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Axisymmetric vibrations of closed spherical shells: equations of motion and bifurcation analysis
Author(s) -
Nayfeh A.H.,
Arafat H.N.
Publication year - 2006
Publication title -
structural control and health monitoring
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.587
H-Index - 62
eISSN - 1545-2263
pISSN - 1545-2255
DOI - 10.1002/stc.121
Subject(s) - rotational symmetry , bifurcation , eigenvalues and eigenvectors , equations of motion , spherical shell , motion (physics) , shell (structure) , vibration , classical mechanics , physics , resonance (particle physics) , mathematical analysis , mathematics , mechanics , nonlinear system , engineering , acoustics , civil engineering , particle physics , quantum mechanics
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.