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Stability of average acceleration method for structures with nonlinear damping

Li Yan (李妍), Wu Bin (吴斌) and Ou Jinping (欧进萍)

School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China

Abstract: The energy approach is used to theoretically verify that the average acceleration method (AAM), which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.

Keywords: unconditional stability; average acceleration method; nonlinear systems; nonlinear damping