INFLUENCE OF THE BENDING RIGIDITY FACTOR ON VIBRATION AND INSTABILITY OF A COLUMN WITH INTERNAL CRACK

Abstract eng:
In this paper, the results of studies on transverse vibrations and instability of a geometrically nonlinear column with internal crack subjected to Euler’s load are presented. The investigated column is composed of two members. The bending rigidity stiffness between members is described by the bending rigidity ratio. The internal member consists of two elements, connected by a pin and a rotational spring of stiffness C. The rotational spring stiffness C shows the size of crack. The boundary problem has been formulated on the basis of the Hamilton's principle. Due to the geometrical nonlinearity of the system, the solution of the problem was performed by means of the perturbation method. The natural vibration frequencies were computed after obtaining the equations from the first power of the small parameter ε. The results of numerical calculation illustrate the influence of the bending rigidity factor and crack size on vibration frequency and critical loading of the system.

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