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For the displacement-constraint device with hysteric-friction isolation system, the judgment condition of soft-collision between the isolation layer and displacement-constraint device is put forward, the motion equation of the isolation system in consideration of friction and soft-collision is established, the nonlinear analysis program is worked out, and several kinds of inflection points in the program are given and the corresponding processing method of the inflection points is introduced. The nonlinear response analysis of the isolation system results indicate the displacement-restraint device can ensure the upper structure safety; also can decrease the displacement of the isolated layer.

For a building under evolutionary random excitations, a new random vibration analysis based on equivalent excitation method is presented, in which, the equivalent excitation is constructed by using continuous wavelet transform. When the input power spectral density of a seismic excitation is modulated by a time varying function, the continuous wavelet coefficients are calculated firstly by using scales and the evolutionary power spectral density, then the equivalent excitation is constructed by inverse continuous wavelet transform, finally the random vibration analysis is carried out following the procedures of the equivalent excitation method. An example is given to show the whole procedure, in which the special ability of the method for dealing with the evolutionary random excitation is discussed in detail.