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On precise time integration method for non-classically damped MDOF systems

Wang Mengfu (汪梦甫)1 and Zhou Xiyuan (周锡元)2,3

1. Department of Civil Engineering, Hunan University, Changsha 410082, China

2. China Academy of Building Research, Beijing100013, China

3. Beijing Polytechnic University, Beijing 100022, China

Abstract: In the complex mode superposition method, the equations of motion for non-classically damped multiple-degree-of-freedom (MDOF) discrete systems can be transferred into a combination of some generalized SDOF complex oscillators. Based on the state space theory, a precise recurrence relationship for these complex oscillators is set up; then a delicate general solution of non-classically damped MDOF systems, completely in real value form, is presented in this paper. In the proposed method, no calculation of the matrix exponential function is needed and the algorithm is unconditionally stable. A numerical example is given to demonstrate the validity and efficiency of the proposed method.

Keywords: non-classically damped systems; motion equation; generalized SDOF complex oscillator; state space theory; unconditionally stable algorithm