R-function theory method for free vibration of slip clamped trapezoidal shallow spherical shell on Winkler foundation

DOI

10.2991/iccte-17.2017.120How to use a DOI?

Keywords

R-function, Green's function, integral equation, Winkler foundation, free vibration, shallow spherical shell

Abstract

In this paper, the R-function theory(RFT) is applied to solve the free vibration of slip clamped trapezoidal shallow spherical shell on Winkler foundation. Firstly the fundamental solution of the biharmonic operator, the boundary equation and the R-function are used to construct the quasi-Green's function. Then the model governing differential equation of the problem is reduced to the Fredholm integral equation of the second kind by Green's formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation by the R-function. A numerical example shows that this method is an effective numerical method.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Shanqing Li
PY  - 2017/07
DA  - 2017/07
TI  - R-function theory method for free vibration of slip clamped trapezoidal shallow spherical shell on Winkler foundation
BT  - Proceedings of the 2017 2nd International Conference on Civil, Transportation and Environmental Engineering (ICCTE 2017)
PB  - Atlantis Press
SP  - 679
EP  - 682
SN  - 2352-5401
UR  - https://doi.org/10.2991/iccte-17.2017.120
DO  - 10.2991/iccte-17.2017.120
ID  - Li2017/07
ER  -