Eigenfunctions of the fluid charged elastic cylindrical capillary of final length. I. The theory

The problem of natural elastic-ultrasonic oscillations of the nonuniform cylinder consisting of an elastic tube of final length filled in with fluid is theoretically discussed in the work. The problem is set in the most general way. The solution is searched in classical style by a method of separation of variables. It was shown, that the satisfaction of boundary conditions at ends of a tube is impossible within the frames of this method. The algorithm for definition of natural frequencies of a vibrating system is suggested. The results of the work can be used in cases of ultrasound application for the problems of particle coagulation.