An assessment of the newmark method for solving chaotic vibrations of impacting oscillators

Moorthy, R. I. K. ; Kakodkar, A. ; Srirangarajan, H. R. ; Suryanarayan, S. (1993) An assessment of the newmark method for solving chaotic vibrations of impacting oscillators Computers & Structures, 49 (4). pp. 597-603. ISSN 0045-7949

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/004579...

Related URL: http://dx.doi.org/10.1016/0045-7949(93)90064-K

Abstract

The fourth-order Runge-Kutta method has been the preferred numerical integration scheme for solving chaotic problems in non-linear systems. This method is very accurate, but requires very small time-steps and four equation solutions per time-step. These drawbacks hinder the solution of chaotic problems in multi-degree-of-freedom (MDOF) systems. This paper presents the solution of the chaotic problem of impacting single-degree-of-freedom (SDOF) oscillators, using the Newmark method which is computationally efficient and unconditionally stable. The scheme incorporates an equilibrium iteration and variable time-stepping algorithm based on a convergence criteria which ensures that solution errors are minimized at each step. The results are compared with those obtained from the fourth-order Runge-Kutta method. It is concluded that the Newmark method with an adequate check on the solution accuracy could give qualitatively the same results as the Runge-Kutta method. The method has the advantage of an extension to MDOF real-life problems of chaos which could be solved using numerical techniques like FEM with limited computing effort. Such an extension is being pursued separately.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:15828
Deposited On:13 Nov 2010 12:28
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