Free axisymmetric vibrations of finite-length hollow cylinder made from functionally graded material (Q2812891)

The authors consider free vibrations problem for inhomogeneous finite-length hollow cylinders made from functionally graded materials under different boundary conditions at the ends. The material elastic properties vary continuously in radial direction. For the solution of the problem a numerical-analytical method is proposed. The spline approximation and collocation methods are used to reduce the initial elasticity theory problem in partial derivatives to the boundary value problem for high-order system of ordinary differential equations with respect to the radial coordinate. The obtained one-dimensional problem is solved by the stable numerical method of discrete orthogonalization combined with the method of step-by-step search.