Analytical Study On Dynamic Characteristics Of Spiral Case With Cushion Layers

Structure of spiral case with cushion layers is widely used in large and medium-sized hydropower stations in China.According to the previous research on the spiral case with cushion layers,it can be seen that laying thin soft cushion between spiral case and peripheral concrete can adjust the distribution ratio of internal water pressure between spiral case and peripheral concrete,and improve the mechanical properties of the structure.However,the existence of cushion will reduce the restraint effect of peripheral concrete on steel shell,change the stiffness of the structure,and then have an impact on the dynamic characteristics of the structure.In the past,numerical simulation methods(such as finite element method)were used to study the dynamic characteristics of steel shell,cushion and concrete composite structures,but the application of analytical method was very few,almost no.Therefore,the effects of cushion material parameters,peripheral concrete thickness and steel shell thickness on radial vibration of spiral case of cushion layers are studied by analytical method in hydropower station.The main results are as follows:(1)By means of mechanical analysis,the steel shell,cushion and peripheral concrete in the spiral case with cushion layers are simplified into a three-degree-of-freedom system,and the pulsating water pressure acts on the inner wall of the steel shell and is assumed to be a harmonic load.The matching expressions of stiffness,damping and structural vibration response of cushion materials are derived.Pipe structure with cushion layers is regarded as the axisymmetric plane strain problem of multi-layer cylinder,and the stiffness expressions of steel shell,cushion and peripheral concrete are derived.(2)Taking Lasiva Hydropower Station project as an example,the stiffness and natural vibration frequency of volute composite structure under different cushion elastic modulus,thickness,peripheral concrete thickness and steel shell thickness are calculated by using the derived analytical formula.The results show that the natural frequency of each order of the structure increases with the increase of elastic modulus of the cushion,and the natural frequency of each order of the structure can be reduced by increasing the thickness of the cushion.The increase of Poisson's ratio of cushion will increase the natural frequency of each order of the structure.With the increase of concrete thickness,the frequency of steel shell and cushion increases gradually,while the frequency of concrete decreases gradually.With theincrease of steel shell thickness,the frequency of steel shell and concrete decreases,while the frequency of cushion increases.(3)Under different hydraulic pulsating frequencies,the vibration displacement amplitudes of steel shell and concrete are calculated by changing the material parameters(elastic modulus,thickness,damping)and the thickness of peripheral concrete.The results show that the elastic modulus of cushion has great influence on the displacement of spiral case and concrete,the thickness of cushion mainly affects the displacement of spiral case at low frequency of hydraulic pulsation,and the thickness of cushion mainly affects the displacement of concrete at high frequency of hydraulic pulsation.When the hydraulic pulsating frequency is low,the increase of Poisson's ratio of cushion material will reduce the amplitude of volute and concrete.When the hydraulic pulsating frequency is high,the increase of Poisson's ratio of cushion material will increase the vibration displacement of steel shell and concrete.Cushion damping can greatly reduce the displacement of the structure when the structure may resonate,and the amplitude can be greatly reduced with the increase of concrete thickness,but the effect on the amplitude of volute is not significant.In most cases,the displacement of the structure can be greatly reduced with the increase of concrete thickness.And the increase of the thickness of the steel shell can reduce the amplitude of the concrete and the spiral case.(4)Due to the different size of spiral case structure of each hydropower station,the structural stiffness of each hydropower station is also different.Combined with practical engineering,the amplitude of spiral case and concrete under different stiffness ratio(the ratio of external concrete stiffness to cushion stiffness)is calculated in this paper.The research methods and conclusions of this paper can provide theoretical reference for the selection of cushion material parameters.