General integration scheme for linear dynamic analysis

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (10) : 43-48.

WANG Haibo,HE Chongjian,JIA Yaowei

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Abstract

For the state equation v?=H?v+r(t) used in describing linear dynamics systems, a general integration scheme was proposed with the combination of the Taylor series expansion and generalized precise time step integration method.The non-homogenous term at the moment of ti+1(i=0, 1, 2, …, n) was developed into a power series by the Taylor formula,and then the dynamic response due to the non-homogenous term was solved by introducing the recursive formula in the generalized precise time step integration method.The algorithm has an uniform computing scheme,which makes the programming simpler.Moreover, the different calculation accuracy can be obtained by selecting the term number of power series.Compared with the traditional numerical integration method, the proposed algorithm has higher precision, better stability and proper efficiency.Therefore ,it can be used to solve the dynamic response of a structure under arbitrary excitation.

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linear dynamic analysis / precise integration method / Taylor's series / recursive algorithm / general scheme

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WANG Haibo,HE Chongjian,JIA Yaowei. General integration scheme for linear dynamic analysis[J]. Journal of Vibration and Shock, 2019, 38(10): 43-48

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