Oscillations of a longitudinally reinforced orthotropic cylindrical shell filled with a viscous fluid

The paper is devoted to variational approach to the problem of free oscillations of a longitudinally reinforced orthotropic cylindrical shell filled with a viscous fluid. The Ostrogradskii-Hamilton variational principle has laid the basis for the devised and numerically implemented frequency equation on the shell oscillations. The actual fluid loads upon a longitudinally reinforced orthotropic cylindrical shell are determined via the linearized Navier-Stokes equation. The problem of oscillations of the reinforced by longitudinal ribs orthotropic cylindrical shell is reduced to a joint integration of fluid membrane equations, if the above conditions on the surface of their contact are observed. The contact and boundary conditions reduce the problem to a homogeneous system of linear algebraic equations of the third order. A nontrivial solution of the system of linear algebraic equations of the third order results in a transcendent frequency equation that is numerically implemented.

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