Stress state of a rotating inhomogeneous anisotropic cylinder of variable density (Q1326114)

The stress state of a disk of constant cross section and an isotropic homogeneous cylinder rotating at constant angular velocity around the symmetry axis was considered earlier. However, in a more complex formulation (variability of the disk cross section, anisotropy and inhomogeneity of the elastic properties of the cylinder material), this problem continues to attract attention. For a rotating inhomogeneous cylinder, results have only been obtained with a simple power law of the variation of the elastic characteristics along the radius. At the same time, it remains unclear for what other laws of inhomogeneity closed solutions may be constructed. The present work addresses this problem, which is associated with the integrability of second-order linear differential equations with variable coefficients. The equations of motion are integrated in terms of elementary functions and also Pochhammer and Bessel functions. An example of the calculation is given.