Geometrically Non-Linear Free In-Plane Vibration Of Circular Arch Elastically Restrained Against Rotation At The Two Ends
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International Journal of Engineering Trends and Technology (IJETT) |  |
| © 2021 by IJETT Journal | ||
| Volume-69 Issue-3 |
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| Year of Publication : 2021 | ||
| Authors : Omar Outassafte, Ahmed Adri, Yassine El khouddar, Said Rifai, Rhali Benamar |
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| DOI : 10.14445/22315381/IJETT-V69I3P215 |
Citation
MLA Style: Omar Outassafte, Ahmed Adri, Yassine El khouddar, Said Rifai, Rhali Benamar "Geometrically Non-Linear Free In-Plane Vibration Of Circular Arch Elastically Restrained Against Rotation At The Two Ends" International Journal of Engineering Trends and Technology 69.3(2021):85-95.
APA Style:Omar Outassafte, Ahmed Adri, Yassine El khouddar, Said Rifai, Rhali Benamar. Geometrically Non-Linear Free In-Plane Vibration Of Circular Arch Elastically Restrained Against Rotation At The Two Ends International Journal of Engineering Trends and Technology, 69(3),85-95.
Abstract
In this present paper, the geometric non-linearity in free in-plane vibration of inextensible circular arch with uniform cross section and elastically restrained against rotation at the two ends has been investigated. Using the ends conditions and the transfer matrix, the eigen values of problem are determined iteratively using the Newton-Raphson algorithm. The kinetic and potential energy are discretized into a series of a finite spatial functions which are a combination of linear modes and basic function contribution coefficients. The use of Hamilton principle energy reduces the problem to a set of non-linear algebraic system that solved numerically using an approximate explicit method developed previously the so-called a second formulation. Considering the multi-mode approach, the effect of the dimensionless rotational stiffness of springs at the two ends has been presented with their corresponding non-linear deflections and curvatures.
Reference
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Keywords
Geometrical nonlinearity, circular arch, free and forced vibration, Hamilton principle, second formation, rotational springs.