Natural vibration characteristics of gravity structures

A forced vibration procedure is presented to estimate fundamental and higher frequencies of vibrations and associated mode shapes of gravity structures. The gravity structures considered are retaining walls and gravity dams. The validity of the proposed procedure is tested on three test problems of varying complexity for which the natural vibration frequencies and mode shapes either have known analytical solutions or have been determined via numerical means/field tests by others. Also included are the results of natural vibration frequencies and associated mode shapes for a spillway control structure located near the abutment end of an embankment dam obtained using the proposed procedure. For all problems considered, fundamental frequency and mode shape results using the proposed procedure are compared with the results obtained using an alternative procedure in which static deflections due to the structure's own weight are used as the starting point for free vibrations by setting the gravity vector to zero. All results compare well. The merits of the proposed procedure are discussed. Published in 2006 by John Wiley & Sons, Ltd.