基于速度势法的水电站进水塔弯曲自由振动解析解

介绍了基于速度势解析算法求解水电站进水塔在水中弯曲自由振动的方法。分析进水塔的主要受力特点,为引入流体速度势解析算法对结构进行简化和假设。以分布参数梁体系推导得到无水时进水塔弯曲自由振动频率方程,根据速度势拉普拉斯方程确定了所求解问题的边界条件,通过内外水压力表达式建立进水塔的弯曲自由振动方程。推导振动方程得到频率方程,经过数学软件编程求解,最终可得到结构振型和频率。推导过程表明流体速度势法是将水体转化成与塔体振型相关的质量附加于结构,从而影响结构的振动。与数值方法对比和探讨,分析了两者异同,提出本文方法适用范围。结果表明,本文解法可以引入内外含水矩形横截面进水塔的弯曲自由振动问题的求解,为下一步进水塔地震响应分析提供一种新的思路。

The analytical solution of free bending vibration of intake tower in hydroelectric power station based on the velocity potential analysis method

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.