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Determination of natural vibration frequencies of reinforced cylindrical shell

Free vibrations of a reinforced cylindrical shell filled with liquid are investigated. The case of an orthotropic shell is considered when the cord filament is placed symmetrically with respect to the meridian of the shell. The motion of a fluid is potential and is described by a wave equation. The fluid moves without separation from the walls of the cylinders. The fluid pressure is taken into account in the equations of motion of the shells, and the velocities of the fluid and the shell are equalized at the boundaries. Representing a solution in a harmonic form reduces to a system of transcendental equations. Comparison of the solutions of the problems without a liquid and with a liquid shows the dependence of the frequency of the system without a liquid at the frequency of the system with the liquid. An inverse method is proposed for solving the equation. The inverse method for solving the problem has made it possible to construct a more accurate frequency spectrum of free oscillations of the system. For some values of the system parameters, the natural frequencies of the cylinder are determined.