A Selective Review of Direct, Semi-Inverse and Inverse Eigenvalue Problems for Structures Described by Differential Equations with Variable Coefficients
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Article
Publication/Event/Conference Title
Archives of Computational Methods in Engineering
Publication Status
Version of Record
Abstract
This selective review (with emphasis on the word "selective") gives only a taste of extensive research that has been conducted since 1759 when Leonhard Euler posed, apparently for the first time, a boundary value problem. Since then numerous studies have been conducted for rods, Bernoulli-Euler beams, Bresse-Timoshenko beams, Kirchhoff-Love and Mindlin-Reissner plates and shells and structures analyzed via finer, higher-order theories. This selective review classifies the solutions as belonging to either of three main classes: (1) direct problems, (2) semi-inverse problems, (3) inverse problems. In addition, some new closed-form solutions are reported, that have been obtained via posing an inverse vibration problem. Due to the huge body of literature, author limits himself with discussing classic theories of structures.
First Page
451
Last Page
526
DOI
10.1007/BF02736214
Publication Date
1-1-2000
Recommended Citation
Elishakoff, I., "A Selective Review of Direct, Semi-Inverse and Inverse Eigenvalue Problems for Structures Described by Differential Equations with Variable Coefficients" (2000). Faculty Scholarship. 479.
https://digitalcommons.fau.edu/faculty_papers/479