A novel decoupling dynamic method with third-order accuracy and controllable dissipation

In this paper, an efficient explicit integration method with third-order accuracy and controllable dissipation properties is proposed, and a new accuracy criterion is presented to evaluate relative errors of integration methods. By using this method, a desirable accuracy for responses in the low-frequency domain can be attained, spurious vibrations in the high-frequency domain can be strongly suppressed. Moreover, for the proposed method, update values of the displacement and velocity do not depend on the new state. Hence, it is convenient for decoupling a multi-spring coupling dynamic system to achieve high computational efficiency. The standard formulations of the proposed method, including the second-order and third-order accuracy schemes, are derived by discussing the local truncation error, difference accuracy, and stability firstly. Subsequently, the accuracy properties of the proposed method, e.g., the period elongation and amplitude decay, are analyzed in comparison with other available state-of-the-art explicit integration methods. Additionally, the properties of the proposed method, including the accuracy, convergence, dissipation, efficiency, and nonlinearity, are evaluated by using three examples. More specifically, the accuracy and convergence are evaluated through an example with theoretical solutions; the dissipation and efficiency are investigated by analyzing a geodesic dome truss; and the effectiveness in terms of the nonlinearity is investigated via a typical nonlinear dynamic system. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

An efficient explicit integration method with third-order accuracy and controllable dissipation properties is proposed in this paper, which can achieve desirable accuracy for low-frequency responses and strongly suppress spurious vibrations in high-frequency domain. The method's update values of displacement and velocity are independent of the new state, making it convenient for decoupling multi-spring coupling dynamic systems and achieving high computational efficiency. The method's standard formulations, including second-order and third-order accuracy schemes, are derived by discussing local truncation error, difference accuracy, and stability.