Abstract/Details

Numerical investigation of periodic solutions for a suspension bridge model

Jen, Kuo-Ching. 
 University of Connecticut ProQuest Dissertations Publishing,  1990. 9101397.

Abstract (summary)

Numerical methods are discussed for the computation of periodic solution paths for a suspension bridge model(UNFORMATTED TABLE OR EQUATION FOLLOWS)$$\cases{&{\it u}\sb{\it tt} + \delta{\it u}\sb{\it t} + EIu\sb{xxxx} + Ku\sp+ = W + \lambda f(x,t,\mu)\cr\cr& {\it u}(0, {\it t}) = {\it u}(1, {\it t}) = {\it u}\sb{\it xx}(0, {\it t}) = {\it u}\sb{\it xx}(1,{\it t}) = 0,\cr}$$(TABLE/EQUATION ENDS)where $\delta, E, I, K,$ and $W$ are constants, $\lambda$ and $\mu$ are parameters, and $f$ is a periodic function in $t$.

The shooting method with Newton's and quasi-Newton's solver, and pseudoarclength continuation method around simple turning points are treated. The initial value problem solver that we adopted in the shooting method is implicit in the linear part, and explicit in the nonlinear part and forcing terms. We call it two-step Crank-Nicolson scheme.

Multiple periodic solutions for the suspension bridge equations are found, with their stability investigated. The unconditional stabilities of the Crank-Nicolson implicit scheme for solving suspension bridge equations in both infinite domain and finite domain are proved.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
Numerical investigation of periodic solutions for a suspension bridge model
Author
Jen, Kuo-Ching
Number of pages
137
Degree date
1990
School code
0056
Source
DAI-B 51/08, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-207-83091-9
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9101397
ProQuest document ID
303844547
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303844547/abstract