The dynamics of linearly elastic, imperfect rings vibrating in their own plane is considered in this paper. Imperfections are modeled as perturbations of the uniform linear mass density and bending stiffness of a perfect ring. A perturbation expansion and a spectral representation are employed, and a variational formulation of the vibration problem is obtained. A linear theory is deduced by retaining only the leading-order terms in the variational formulation. The linear theory yields simple, closed-form expressions for the eigenfrequencies and the modal shapes, which are accurate when the imperfections are sufficiently small. An enhanced, nonlinear theory is also derived, which is accurate even when the ring imperfections are not small: in this case, an iterative solution procedure is developed. The proposed theories are validated by considering some case-study problems and using the Ritz-Rayleigh solution as a benchmark. Finally, the linear theory is applied to the frequency trimming problem of an imperfect ring. A simple, closed-form expression for the trimming masses is presented, valid for trimming any selected number of eigenmodes. 2007 Elsevier Ltd. All rights reserved.

Bisegna, P., Caruso, G. (2007). Frequency split and vibration localization in imperfect rings. JOURNAL OF SOUND AND VIBRATION, 306, 691-711 [10.1016/j.jsv.2007.06.027].

Frequency split and vibration localization in imperfect rings

BISEGNA, PAOLO;
2007-01-01

Abstract

The dynamics of linearly elastic, imperfect rings vibrating in their own plane is considered in this paper. Imperfections are modeled as perturbations of the uniform linear mass density and bending stiffness of a perfect ring. A perturbation expansion and a spectral representation are employed, and a variational formulation of the vibration problem is obtained. A linear theory is deduced by retaining only the leading-order terms in the variational formulation. The linear theory yields simple, closed-form expressions for the eigenfrequencies and the modal shapes, which are accurate when the imperfections are sufficiently small. An enhanced, nonlinear theory is also derived, which is accurate even when the ring imperfections are not small: in this case, an iterative solution procedure is developed. The proposed theories are validated by considering some case-study problems and using the Ritz-Rayleigh solution as a benchmark. Finally, the linear theory is applied to the frequency trimming problem of an imperfect ring. A simple, closed-form expression for the trimming masses is presented, valid for trimming any selected number of eigenmodes. 2007 Elsevier Ltd. All rights reserved.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore ICAR/08 - Scienza delle Costruzioni
English
Con Impact Factor ISI
Elastic waves; mathematical models; natural frequencies; perturbation techniques; problem solving; vibration analysis; imperfect rings; perturbation expansion; vibration localization; vibration problems; rings (components)
Bisegna, P., Caruso, G. (2007). Frequency split and vibration localization in imperfect rings. JOURNAL OF SOUND AND VIBRATION, 306, 691-711 [10.1016/j.jsv.2007.06.027].
Bisegna, P; Caruso, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/23580
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