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AN ASSESSMENT OF THE NEWMARK METHOD FOR SOLVING CHAOTIC VIBRATIONS OF IMPACTING OSCILLATORS

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Title AN ASSESSMENT OF THE NEWMARK METHOD FOR SOLVING CHAOTIC VIBRATIONS OF IMPACTING OSCILLATORS
 
Creator MOORTHY, RIK
KAKODKAR, A
SRIRANGARAJAN, HR
SURYANARAYAN, S
 
Description 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.
 
Publisher PERGAMON-ELSEVIER SCIENCE LTD
 
Date 2011-08-23T11:33:00Z
2011-12-26T12:56:26Z
2011-12-27T05:45:10Z
2011-08-23T11:33:00Z
2011-12-26T12:56:26Z
2011-12-27T05:45:10Z
1993
 
Type Article
 
Identifier COMPUTERS & STRUCTURES, 49(4), 597-603
0045-7949
http://dx.doi.org/10.1016/0045-7949(93)90064-K
http://dspace.library.iitb.ac.in/xmlui/handle/10054/10503
http://hdl.handle.net/10054/10503
 
Language en