Semi-analytical solution of seismic response of serially isolated equipment and supporter

Serially isolated system of electrical equipment andsupporter is presented by in-parallel laminated rubber support and themechanical model of this system is developed. Based on the vibration theoryof beam with distributed parameters and the boundary conditions ofconcentrated parameters, the frequency equation of this serially isolatedsystem is derived, and the frequencies and mode shapes are obtained by thenumerical method. According to the Betti law, the orthogonal conditions ofmodes of this serially isolated system with concentrated and distributedparameters are deduced and the generalized mass and stiffness can beobtained. By decomposing the non-proportional damping of serially isolatedsystem to the parts of proportional damping and non-proportional damping,the damping ratio of the non-proportional damping in the equivalent mode isderived by Hamilton principle. Therefore the vibration equation of thenon-proportional damping of the isolated system is decoupled, and theresponses of structure under earthquake excitation can be solved by the modesuperposition method. A seismic response case of the 330\,kV voltagetransformer is analyzed by the semi-analytical solution and numericalintegration solution of FEM, suggesting that the serially isolated systemhas an obvious function of shock absorption. In addition, the systemresponses obtained with the two methods are basically consistent to indicatethe effectiveness of this serially isolated system and the correctness ofthis semi-analytical solution.