Generalized formula for estimating the oscillation frequency response of a cantilever bar with point masses

Abstract

This paper presents a study of natural oscillations of a cantilever bar with five point masses with variable geometric and stiffness parameters (distances between locations of the masses, coefficients of variability of the bending stiffness of the bar sections). Using the exact method of forces based on the Mohr formula, there have been obtained expressions in general form for calculating the main unit coefficients of the secular equation, which makes it possible to perform calculations and to determine the oscillation frequency response of natural oscillations with a wide range of changes in the initial parameters of the physical and geometric state of cantilever bars. A numerical example has been given to illustrate the proposed theoretical approaches. The results have been compared with the results based on calculating a similar can tilever bar with one( reduced by masses) degree of freedom. A graphical dependence of the oscillation frequency response value on changing the value of the bending stiffness along the length of the cantilever bar gas been obtained. The theoretical provisions and applied results presented in the work will be widely used both in the practical design of bar systems and in scientific research in the field of mechanics of a deformable solid body.