Vibration of thin, tensioned, helically wrapped plates

López, Ernesto Ponce; Müftü, Sinan

doi:10.1016/j.jsv.2010.08.043

Cited by 2 publications

(2 citation statements)

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“…2), the governing equations can be derived. 13 Using a reference neutral surface as shown in Fig. 2, the differential variation of the displacement vector r between neighboring points P and P is 16,17 …”

Section: General Equation Of Cylindrical Shellmentioning

confidence: 99%

“…The helical wrapping case has also been investigated separately by Müftü. 12 Lopez and Müftü 13 analysed vibration of a thin tensioned web that had been helically wrapped around a turn-bar based on Kirchhoff-Love assumptions. They extracted dynamic properties including natural frequencies and mode shapes in the stable case by finite element method, and later, Sadeqi et al, 1,14,15 followed and extended their investigations to orthotropic and anisotropic moving web, utilizing numerical Rayleigh-Ritz solution.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Developing Vibration Equations of an Orthotropic Wrapped Shell, Considering Residual Stress Effects; A Mathematical Approach

Sadeqi¹,

Mahzoon²,

Kadivar³

2016

IJAV

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In this paper, vibration equations of an orthotropic, thin rectangular plate wrapped around a porous drum are developed, considering residual stress effects. It is assumed that the plate is subjected to tension from both opposite sides and wrapped continuously around a cylindrical drum so that the wrapped portion behaves like a circular cylindrical shell. First of all, the Lame' parameters, required to constitute the geometry relations, are established for typical cylindrical shallow shell in cylindrical coordinate system. Then, the equations of motion are derived by utilizing the stored strain energy principle based on the Love assumptions. Finally, a set of more complete vibration equations is introduced by applying the simplifications of the Donnell-Mushtari-Vlasov theory. The equations derived under more stringent and precise assumptions are compared with those obtained and available in literature, and the discripancies are highlighted. The present study only aims to mathematically develop the governing relationships, where a numerical solution separately done by the authors can be found in other literature in which vibrational behavior has been completely discussed for moving and stable anisotropic wrapped plates.

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Section: General Equation Of Cylindrical Shellmentioning

confidence: 99%