Study On Hybrid Test Algorithm Applied To The Collision Problem

Strong earthquakes often cause collisions between both engineering structures, the primary and secondary structures, and the structure and geotechnical structures, which exert two levels of influence on structures, i.e., the local damage in a mircoscopic perspective, and the abrupt change in the global responses, such as the vibration mode transition suddenly from the lower mode to a higher mode dominated type. The latter actually reflect the variation in the stiffness. This study focuses on the collision resulted variation in global responses. In order to reproduce the change by an experiment, two issues have to be resolved. One is the real-time loading system, and the other is a stable and efficient time integration algorithm. The latter is the main research content of this article, that is, put forward a new type of unconditionally stable explicit algorithm for pseudo dynamic tests, in order to overcome the instability problem of traditional algorithms when the stiffness suddenly gets bigger.This dissertation first proposes an explicit time integration algorithm with unconditional stability using the initial stiffness as one of the major parameters, which is verified numerically and experimentally. Then the stability tolerance is examined by use of the root locus method considering the abrupt change in the stiffness. In order to improve the stability for a colliding problem, the stiffness is online identified and algorithm parameters are updated. The effectiveness of the stiffness-updating algorithm is verified through pseudo dynamic testing. Finally, an idea to control structural responses by use of colliding effect is examined which could be a potential solution to control plastic structural responses. Major findings are as follows:1. The implicit HHT-a method is reconstructed theoretically to an explicit form by taking the initial stiffness as one of the primary parameters. During the derivation, the equation of motion is solved together with the differential express of the displacement and velocity, so that the current state variables are obtained at the (n+1)-th step. Meanwhile the second order small amount At2 fn+l and At2 fn are ignored.2. The spectral radius of the proposed algorithm is examined to analyze the stability and accuracy characteristics. When being applied to a linear system, the proposed algorithm is unconditionally stable if -0.5<α<0. The numerical damping ratio and the period distortion are also investigated. It is observed that the accuracy is worse than the linear acceleration algorithm with conditional stability but better than the Wilson-θ method with unconditional stability. These conclusions are verified by pseudo dynamic tests.3. When being applied to a nonlinear system, the stability of the proposed algorithm is examined by the root locus method. The concept of the critical stiffness is put forward, and the relationship between the critical stiffness and the initial stiffness is analyzed. It shows that when the tangent stiffness is less than or equal to the initial stiffness, the roots are locates within the unit circle, meaning that the algorithm is stable; while the tangent stiffness is greater than the initial stiffness, the roots are located outside the unit circle, meaning not stable. So the critical stiffness equals to the initial stiffness of the structure.4. The stability of the proposed algorithm is improved by online updating the stiffness used in the parameters to adapt to the colliding problem. Different stiffness identification algorithms are examined numerically and experimentally. The pseudo dynamic tests of a colliding structure demonstrate the effectiveness of the improved algorithm with online updating stiffness parameters. It is found that the least square fitting method based on correlation judgment can better identify the stiffness variation during the test, and the stability of the algorithm is optimized in the colliding test.5. Pseudo dynamic tests are carried out using the improved algorithm on a four-story frame with colliding mechanism. It is observed that the colliding could be one of the potential methods to control structural responses. The distribution of story drifts is getting more uniform, while the acceleration responses get larger which exert adverse effect on nonstructural components.