A RESPONSE SPECTRUM CCQC METHOD FOR NON-PROPORTIONALLY DAMPED SYSTEMS BASED ON EQUIVALENT VISCOUS DAMPING MODEL

The damping matrix of a hybrid structure no longer satisfies the proportional relationship with its mass matrix and its stiffness matrix, which has non-proportional characteristics. Therefore, the common seismic design method of the design code, which assumes of proportional damping, is not strictly applicable to the calculation of the structural earthquake effects of non-proportionally damped systems. On the basis of the complex mode superposition method based on the equivalent viscous damping model, combined with the virtual excitation method and the stationary random theory, the corresponding real value form formulas are derived for the response spectrum complete quadratic combination (CCQC). Then a theoretical method is proposed, which could be used directly to calculate the earthquake effects of non-proportionally damped hybrid structures composed of different materials. The cases show that: compared with the response spectrum CCQC method based on the Rayleigh damping model of the substructures, the response spectrum CCQC method based on the equivalent viscous damping model directly depends on the quality, on stiffness, and on damping parameters, which is not influenced by the mode combination. The corresponding calculation results are unique, and the calculation of the displacement correlation coefficient is only involved. Compared with the response spectrum CQC method based on the energy method, the response spectrum CCQC method based on the equivalent viscous damping model can effectively consider the non-proportional characteristics of the hybrid structures and is suitable for the hybrid structures with significant non-proportional damping characteristics.