Abstract
In this study, under harmonic multiple frequency excitations, the dynamic response of a cracked cantilever beam is investigated. The breathing crack model is assumed to show the nonlinear behaviour of a transverse crack. The first mode of vibration and the single degree freedom lumped system is considered to simplify the case study. Because of applying the multiple frequency excitations, the analysis is applied in a combinational resonance. Multiple time scales method is employed to solve the motion equation of the crack, and the nonlinear vibrational responses are obtained. Then, by changing the crack parameters and frequency of the excitations, the different dynamic responses of the crack are demonstrated. The proposed model shows that the crack parameters analysis in nonlinear vibration of multiple excitations could be an appropriate method to recognise the crack and the depth of the damage. Results indicate that the beam analysis under multiple frequency excitations is more sensitive than the single frequency excitation to illustrate the impacts of the crack parameters on its vibrational nonlinearity responses.
Highlights
Beam-like structures are widely used in most engineering fields
By comparing the response of multiple excitations, which is significant in Fig. 7, the result shows that excitation with a constant pre-force could increase the sensitivity of the crack analysis in nonlinear frequency curves again
Applying multiple frequency excitations lead to some combinational resonances
Summary
Beam-like structures are widely used in most engineering fields. These structures are mostly employed in mechanical, civil, and aerospace engineering. Many other researchers like Prawin and Rao (2019); Lengyel and Németh (2018); Carneiro and Ribeiro (2016); Caddemi et al (2010); Bolotin and Shipkov, (2001); Fu et al (2018); Cicirello and Palmeri (2014); Giannopoulos et al (2015); Wauer (1990); Ogam et al (2014); Liu and Barkey (2017, 2018) have considered the nonlinear effect of cracks in their studies using breathing crack model. Applying multiple frequency excitations leads to some combinational resonances instead of super-harmonic or sub-harmonic resonance One of these resonances is employed to study the cracked beam's nonlinear behaviours. We solved the equation of motion using multiple time scales method to reach the nonlinear amplitude-frequency responses of multiple frequency excitations
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