Cracked and uncracked beam stability have been deeply studied over the years [1, 2]. In this paper the dynamic stability of circular cross section beams with multiple cracks have been developed. A doubly cracked Euler-Bernoulli beam under subtangential forces and different boundary conditions is considered. The subtangential forces are the combination of axial forces and tangential follower forces. The stability behaviour of structures subjected to nonconservative forces requires special consideration with respect to the alternative modes of instability (e.g. divergence or flutter). The aim of this paper is to construct an algorithm for the analysis of the frequencies and the critical loads level of cracked beams under subtangential forces. The presence of one or more cracks introduces discontinuites in the deformed shape of the beam, and its effect upon the stability and vibration of the elastic system will be evaluated. The governing partial differential equation has been solved by finite element method and the eigenfrequencies and critical loads have been obtained. Transition from flutter to divergence has been previously found to occur for specific boundary conditions of the beams and for nonconservativeness of load. In a finite element formulation the presence of the nonconservative forces gives a nonsymmetric stiffness matrix known as the nonconservative matrix or load correction matrix. Cracks are modelled by a line-spring model [3] and the local flexibility matrix is used to model the cracked section. The fundamental system was reduced to a classical eigenvalue problem. Hence critical loads have been found from eigenfrequency plots as a function of the crack parameters: crack depth, and crack location, hf . The results show that for given boundary conditions the cracked beams become unstable in the form of either flutter or divergence depending on the crack parameters, the nonconservativeness of the applied load as well as the iteraction of the two cracks.

Dynamic stability and critical loads of cracked beams under subtangential forces

VIOLA, ERASMO;FANTUZZI, NICHOLAS;MARZANI, ALESSANDRO;LI, YONG
2011

Abstract

Cracked and uncracked beam stability have been deeply studied over the years [1, 2]. In this paper the dynamic stability of circular cross section beams with multiple cracks have been developed. A doubly cracked Euler-Bernoulli beam under subtangential forces and different boundary conditions is considered. The subtangential forces are the combination of axial forces and tangential follower forces. The stability behaviour of structures subjected to nonconservative forces requires special consideration with respect to the alternative modes of instability (e.g. divergence or flutter). The aim of this paper is to construct an algorithm for the analysis of the frequencies and the critical loads level of cracked beams under subtangential forces. The presence of one or more cracks introduces discontinuites in the deformed shape of the beam, and its effect upon the stability and vibration of the elastic system will be evaluated. The governing partial differential equation has been solved by finite element method and the eigenfrequencies and critical loads have been obtained. Transition from flutter to divergence has been previously found to occur for specific boundary conditions of the beams and for nonconservativeness of load. In a finite element formulation the presence of the nonconservative forces gives a nonsymmetric stiffness matrix known as the nonconservative matrix or load correction matrix. Cracks are modelled by a line-spring model [3] and the local flexibility matrix is used to model the cracked section. The fundamental system was reduced to a classical eigenvalue problem. Hence critical loads have been found from eigenfrequency plots as a function of the crack parameters: crack depth, and crack location, hf . The results show that for given boundary conditions the cracked beams become unstable in the form of either flutter or divergence depending on the crack parameters, the nonconservativeness of the applied load as well as the iteraction of the two cracks.
ATTI DEL XX CONGRESSO DELL’ASSOCIAZIONE ITALIANA DI MECCANICA TEORICA E APPLICATA
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E.Viola; N.Fantuzzi; A.Marzani; Y.Li
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/107069
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