Free vibration analysis of a rotating single edge cracked axially functionally graded beam for flap-wise and chord-wise modes

Güler, Serkan

doi:10.1016/j.engstruct.2021.112564

Cited by 18 publications

(2 citation statements)

References 59 publications

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“…A double beam consists of two identical beams with similar material and geometric properties. Combining the classical beam theory (18) and the nonlocal theory of elasticity (22), the coupled equations for the double nanobeam can be written as:…”

Section: Governing Equationmentioning

confidence: 99%

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Analysis of free vibration of tapered cracked double nanobeams using Maclaurin series

Hossain¹,

Lellep²

2022

Eng. Res. Express

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In the study, the Maclaurin series technique is presented to analyse the vibration of cracked tapered double nanobeams. The equation of motion is derived from the Euler-Bernoulli beam theory based on the Hamiltonian principle and Eringen's nonlocal theory of elasticity. The double-nanobeam system consists of two parallel nanobeams attached by a Winkler elastic layer. Both beams are identical and their widths vary along the x-axis. A single crack is considered at the upper beam of the system. The mechanical behaviour of cracked cross-sections is simulated by the local stiffness model. According to the model, the cracked double-beam system is divided into two intact segments. A numerical investigation is carried out to scrutinize the effects of nonlocal parameters, crack severity, taper ratio, and spring constant on the vibration of the double nanobeam. The results reveal that the effects of crack depth, crack location, nonlocal parameters, taper ratio, and spring constant influence the natural frequency and dynamic response of the system significantly. This study highlights that a crack at the upper beam influences the mode shape of the upper beam as well as the intact lower beam. Numerical results have been examined with the previously published works and found a good agreement with them.

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Section: Governing Equationmentioning

confidence: 99%

“…A crack creates a discontinuity on the slope of the beam at the crack position. It can be expressed as [15,[21][22][23]:…”

Section: Cracked Beamsmentioning

confidence: 99%