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Title: Vibration characteristics of the North Fork Dam model
Authors: United States. Army. Office of the Chief of Engineers.
Balsara, Jimmy P.
Walker, Robert Evans.
Fowler, Jack, 1938-
Keywords: Arch dams
Finite element method
North Fork Dam
Issue Date: Mar-1974
Publisher: Weapons Effects Laboratory (U.S.)
Engineer Research and Development Center (U.S.)
Series/Report no.: Technical report (U.S. Army Engineer Waterways Experiment Station) ; N-74-2.
Description: Technical report
Abstract: Vibration tests were conducted on a 1/24-scale model of the North Fork Dam, a double curvature arch dam, to determine natural frequencies, mode shapes, and damping ratios. The measured results were compared with results calculated using a linear elastic three-dimensional finite element method. The objective of the study was to evaluate the use of physical models and three-dimensional finite element methods for earthquake response predictions. Mode shapes, frequencies, and damping ratios were determined from vibration tests of the model using two vibrators mounted on the crest of the dam and from tests with a vibrator mounted at the base of the dam on the downstream foundation. The- crest-mounted vibrators were run both in-phase and 180 deg out-of-phase to define the symmetric and unsymmetric modes. The vibration excitation of the base resulted in lower natural frequencies as the force level was increased from 5,000 to 40,000 lb. However, the frequencies at the low force levels approached those obtained from the crest vibration tests. Damping determined by turning off the crest vibrators at a resonance peak was about 5 percent of critical and was about 10 percent of critical when the base was vibrated at the 20,000-lb force level. The higher damping ratio determined from the base excitation tests was probably due to the participation of the soil under the dam foundation. The modal analysis of the dam was performed using a three-dimensional, finite element computer program, the Structural Analysis Program. The dam was modeled with 110 solid elements and 278 nodes and with the boundary totally fixed at the canyon walls. The reservoir was assumed to exert a static water pressure on the dam. This load, the mass of the vibrators, and an apparent mass based on an approximation by Westergaard to account for the mobilized water were included in the analysis. The Rayleigh-Ritz technique was used to determine mode shapes and frequencies. The calculated frequencies were higher than the measured frequencies by factors of 1.5 to 2. The over-prediction of the natural frequencies is due to the analysis scheme, the assumed base fixity of the dam, and probably to the water mass approximation.
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