Nonlinear Periodic Oscillation of a Cylindrical Microvoid Centered at an Isotropic Incompressible Ogden Cylinder
Joint Authors
Zhang, Wenzheng
Yuan, Xuegang
Zhang, H. W.
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-24
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We study the dynamic mathematical model for an infinitely long cylinder composed of an isotropic incompressible Ogden material with a microvoid at its center, where the outer surface of the cylinder is subjected to a uniform radial tensile load.
Using the incompressibility condition and the boundary conditions, we obtain a second-order nonlinear ordinary differential equation that describes the motion of the microvoid with time.
Qualitatively, we find that this equation has two types of solutions.
One is a classical nonlinear periodic solution which describes that the motion of the microvoid is a nonlinear periodic oscillation; the other is a blow-up solution.
Significantly, for the isotropic incompressible Ogden material, there exist some special values of material parameters, the phase diagrams of the motion equation have homoclinic orbits, which means that the amplitude of a nonlinear periodic oscillation increases discontinuously with the increasing load.
American Psychological Association (APA)
Zhang, Wenzheng& Yuan, Xuegang& Zhang, H. W.. 2012. Nonlinear Periodic Oscillation of a Cylindrical Microvoid Centered at an Isotropic Incompressible Ogden Cylinder. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-993791
Modern Language Association (MLA)
Zhang, Wenzheng…[et al.]. Nonlinear Periodic Oscillation of a Cylindrical Microvoid Centered at an Isotropic Incompressible Ogden Cylinder. Journal of Applied Mathematics No. 2012 (2012), pp.1-9.
https://search.emarefa.net/detail/BIM-993791
American Medical Association (AMA)
Zhang, Wenzheng& Yuan, Xuegang& Zhang, H. W.. Nonlinear Periodic Oscillation of a Cylindrical Microvoid Centered at an Isotropic Incompressible Ogden Cylinder. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-993791
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993791