Comparison and assessment of time integration algorithms for nonlinear vibration systems

Abstract

A corrected explicit method of double time steps (CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the generalized-α method and the precise integration method were implemented in typical nonlinear examples for the purpose of comparison. Both conservative and non-conservative systems were examined. The results show that it isn’t unconditionally stable for the precise integration method, the Newmark method and the generalized-α method in nonlinear systems. The stable interval of the three methods is less than that of the CEMDTS. When a small time step (Δt≤T_min/20) is employed, the precise integration method is endowed with the highest accuracy while the CEMDTS possesses the smallest computation effort. However, the CEMDTS becomes the most accurate one when the time step is large (Δt≥0.3T_min) or the system is strongly nonlinear. Therefore, the CEMDTS is more applicable to the nonlinear vibration systems.

Keywords

nonlinear vibration / conservative system / explicit algorithm / accuracy

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