Abstract
The free axisymmetric vibrations of cylindrical shells made of a functionally graded material and subject to various boundary conditions are studied using the three-dimensional theory of elasticity and the Timoshenko–Mindlin refined theory of shells. The possibility of applying the refined theory to shells made of a material with properties gradually varying over the thickness is examined. The influence of different laws of variation in mechanical properties on the dynamic characteristics of cylindrical shells during axisymmetric vibrations is studied. The numerical results presented in the form of tables and graphs are analyzed
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