Effect of membrane weight on vibrations of air-inflated dams

Abstract

Inflatable dams are flexible membrane structures, pressurized with either air, water, or both, which have been used in recent years as a means of temporarily impounding water. A number of procedures have been developed to investigate the static behavior of the dams, but the dynamic behavior has been largely neglected. The few studies that have been done on dynamic behavior have used the simplifying assumption that the weight of the membrane was negligible.

In this study, equations of equilibrium and equations of motion were derived for an air inflated dam impounding no water, but loaded with its own membrane weight. It was assumed that the effect of membrane extensibility is negligible in the analysis. Derivatives required in the equations of motion were approximated using finite difference equations. Computer programs were written to find solutions for the eigenvalues and eigenvectors of the equations of motion. The computer program plotted the mode shapes of vibration associated with the four lowest eigenvalues, as well as the static shape of the dam. The eigenvalues obtained were the square of the frequencies of the system, so the effects of a series of membrane weights on the frequencies of dams of various base lengths could be analyzed.