A selective review of direct, semi-inverse and inverse eigenvalue problems for structures described by differential equations with variable coefficients

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 Tia 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.