Geometrically non-linear vibration of concrete shallow funicular shells

Sabermahany, H ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1680/jstbu.18.00115
  3. Publisher: ICE Publishing , 2021
  4. Abstract:
  5. This study deals with the geometrically non-linear vibration analysis of concrete shallow funicular shells of rectangular plan with four clamped edges under impulse loads. The shape of a concrete funicular shell is such that the shell is subjected to pure compression under its dead weight. Following the existing method presented for the linear vibration analysis, the geometrically non-linear vibration analysis is considered through the use of non-linear shallow shells theory. Each displacement component is expanded in a double Fourier series and the kinetic energy, the elastic strain energy and the virtual work done by external forces are calculated in terms of the displacement components. Then, the equations of motion are obtained using the Lagrangian approach and are solved with the Runge-Kutta fourth-order method. The solution is verified against the results obtained with the finite-element method. The difference between the results of the linear and non-linear vibration analyses has been considered. Furthermore, it is indicated that under the considered dynamic loads, internal moments and consequentially tensile stresses are formed in the funicular shell and the shell does not behave purely as a funicular element. Finally, the plan aspect ratio effect on the time response of funicular shells has been shown. © 2019 ICE Publishing: All rights reserved
  6. Keywords:
  7. Aspect ratio ; Concretes ; Dynamic loads ; Equations of motion ; Fourier series ; Kinetic energy ; Kinetics ; Lagrange multipliers ; Runge Kutta methods ; Shells (structures) ; Strain energy ; Aspect ratio effects ; Displacement components ; Double Fourier series ; Elastic strain energy ; Fourth-order method ; La-grangian approaches ; Linear vibration analysis ; Non-linear vibrations ; Vibration analysis ; Concrete structure ; Displacement ; Vibration
  8. Source: Proceedings of the Institution of Civil Engineers: Structures and Buildings ; Volume 174, Issue 3 , 2021 , Pages 169-180 ; 09650911 (ISSN)
  9. URL: https://www.icevirtuallibrary.com/doi/abs/10.1680/jstbu.18.00115