Free lateral vibration analysis of inhomogeneous beams under various boundary conditions

Authors

1 Young Researchers and Elite Club, South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Assis. Prof., Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran

Abstract

In this paper, free lateral vibration of exponentially functionally graded beams is studied. For these inhomogeneous axial beams, characteristic equations in closed form are derived under various boundary conditions. The frequency and characteristic equations convert to analytical classical Euler-Bernoulli beams equations with ignoring gradient index. In addition, variation of mode shapes of the structure in terms of gradient parameter is demonstrated and compared with isotropic materials. In order to comparison and validation, the obtained results were compared with other available references. The results show that the natural frequency of the beams and mode shapes of the systems are strongly dependent to end conditions and gradient index. Furthermore, for functionally graded beams, there exists a critical frequency which leads to jump phenomenon in frequency spectrum so that harmonic vibration occurs in frequencies higher than the critical value and in frequencies lower than the critical value or pseudo-frequency, non-propagating fields occur. This feature does not exist in homogeneous beams. The presented results can be used for beams with exponentially decaying width and constant thickness. Moreover, the minimum frequency of the considered systems is helpful for engineers to design optimum non-uniform and nonhomogeneous structures.

Keywords

Main Subjects

References

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Journal of Solid and Fluid Mechanics
Volume 8, Issue 3
October 2018
Pages 123-135

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