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An optimization method for the consistent evaluation of two Rayleigh damping coefficients is proposed. By minimizing an objective function such as an error term of the peak displacement of a structure, the two coefficients can be determined with response spectral analysis. The optimization method degenerates into the conventional method used in current practices when only two modes of vibration are included in the objective function. Therefore, the proposed method with all significant modes included for simplicity in practical applications results in suboptimal damping coefficients. The effects of both spatial distribution and frequency content of excitations as well as structural dynamic characteristics on the evaluation of Rayleigh damping coefficients were investigated with a five-story building structure. Two application examples with a 62-story high-rise building and a 840 m long cable-stayed bridge under ten earthquake excitations demonstrated the accuracy and effectiveness of the proposed method to account for all of the above effects.

Room temperature ionic liquids （RTILs） with dispersed carbon pieces exhibit distinctive physiochemical properties. To ex- plore the molecular mechanism, RTILs/carbon pieces mixture was investigated by molecular dynamics （MD） simulation in this work. Rigid and flexible carbon pieces in the form of graphene with different thicknesses and carbon nanotubes in different sizes were dispersed in a representative RTIL 1-butyl-3-methyl-imidazolium dicyanamide （[Bmim][DCA]）. This study demonstrated that the diffusion coefficients of RTILs in the presence of flexible carbons are similar to those of bulk RTILs at varying temperatures, which is in contrast to the decreased diffusion of RTILs in the presence of rigid carbons. In addition, in- terfacial ion number density at rigid carbon surfaces was higher than that at flexible ones, which is correlated with the accessi- ble external surface area of carbon pieces. The life time of cation-anion pair in the presence of carbon pieces also exhibited a dependence on carbon flexibility. RTILs with dispersed rigid carbon pieces showed longer ion pair life time than those with flexible ones, in consistence with the observation in diffusion coefficients. This work highlights the necessity of including the carbon flexibility when performing MD simulation of RTILs in the presence of dispersed carbon pieces in order to obtain the reliable dynamical and interfacial structural properties.