A Selective Review of Direct, Semi-Inverse and Inverse Eigenvalue Problems for Structures Described by Differential Equations with Variable Coefficients

Author Type

Faculty

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

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

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