Non-linear vibration and thermal buckling of an orthotropic annular plate with a centric rigid mass

Effect of elastic foundation on axisymmetric vibrations of polar orthotropic circular plates of variable thickness

Shooting method for non-linear vibration and thermal buckling of heated orthotropic circular plates

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.

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

A computational analysis of the nonlinear vibration and thermal buckling of a heated orthotropic annular plate with immovably hinged edges was presented. First, based on von Karman's plate theory and Hamilton's principle, the governing equations, in terms of the displacements of the middle plane, of the problem are derived. Then, upon assuming that harmonic responses of the system exist, the nonlinear dynamic equations in the von Karman version were converted into the corresponding nonlinear ordinary differential equations through elimination of the time variable using the Kantorovich time-averaging method. Finally, by applying a shooting method, the fundamental responses of the linear as well as nonlinear vibration and thermal postbuckling of the heated plate were numerically obtained.

C.D. Galles

Papers

Vibrations and elastic stability of polar orthotropic circular plates of linearly varying thickness