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A Solution of Nonlinear Vibration Problems in Reactor Components

Amir N. Nahavandi and George J. Bohm

Nuclear Science and Engineering

Volume 26 / Number 1 / September 1966 / Pages 80-89


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The dynamic response of reactor structural components is obtained by direct numerical solution of the differential equations for a linear or a nonlinear situation considering the components to be a continuous network. The equation of motion of each element is expressed in spatial finite-difference form and integrated to determine deflections as a function of time. The deflection curves and excitation frequencies in a vertical beam, sinusoidally excited at the top and striking an elastic spring at the bottom, are determined satisfactorily as an example of the method. The pattern in this nonlinear system is shown to be similar to the modal behavior of linear structures. The single-valuedness and the lack of discontinuous jumps in the response curve characterize the dynamic stability of the system. The time variation of the beam-end displacements demonstrate the existence of nonuniform distributions of sub- and super-harmonics in the response frequency spectrum. A numerical stability analysis is performed for the problem under study and a criterion for the convergence of the numerical solution is developed. This criterion proved to be satisfactory for the analysis.

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