Issue 29

W. Guodong, Frattura ed Integrità Strutturale, 29 (2014) 376-384; DOI: 10.3221/IGF-ESIS.29.33 378 relative displacement should be taken as the power balance equation of basic variable, then the dynamic relative displacement is derived, as well as the pseudo-static displacement of internal node caused by support movement will be solved, the sum of the two is the absolute displacement, and the solution procedure also avoids the participating computing of support quality matrix. But actually seismic action process is the quality mass vibration of support node generated by seismic excitation, the vibration of internal node is generated by the vibration of support node, earthquake force is directly added on support node, the quality of support node is not easy to determine, thus we usually solve the equation through applying this approach. Type (2) could be written into partitioned matrix model: s s s sb s s sb s b bs b bs b b b b b 0 y y y 0 0 y y y M C C K K M C C K K F                                                          (5) where b y denotes the force displacement on ground of N supports, s y denotes the displacement of all unsupported node in construction system, b F denotes the force of ground effect on N supports, M, C, K denote mass matrix, damping matrix and stiffness matrix respectively, the small sign s, k correspond to the freedom degree of the internal structure node and support node respectively. We assume the damping force is in direct proportion to relative velocity in type (5), d u  , {0} is used to replace the freedom degree of internal nodes and support nodes in type(5), by which to derive the equation: s d s d s d s b u u u y M C K M A        (6) Virtual acceleration excitation is constructed on Eq. (6): * i t j j j x e     (7) where superscript“*”represents taking complex conjugate, ,   denote the complex characteristics pair of power spectrum matrix of input ground motion. The product of virtual acceleration excitation and b M in Eq. (7) is taken as b F , then it will be substituted into Eq. (5): s s s sb s s sb s * i t b j j b bs b bs b b b b 0 0 y y y e 0 y y y M C C K K M M C C K K                                                               (8) Type (8) could be expanded as: * i t b b bse s be b bse s bse b b j j y t y y y y e M C C K K M            (9) Both sides of type (9)is multiplied by 1 b M  : 1 * i t b b bse s be b bse s bse b j j y t y y y y e M C C K K             (10) When b M mass is big, b M  ; when 1 b bse s be b bse s bse b ( y y y y ) M C C K K       is 0, type (10) could obtain virtual acceleration excitation of support: * i t b j j y (t ) e      (11) In conclusion, as long as giving a larger mass on support and exerting stimulation, we could realize the load of virtual acceleration excitation. And support’s virtual velocity and virtual displacement incentives are: * i t b j j 1 y (t ) e       , * i t b j j 2 1 y (t ) e        (12) Type (8) is expanded to be: