Transversely and Axial Free Vibration Analysis of Concrete Gravity Dam without Reservoir effect using Galerkin Method

Articles in Press

Document Type : Original Article

Author

• Bahram Navayi Neya

Babol Noshirvani University of Technoligy

10.22067/jfcei.2025.89758.1320

Abstract

In this study, transverse and axial free vibration analysis of Concrete Gravity Dams is presented. To achieve ordinary differential equations, the undamped governing partial differential equation of vibration of a tapered cantilever beam, based on Euler-Bernuli and Rayleigh theories are transformed to the frequency domain. Galerkin method is then used to solve the free vibration equation for an arbitrary dam geometry. The restrictions that need to be placed on the admissible functions to avoid the infinite terms in the integrals of equations depend on the order of implied differential operators. The corresponding undamped mode shapes of Euler-Bernoulli and Rayleigh beams, which satisfy essential boundary conditions, are chosen as the admissible functions to expand the trial response of the equation of motion. Validation of results shows an excellent agreement between the Galerkin method and exact solutions in this research. Numerical results of free frequency vibration for different cases based on Rayleigh and Euler-Bernoulli theories show that the frequencies of the dam do not match due to the thickness of dams, especially in higher modes. The predicted values of natural frequencies of the dam based on Rayleigh’s theory are less than the values predicted by Euler-Bernoulli’s theory due to the consideration of rotary inertia effect, which becomes significant in very thin dams.

Keywords

• Concrete Gravity Dams:
• Free Vibration: Euler-Bernoulli Theory
• : Rayleigh Theory
• : Galerkin Method

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