Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions

Khaji, N.; Masoud, Shafiei; Jalalpour, Mohammad

doi:10.1016/j.ijmecsci.2009.07.004

Cited by 81 publications

(31 citation statements)

References 44 publications

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“…2. Comparison of the proposed method and exact solution by Khaji et al [10] show the accuracy and convergence of the method presented in this study. Table 2 for different values of the angular velocity of spin.…”

Section: Numerical Results and Discussionmentioning

confidence: 54%

See 1 more Smart Citation

Free Vibration Analysis of a Rotating Non-Uniform Blade with Multiple Open Cracks Using DQEM

Torabi¹,

Afshari²,

Heidari-Rarani³

2014

ujme

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In this paper, differential quadrature element method (DQEM) is used to analyze the free transverse vibration of a multiple cracked non-uniform Timoshenko blade rotating with a constant angular velocity. The blade's deflection is assumed to be small so that the nonlinear terms can be neglected. Governing equations, compatibility conditions at the damaged cross-sections and boundary conditions are derived and formulated by the differential quadrature rules. First, the precision of the proposed method is confirmed by the exact solutions available in the literature. Then, the effect of angular velocity value as well as the location, depth and numbers of the cracks are investigated on the natural frequencies of the blade. The advantages of the proposed method are applicable for blades with any arbitrary variable section and less time-consuming for cases with several cracks.

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Section: Numerical Results and Discussionmentioning

confidence: 54%

“…Lin [9] presented a closed-form solution for prediction of natural frequencies of a cracked simply supported Timoshenko beam. Using transfer matrix technique, Khaji et al [10] introduced a closed-form solution for crack detection problem of Timoshenko beams for the various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of a Rotating Non-Uniform Blade with Multiple Open Cracks Using DQEM

Torabi¹,

Afshari²,

Heidari-Rarani³

2014

ujme

View full text Add to dashboard Cite

show abstract

“…Here, the length of the beam is 175 mm, the non-dimensional crack-depth ratio, a c / h, is 0.5 and the shear factor k is 5/6. The results are obtained from the differential transform method and compared with the values obtained by Khaji et al [56]. That the differences are small and satisfactory can be observed in Table 9.…”

Section: Case Studymentioning

confidence: 74%

Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

Talebi

Ariaei

2014

Arch Appl Mech

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An analytical method is presented to determine the vibration characteristics of a rotating Timoshenko beam with variable cross section and intermediate flexible connections using the differential transform method. Based on the application of Timoshenko beam theory on separate beams and the compatibility requirements on each connection point, the correlations between every two adjacent spans are obtained. The formulation is extended to a point where it would be able to evaluate the cases with internal and external flexible connections. The results will be validated against those reported in the literature and compared with the ones from the modal test. A number of parametric studies are conducted to assess the stiffness of elastic connections, rotating speed, hub radius and tapered ratio effects on the beam natural frequencies and mode shapes. It is observed that by changing the stiffness of the intermediate springs, the general formulation developed here can cover a large array of problems such as cracked or intermediately constrained beams.

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“…Because of its increasing use as robot arms, machines or structures, Bruch and Mitchell (1987), Oguamanam (2003), Salarieh and Ghorashi (2006) and Ansari et al (2011) investigated the free vibrations of an Euler-Bernoulli or a Timoshenko cantilever beam with a rigid tip in the perspective of studying the behaviour of a flexible member. More recent contributions dealt with non-homogeneous or cracked beams (Li et al, 2013a;Khaji et al, 2009). The influence of the support conditions was also considered, as for example Timoshenko beams on Pasternak foundations (Calio and Greco, 2012) and beams on elastic end support (Li, 2013).…”

Section: Introductionmentioning

confidence: 99%

Identification of equivalent mechanical properties for unreinforced masonry walls

Denoël¹,

Mordant

Degée

2017

IJMRI

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Transverse vibrations of beams are an interesting topic for numerous engineering fields. The equations of motion develop under various assumptions and associate a frequency equation. This paper expresses the frequency equation for two specific models, using the Timoshenko beam theory. The first model is a typical cantilever beam with an additional mass attached to the free end. The second model considers a beam partially clamped at the base and with an elastic connection of the additional mass to the free end. The relevance of the used theory is discussed and the importance of each term of the equation is studied. These models find applications in unreinforced masonry. They are indeed fitted to identify, from white noise tests, equivalent mechanical properties of unreinforced load-bearing clay masonry walls including soundproofing devices in the perspective of modelling these elements with a macro-scale approach. Discrepancies with respect to current standards are underscored.

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Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions

Cited by 81 publications

References 44 publications

Free Vibration Analysis of a Rotating Non-Uniform Blade with Multiple Open Cracks Using DQEM

Free Vibration Analysis of a Rotating Non-Uniform Blade with Multiple Open Cracks Using DQEM

Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

Identification of equivalent mechanical properties for unreinforced masonry walls

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