Numerical solution of the problem of axisymmetric free vibrations of a cylinder from continuously inhomogeneous material with in the spline-approximation method
DOI:
https://doi.org/10.15407/dopovidi2015.09.039Keywords:
3-D theory of elasticity, continuously inhomogeneous material, hollow cylinder of finite length, natural vibrations, the method of spline-collocationAbstract
On the base of 3-D theory of elasticity, a problem of natural vibrations of a hollow cylinder of finite length made of a continuously inhomogeneous material is considered. The original partial equations of the theory of elasticity, using the spline-approximation and collocation, are reduced to the problem for the systems of ordinary differential equations of high order.The problems is solved by the steady-state numerical method of discrete orthogonalization with incremental search. The calculation results for the frequencies of vibrations are presented in the case of cylinders made of FGM, which are compositions of stainless steel and nickel, for some types of boundary conditions at the ends for different values of temperature.
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