The analytical solution of free bending vibration of intake tower in hydroelectric power station based on the velocity potential analysis method
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Abstract:
This paper introduces the velocity potential analysis method for solving the free bending vibration of an intake tower in water in a hydroelectric power station. It analyzes the basic mechanical characteristics of an intake tower and makes some simplification and hypothesis for the structure in order to introduce the velocity potential analysis method. The frequency equation of the free bending vibration of a standalone intake tower is derived from the distribution parameter beam system. The boundary conditions of the problem are determined according to the Laplace equation of the velocity potential. The bending vibration equation of the intake tower is established via the expression of internal and external water pressure. The frequency equation is derived from the vibration equation. The structural vibration mode and frequency can be obtained through mathematical software programming. The derivation shows that the fluid velocity potential method converts the water into added mass that is associated with the vibration mode of the tower and thus affects the vibration of the structure. This paper then compares this method with the numerical method, analyzes their similarities and differences, and proposes the scope of application of this method. Results show that this method can be used to solve the free bending vibration problem of intake towers with a rectangular cross-section and water on both the inside and the outside, and provides a new way of thinking for further analysis of the seismic response of intake towers.
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