Precise Integration Method For Dynamic Time History Analysis Of Framework With TMD

The upper suspension structure and component will produce unrecoverable plastic deformation during earthquake due to strong ground shaking. The earthquake damage refers to the damage and collapse that the architectural structure can’t support the weight itself. There are many defects in the traditional earthquake resistant design. The structural vibration control theory is introduced into the modern structural engineering calculation to overcome those defects to make the structure strategy enter the stage of structural vibration control, which is named as the structural control, it is from the stage of traditional earthquake resistant design to the structural damping design stage. And TMD is the passive control device of earliest application. It is because that TMD reduces the structure dynamic response by its quality without the external power supply in earthquake, so it is called as “Passive tuned vibration absorption control”.The time history of the frame structure is analyzed under considering to install TMD of the top during earthquake. The specific researching contents are as follows:(1) Introduce briefly the shock absorption. The simplified calculation model with the multi-particle is established based on the vibration control theory. And the analysis of the seismic control of the frame structure with TMD is finished.(2) The matrix expression of main structure layer stiffness is given according to the relationship between the generalized force and displacement. And the displacement method theory of FEM is applied to integrate the layer stiffness matrix to main structure stiffness matrix. The quality matrix is determined by mass centralized method. The damping matrix uses the Rayleigh damping. Then, the motion differential equations of the main structure and TMD damping structure are established.(3) The overall dynamic equation of structure-TMD damping frame is derived, and the dual variables are introduced. The acceleration component is removed from dynamical equation. Thus, the dynamical equation becomes a first-order ordinary differential equation group from the second order ordinary differential equation group to make the solutions from Lagrange system transfer to Hamilton system. Then, the Hamilton dual system of the frame structure is established and its normal equation is derived. Afterwards, the precise integration method is used to solve damper seismic response of the frame structure before and after setting TMD on the top.(4) In order to achieve the optimal control effect, the vibration control optimization design of the frame structure is finished to seek the optimal tuning quality, stiffness and damping configuration.