Investigation of vibration

ABSTRACT Investigation of vibration

In this paper, an analytical method is proposed to study the effect of crack and axial load on vibration behavior and stability of the cracked columns.

Using the local flexibility model, the crack has been simulated by a torsional spring with connecting two segments of column in crack location.

By solving the governing eigenvalue equation, the effects of crack  investigated.

The results show that the presence of the crack cause to reduction in natural frequencies and buckling.

As expected, when the crack depth increases, the critical buckling load decreases.

For a given crack depth, the maximum reduction in the buckling load due to the crack .

In addition, as the crack approaches to the inflection points of the column, it has no effect on the buckling load.

The accuracy of the model is validated through the experimental data reported in the literature.

Introduction

Structures undergo different changes such as formation and expansion of cracks, exhaustion, corrosion, and other probable damages.

The effects of these parameters on the structure load capacity and safety should be considered in its design.

Existence of cracks in structures may impact their mechanical and dynamical behavior, and considerably reduce the load capacity and strength of structures.

Conclusion

In this paper, an analytical method is presented to investigate the stability and vibration behavior of cracked columns under axial load.

The crack is modeled using the torsional spring with equivalent stiffness calculated from fracture mechanics theory.

Results show that tensile axial load increases the natural frequencies.

On the other hand, compressive axial load decreases the natural frequencies, and at the buckling load the first natural frequency becomes zero.

Hence, instability occurs in the system.

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