A three-dimensional Peano series solution for the vibration of functionally graded piezoelectric laminates in cylindrical bending

The available three-dimensional (3d) solutions reported for the analysis of functionally graded piezoelectric (fgp) laminates are based on this simplifying assumption that the fgp layer is consists of a number of homogeneous sub-layers. the accuracy of these formulations not only is dependent on the number of sub-layers but also leads to inaccurate results in the prediction of higher natural frequencies of the fgp laminates. in the present paper، a 3d peano series solution is developed for the cylindrical bending vibration of the fgp laminates. this novel formulation satisfies exactly the equations of motion، the charge equation، and the boundary and interface conditions of the continuously nonhomogeneous piezoelectric layers. the obtained solution is exact because no priori assumption for the displacement components and the electric potential along the thickness direction of fgp layers is introduced. the influences of the different functionally gradient material properties and different electric boundary conditions on the natural frequencies and mode shapes of the fgp laminate have been also studied through examples. the present solution and its obtained numerical results can be employed to assess the accuracy of different fgp laminated beam/plate theories.it can be also used for fgp vibration behavior comprehension purposes.