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Steady state periodic response of truncated conical shell undergoing large amplitude vibration.

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Title: Steady state periodic response of truncated conical shell undergoing large amplitude vibration.
Authors: Parvez, Mohd Taha1 (AUTHOR) mohdtaha.ism@gmail.com, Khan, Arshad Hussain1 (AUTHOR)
Source: Mechanics of Advanced Materials & Structures. Dec2024, Vol. 31 Issue 30, p13261-13272. 12p.
Subjects: Conical shells, Hamilton's principle function, Equations of motion, Shear (Mechanics), Finite element method
Abstract: The large amplitude steady state periodic response of truncated conical shell panels under the influence of transverse harmonic excitation is analyzed by considering the nonlinear strain displacement relations. The finite element analysis is based on the kinematics of first-order shear deformation theory and the constrained strain terms have been interpolated using field-consistent modified shape functions to avoid shear locking. The governing equation of motion has been obtained using Hamilton's principle, which has been solved using the Modified shooting method and continuation schemes to yield the complete frequency response. The influence of boundary conditions, the amplitude of the forcing function and curvature on the periodic response was investigated. The hardening or softening nonlinear behavior has been obtained depending upon boundary conditions, geometry and forcing function amplitude. The combined influence of geometric nonlinearity and varying curvature of the truncated conical shell leads to significantly greater negative half-cycle amplitude. The peculiar nature of the restoring force dynamics with increased inward deflection causes the restoring forces to act in a destabilizing sense leading to increase in negative half-cycle amplitude. The periodic stress variation reveals multiple stress reversals during a loading cycle and is very critical for the fatigue design of such components. The multiple slope changes/bifurcations in the frequency response have been examined using response history, frequency spectra and the phase plane plots where it is revealed that for some cases the higher harmonic contributions are even greater than the fundamental harmonic. The deformed configuration at various instants during the periodic cycle reveals modal interaction between first and higher modes. Moreover, the nonlinear frequency response curves depict softening nonlinear behavior for deeper shells which gradually transforms into hardening behavior for shallow shell panels. [ABSTRACT FROM AUTHOR]
Copyright of Mechanics of Advanced Materials & Structures is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Steady state periodic response of truncated conical shell undergoing large amplitude vibration.
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  Data: <searchLink fieldCode="AR" term="%22Parvez%2C+Mohd+Taha%22">Parvez, Mohd Taha</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mohdtaha.ism@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Khan%2C+Arshad+Hussain%22">Khan, Arshad Hussain</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Mechanics+of+Advanced+Materials+%26+Structures%22">Mechanics of Advanced Materials & Structures</searchLink>. Dec2024, Vol. 31 Issue 30, p13261-13272. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Conical+shells%22">Conical shells</searchLink><br /><searchLink fieldCode="DE" term="%22Hamilton's+principle+function%22">Hamilton's principle function</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+of+motion%22">Equations of motion</searchLink><br /><searchLink fieldCode="DE" term="%22Shear+%28Mechanics%29%22">Shear (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink>
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  Label: Abstract
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  Data: The large amplitude steady state periodic response of truncated conical shell panels under the influence of transverse harmonic excitation is analyzed by considering the nonlinear strain displacement relations. The finite element analysis is based on the kinematics of first-order shear deformation theory and the constrained strain terms have been interpolated using field-consistent modified shape functions to avoid shear locking. The governing equation of motion has been obtained using Hamilton's principle, which has been solved using the Modified shooting method and continuation schemes to yield the complete frequency response. The influence of boundary conditions, the amplitude of the forcing function and curvature on the periodic response was investigated. The hardening or softening nonlinear behavior has been obtained depending upon boundary conditions, geometry and forcing function amplitude. The combined influence of geometric nonlinearity and varying curvature of the truncated conical shell leads to significantly greater negative half-cycle amplitude. The peculiar nature of the restoring force dynamics with increased inward deflection causes the restoring forces to act in a destabilizing sense leading to increase in negative half-cycle amplitude. The periodic stress variation reveals multiple stress reversals during a loading cycle and is very critical for the fatigue design of such components. The multiple slope changes/bifurcations in the frequency response have been examined using response history, frequency spectra and the phase plane plots where it is revealed that for some cases the higher harmonic contributions are even greater than the fundamental harmonic. The deformed configuration at various instants during the periodic cycle reveals modal interaction between first and higher modes. Moreover, the nonlinear frequency response curves depict softening nonlinear behavior for deeper shells which gradually transforms into hardening behavior for shallow shell panels. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Mechanics of Advanced Materials & Structures is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/15376494.2024.2336219
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      – Code: eng
        Text: English
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      – SubjectFull: Hamilton's principle function
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      – SubjectFull: Equations of motion
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      – SubjectFull: Shear (Mechanics)
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              Text: Dec2024
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