functions is given at first in the case of distinct eigenvalues. Then, the expressions of specific solutions of piezoelectric plane problems with body force are derived. Finally, a series of beam problems is solved by the trial-and-error method, including cantilever beam with body forces varying exponentially only in the z direction or depending only chi coordinate and expressed by chi polynomial. Numerical examples are given and discussed to show the significant influence of material inhomogeneity, and adopting certain value of in-homogeneity parameter lambda, C_n can optimize the mechanical-electric responses. This will be of particular importance in modern engineering design.