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In the proposed article, a mathematical model of unsteady torsional vibrations of a conical elastic shell is developed taking into account the nonlinear relationship between stresses and deformations. Refined, physically nonlinear equations of torsional vibrations of a conical shell from a homogeneous and isotropic material are derived, from which, in a particular case, some well-known classical-type vibration equations can be obtained. An algorithm is proposed that makes it possible todoi:10.1063/5.0118846 fatcat:c4qaqzs44zcozasxsx5bzdwaiq