Natural modes of Bernoulli-Euler beams with symmetric cracks

Shen, M.-H. Herman; Pierre, Christophe

doi:10.1016/0022-460x(90)90707-7

Cited by 193 publications

(73 citation statements)

References 16 publications

(13 reference statements)

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“…(13) (16). The perturbative solution is obtained by extending the method originally proposed by Morassi [26] for the cracked Euler Bernoulli beam, with the assumption that the solutions for the cracked and the uncracked beams are slightly different.…”

Section: First-order Perturbative Solutionmentioning

confidence: 99%

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Natural frequencies for bending vibrations of Timoshenko cracked beams

Loya

Rubio

Fernández-Sáez

2006

Journal of Sound and Vibration

174

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The natural frequencies for bending vibrations of Timoshenko cracked beams with simple boundary conditions have been obtained. The beam is modelled as two segments connected by two massless springs (one extensional and another one rotational). This model promotes discontinuities in both vertical displacement and rotation due to bending, which are proportional to shear force and bending moment transmitted by the cracked section, respectively. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section. The problem is also solved by the perturbation method and both procedures are applied to the case of a simply supported cracked beam. The results show that the perturbation method provides simple expressions for the natural frequencies of cracked beams and it gives good results for shallow cracks. E mail address: ppfer@ing.uc3m.es (J. Ferna´ndez Sa´ez).

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Section: First-order Perturbative Solutionmentioning

confidence: 99%

“…Alternatively, simplified procedures are available with less computational effort. Among these simplified methods are those proposed by Christides and Barr [15] and Shen and Pierre [16,17]. In both cases, a crack function representing the perturbation in the stress field induced by the crack is considered.…”

Section: Introductionmentioning

confidence: 99%

Natural frequencies for bending vibrations of Timoshenko cracked beams

Loya

Rubio

Fernández-Sáez

2006

Journal of Sound and Vibration

174

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“…Further extension was made by [7] for Bernoulli-Euler beams with symmetric cracks and single-edge cracks [8]. A generalization to the theory was made by [9].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Characteristics of a Simple Blade with Breathing Crack Using Ansys Software

Waheed¹,

Mostafa²,

Jawad³

2011

WJM

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Nonlinear dynamic response represents the most important studies for structures subjected to a dynamic motion so that it provides the researcher by an excellent information especially at critical design levels. The unpredictable nonlinearity in the structure appears when damage is inherited. Most times, the failure of the structure is related to the dynamic nonlinearity. With regard to the breathing phenomena for nonlinear structural systems, very little is known about how the nonlinearities influence the response and the dynamic characteristics of cracked structures. In this research, dynamic nonlinearity is presented in damaged structure due to presence of a crack. The crack is assumed to be open and close simultaneously and then breathing. Effect of breathing phenomenon was studied deeply. Crack breathing is simulated at the crack surfaces using contact elements. The contact, geometrical, penalty, and spin stiffnesses are taken in consideration. In addition, effect of several important parameters such as rotor angular velocity and crack ratio are studied. The study showed that the breathing natural frequency of any structure is ranged between opened (no contact) and closed crack natural frequencies. The larger crack length is, the more nonlinear disturbance in the dynamic response behavior. Also, at a critical crack length, some mode shapes tend to exchange and pass over with other modes. The presence of the mode interchanging and mode crossover was a guide on the nonlinear response for the cracked structure. The numerical modeling is achieved using ANSYS finite element program. Experimental data are used for validating the accurate use of contact elements in ANSYS environment.

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“…In addition the resulted partial differential equation is complex and dependent on some constants which are unknown and must be calculated by correlating the analytically obtained results with those calculated by finite element in each case. Several researchers followed the Christides and Barr approach by modifying their method and gained some improvements [14][15][16][17][18]. However there still exists the inconsistency between strain and displacement fields which causes inaccuracy of the results especially in mode shapes and stress analysis.…”

Section: Introductionmentioning

confidence: 99%