Алгебраический метод последовательной локализации и расчета частот свободных колебаний винтового цилиндрического стержня

Abstract

An original method for calculating the free vibration frequencies of a cylindrical helical rod is proposed. The method uses operator equations of the linearized dynamic model of the rod, allowing a unified position to consider different types of boundary conditions (eg, symmetric and asymmetric versions of securing rod ends), both specified by structure, and resulting from technological errors. We prove a theorem that allows determining a priori the direction and value of frequency shifting when changing boundary conditions. The algorithm of the method is reduced to sequentially localizing all the points of the spectrum while gradually complicating the boundary conditions.