Eigensolution Method Research Articles

Natural Frequencies of Circular Arches

A study of the free vibrations of elastic circular arches is presented, demonstrating the application of a particular direct-iterative eigen-solution method. The model consists of a sequence of straight beam finite elements connecting nodal points lying on the circular elastic axis of the arch. The effect of rotatory inertia is included, but transverse shear deformations are neglected in the analysis. The use of a finite element model facilitates determination of energy distribution in each mode, and permits quantitative analysis of the nature of the frequency spectrum for circular arches of various slenderness ratios. Results also include tables of natural frequencies for circular arches.

Interphase mass transfer for laminar concurrent flow of carbon dioxide and water between parallel plates

AbstractInterphase mass transfer between carbon dioxide gas and water has been investigated. The physical model used was the laminar concurrent flow of gas and liquid in a wide rectangular channel. Because of the high aspect ratio employed, the model was effectively one of parallel plates of infinite width.Three methods of solving the equations of change—the eigensolution method, the boundary layer theory, and penetration theory—were used to compute the diffusion coefficient of carbon dioxide in water from the experimental data. Calculated values of diffusion coefficients from the penetration theory checked well with those from the eigensolution method, but the values computed from the integrated boundary layer equation were about 10% higher.Results from the eigensolution agreed within 5% with the data of other investigators in the temperature range of 20° to 30°C.