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Axisymmetric vibrations of closed spherical shells: equations of motion and bifurcation analysis

Nayfeh, A.H. / Arafat, H.N.

10.1002/stc.121.abs

We investigate the torsionless axisymmetric dynamics of a forced closed spherical shell. The non‐linear equations of motion are formulated using a variational approach and surface analysis. First, we revisit the linear eigenvalue problem. Then, using the method of multiple scales, we assess the possibility of the activation of two‐to‐one internal resonances between the different types of modes. Lastly, we examine the shell's non‐linear responses to an axisymmetric primary‐resonance excitation and analyse their bifurcations. Copyright © 2005 John Wiley & Sons, Ltd.

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Axisymmetric vibrations of closed spherical shells: equations of motion and bifurcation analysis

Nayfeh, A.H. / Arafat, H.N.

10.1002/stc.121.abs

We investigate the torsionless axisymmetric dynamics of a forced closed spherical shell. The non‐linear equations of motion are formulated using a variational approach and surface analysis. First, we revisit the linear eigenvalue problem. Then, using the method of multiple scales, we assess the possibility of the activation of two‐to‐one internal resonances between the different types of modes. Lastly, we examine the shell's non‐linear responses to an axisymmetric primary‐resonance excitation and analyse their bifurcations. Copyright © 2005 John Wiley & Sons, Ltd.

Axisymmetric vibrations of closed spherical shells: equations of motion and bifurcation analysis

Nayfeh, A.H. / Arafat, H.N.

10.1002/stc.121.abs

We investigate the torsionless axisymmetric dynamics of a forced closed spherical shell. The non‐linear equations of motion are formulated using a variational approach and surface analysis. First, we revisit the linear eigenvalue problem. Then, using the method of multiple scales, we assess the possibility of the activation of two‐to‐one internal resonances between the different types of modes. Lastly, we examine the shell's non‐linear responses to an axisymmetric primary‐resonance excitation and analyse their bifurcations. Copyright © 2005 John Wiley & Sons, Ltd.

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Title:

Axisymmetric vibrations of closed spherical shells: equations of motion and bifurcation analysis

Contributors:

Nayfeh, A.H. (author) / Arafat, H.N. (author)

Published in:

Structural Control and Health Monitoring ; 13 ; 388-416

Publication date:

2006-01-01

Size:

29 pages

ISSN:

1545-2263 , 1545-2255

DOI:

https://doi.org/10.1002/stc.121

Type of media:

Article (Journal)

Type of material:

Electronic Resource

Language:

English

Keywords:

spherical shells , two‐to‐one internal resonance , dynamics , bifurcation analysis , non‐linear vibrations

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