Simplified formula for frequency of bending vibration of piles in water

The characteristics of bending vibration of high piles in water are discussed by introducing the additional mass. It is supposed that the mass of some water attaches to the piles and vibrates with them, however it increases the mass of the piles but doesn’t change their bending rigidity. Thus, the piles can be divided into two parts with different densities. The bending vibration equations of the piles are put forward based on the D’alembert principle. A group of equations are obtained and solved by the condition of the continuity of piles and edge-restraints in which the formula of natural frequency of piles in water can be obtained. The determination of the pile length is analyzed. The comparisons are made between the calculated and measured values for one pile in Donghai Sea Wind Farm and for two piles in Tsingdao Sea Bridge. The agreed results indicate the formula has good precision with simple form, which can be applied in projects.