**A Unified Accurate Solution for Three-dimensional Vibration Analysis of Functionally Graded Plates and Cylindrical Shells with General Boundary Conditions**

Guoyong Jin, Zhu Su and Tiangui Ye

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62335

#### **Abstract**

Three-dimensional (3-D) vibration analysis of thick functionally graded plates and cylin‐ drical shells with arbitrary boundary conditions is presented in this chapter. The effective material properties of functionally graded structures vary continuously in the thickness direction according to the simple power-law distributions in terms of volume fraction of constituents and are estimated by Voigt's rule of mixture. By using the artificial spring boundary technique, the general boundary conditions can be obtained by setting proper spring stiffness. All displacements of the functionally graded plates and shells are ex‐ panded in the form of the linear superposition of standard 3-D cosine series and several supplementary functions, which are introduced to remove potential discontinuity prob‐ lems with the original displacements along the edge. The Rayleigh-Ritz procedure is used to yield the accurate solutions. The convergence, accuracy and reliability of the current formulation are verified by numerical examples and by comparing the current results with those in published literature. Furthermore, the influence of the geometrical parame‐ ters and elastic foundation on the frequencies of rectangular plates and cylindrical shells is investigated.

**Keywords:** Three-dimensional elasticity theory, functional graded materials, plate and cylindrical shell, general boundary conditions
