Numerical Simulation And Experimental Investigation Of The Rocking Dynamic Response Of Dual Stacked Rigid Blocks

The multi-body structures stacked by several rigid blocks exhibits rocking behavior in strong earthquakes,which induces favorable seismic performance.As self-centering systems,they are widely used in practical engineering.However,some stacked rigid blocks are prone to collapse or overturn in stronger earthquake,especially the statue-pedestal structures.As the historical relics,their damage will cause unpredictable consequence.Therefore,dynamic analysis of dual stacked rigid blocks is of great importance to improve their seismic performance and collapse resistance.The dynamic analysis of dual stacked rigid blocks involves both complicated geometrically nonlinearity and complex collision analysis.The previous research on dynamic analysis of dual stacked rigid blocks is concentrated on pure numerical simulation or experimental investigation,lacking literature of comparison between numerical simulation and test results.With this in mind,the dynamic response of dual stacked rigid blocks is systematically studied in five aspects,including the theoretical analysis of rocking response,numerical simulation,dynamic investigation,finite element simulation,parameter analysis and application.The following conclusions can be drawn:(1)Under certain assumptions,the Lagrange equation is used to deduce the rocking motion equation of dual stacked rigid blocks under different modes.Moreover,by using the law of conservation of angular momentum,the relationship of angular velocity before and after collision is established,realizing the transformation of different motion modes.(2)The Rosenbrock numerical integration method suitable for solving rigid problems is used to solve the rocking equation of dual stacked rigid blocks.In addition,the substep method is proposed to improve the calculation precision of the collision process and the accuracy of judging motion mode after the collision.Finally,the Matlab programs are provided for the dynamic response of dual stacked rigid blocks.(3)The free vibration tests and seismic excitation tesst of the dual stacked rigid blocks are carried out,and the results are compared with the Matlab numerical simulation results,verifying the viability of the porposed method.(4)Based on the ABAQUS software,the dynamic analysis of dual stackded rigid blocks is conducted,and the results are compared with the Matalb calculation results and the experimental results.The results indicate that the results of the ABAQUS program are also reasonable while having low computional efficiency and poor stability.In addition,the ABAQUS results are very sensitive to the friction coefficient,which is incompatible with reality.(5)Based on the Matlab numerical simulation program,the parameter analysis of the actual statue-pedestal structure are carried out.The study shows that for the statue-pedestal structure,the peak value of statue’s rotation angle decreases with the increase of the aspect ratio of the pedestal under the same thickness;the peak value of statue’s rotation angle increases with the increase of thickness of the pedestal under the condition of the same aspect ratio.The obtained results are of great reference value to improve the vibration-absorbing and anti-collapse performance of dual stacked rigid blocks.