Analytical Study of Nonlinear Vibrations of Marine Risers by Newton Harmonic Balance Method
In this paper, using Newton's Harmonic Balance Method (NHBM), nonlinear vibrations of marine risers are investigated. The Newton harmonic method is approximate and similar to the February series method used for linear oscillator. Many researchers have conducted studies using numerical or approximate methods. Harmonic balance method, which itself has limitations in application. Generally, nonlinear vibration issues are of great importance in physics, mechanical structures, and other engineering research. Vibration response, stability, and frequencies are the main components of a system's vibration check. This method continues to be able to study a wider range of nonlinear differential equations. First, the Hamilton vibration equation is obtained. The effect of various parameters such as riser length and initial displacement of the upper support, etc. on the riser frequency has been investigated and then the equation has been solved, which shows acceptable accuracy after comparing the results of this article with previous research.