A unified modeling method for free vibration of open and closed functionally graded cylindrical shell and solid structures

摘要

In this research, a novel three-dimensional (3D) exact solution for the dynamic analyses of functionally graded (FG) cylindrical structures with arbitrary boundary conditions is put forward. In accordance with the power law distribution of constituents volume, the material properties vary consecutively along the length of the FG cylindrical structures. The theoretical model is derived based on the 3D elasticity theory. The displacements of the FG cylindrical structures are expanded as a 3D cosine series accompanied with auxiliary functions. In comparison with traditional Fourier series, these complementary functions can be helpful to remove the discontinuities of the displacements and the correlated derivatives at the edges. The advantage of the present method compared with others is that it is able to be extended to arbitrary boundary conditions without peculiar procedures. The present results are compared with those from other literature to validate its reliability. Several numerical examples are exhibited for FG cylindrical structures (open cylindrical shell, open cylindrical solid, cylindrical shell and cylindrical solid) with different types of boundary conditions (both classical and elastic boundary conditions). In addition, the effect of gradient index on the FG cylindrical structures is also reported.