Free vibrations of the slender nonprismatic column under the passive and active follower force directed towards the positive pole

Abstract eng:
The presented work deals with the issue of the free vibrations of slender nonprismatic column under active and passive load by the follower force directed towards the positive pole (the case of the specific load). The cross-section of the structure variable along the axis is realized by the division into prismatic segments of constant length and variable width described by the polynomial of degree I or II under the conditions of constant total length and volume. On the basis of the adopted physical model and the Bernoulli-Euler's theory, the mechanical energy of the considered column was determined. Taking into account Hamilton's principle (kinetic criterion of the stability loss), the differential equations of motion and natural boundary condition as well as the continuity conditions were obtained. The theoretical considerations and the results of the numerical simulations presented in this article allow to determine the influence of variable cross-section of the column and the geometry of structures implementing the external load on the values of natural frequencies and critical forces.

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