Research On Calculation Method And Specification Of Vibration Characteristics For Pier In Hydropower Station

As the supporting structure of powerhouse,the pier mainly bears the source load,and its vibration problem can not be ignored.Due to the excessive simplification of the specification method,there are errors in calculation,therefore,the relevant theories need to be further improved.This paper mainly studies the calculation method of pier’s vibration characteristics,including the accurate modeling of finite element numerical analysis method,the calculation method of vibration characteristics for three-dimensional thick walled cylindrical shell model and the calculation method of single degree of freedom in specification method.The specific studies are as follows:(1)The influence factors of natural frequency of pier are verified from the perspective of spatial characteristics.And analyzing the size information of various types of hydropower stations,the dependence between some size ranges of structures are determined,which includes pier,hood,powerhouse and volute.Besides,based on LHS and Sobol spatial sampling methods,the sensitivity of global size parameters and simulation range of numerical model are analyzed for hydropower station.It is found that the sensitivity of the size parameters is low except for pier own sizes(diameter,thickness and height),therefore,the structure size around the pier can be treated with the median value in the initial design stage of pier.The middle floor,pillar of hydraulic layer,surrounding rock,volute,hood have relatively high influence on the natural frequency of pier,which should be simulated.(2)The pier is simplified into a three-dimensional thick walled cylindrical shell structure,and the vibration theory of thick cylindrical shell is deduced by using three-dimensional elastic theory.The axial displacement is similar to the vibration function of beam under certain constraints.The circular displacement is similar to the triangle function of harmonic motion periodicity.The displacement in thickness direction is approximately linear function.And the natural frequency and eigenvector equation are derived by using the principle of energy minimization.In this paper,the beam shape functions under different constraints are derived,therefore,the formulas for the natural frequency and eigenvector of thick walled cylindrical shell under different constraints can be obtained.(3)An interpolation regression method for calculating the natural frequency of pier based on mixing database is proposed,and the feasibility is verified by the example of short pier.By controlling the constraint conditions,the order of the axial mode shape and the order of the circumferential mode shape,the natural frequency mixing database is constructed.The complex connection between the pier and the surrounding structure is transformed into the contribution(weight)of the sensitive mixing factor by interpolation regression.(4)The error in the process of specification derivation is analyzed,where the concept of natural frequency and circular frequency is confused in the derivation process.In addition,the amplitude calculation formula is derived again and the error caused by the mistake in specification method is analyzed.It is found that the amplitude error is small when the frequency of dynamic load is far away from the resonance region,and the influence of formula derivation error is not significant.When the load frequency is close to the natural frequency,the error is very prominent,and the influence of formula derivation error is great.(5)The top vertical load is simplified as the additional mass on the top of the pier,where the influence of the spatial structure of the components around the pier is ignored.And the results of the specification method and the finite element method are compared.It is found that the calculated results of amplitude method according to specification are smaller in the horizontal and torsional directions,which may be unsafe.In order to reduce the amplitude,the frequency of dynamic load should avoid the resonance area,and the calculation accuracy of natural frequency should be improved to make the amplitude calculation more accurate and reliable.The accuracy of gravity value is the key factor of natural frequency calculation.Therefore,by adding the weight coefficient of self weight and top vertical load,the calculation formula of torsional and horizontal natural frequency in the specification is modified to reflect the effect of additional mass and gravity of other components more reasonably and accurately.