Application Of Matrix Perturbation Method On Galloping Characteristic Analysis Of Iced Bundle Conductor

Galloping of iced overhead transmission line has been a huge problem for the last 100 years.For the uncertainty of mechanisms,no general control methods have been raised.Reserch of mechanisms refers to stabilities of two levels:one is the static equilibrium,the other is the stable motion.Based on ??????? first order approximation theory,the stability of the static equilibrium is discussed in this thesis.By means of the matrix perturbation method,first order solutions are obtained.Galloping excitation characteristics are analysed,which are verified by wind tunnel section model test and time-history computation.Next in detail.First of all,the equation of motion is obtained for the 3DOF system.According to the matrix perturbation method,the first order of the real parts of the eigenvalues are derived for the case of discrete modal frequencies.Compared with the single DOF solution by the Den Hartog or Nigol theroy,one or two additional parts arise.Take a JD-6 iced bundle conductor as an example,numerical solutions show that the additional parts has great effects on the galloping excitation characteristics.To know whether galloping or not,it's better to compare the value of the addtinal coefficient ? and the cirtical coefficient ?.Analysis is simplified when two torsional aerodynamic coefficients have the following relationship:K?1>>K?2.Thus aerodynamic force can be classified into six types depend on the plus-minus of C'L+CD?C'L?C'M.Theoretical analyses show galloping interruptions and the closing velocity occur for the 3DOF system galloping,which are totally different from the single DOF one.The onset velocity changes suddenly for several ratios of vertical and torsional frequencies.For attack angles with minus C'L+CD.galloping excitation characteristics are totally different depend on the plus-minus of C'L,which is verified by a wind tunnel section model test.For single span bundle conductor,differential equations are derived by using the Hamilton principle and the Galekin weighted residual method.By diagonalization of the structural damping matrix,the first order perturbation solution of the real parts of the eigenvalues are derived for each modal at the catenary position.It's proved odd and even order real parts are independent each other by the matrix elementary transformation.For higher value of the tention ratio,the first order solution can be simplified into the same form as the 3DOF system.The time-history computation shows the perturbation solution can be applied to predict the shape of stable galloping displacements.The onset velocity changes hugely when the 1st order vetical modal frequency equates with the torsional one.Further analyses verify the application of perturbation solution at the catenary position The antisymmetric disturbance is essential to have the right answer for time-history computation with an average velocity.For aerodynamic force type 5 and 6,when C'L+CD,and C'M are both positive,galloping happens when it meets the sufficient condition raised in the 3DOF system analysis.The amplitude cannot be neglected according to the time-history computation,to which we should pay attention.