Vibration of Mechanical System with Higher Degrees of Freedom: Solution of the Frequency Equations

The solution of the motion equation of the rigid body systems with higher degrees of freedom 2 ≤ p° ≤ 10 is difficult. The presented method allows solving the motion equations of such systems by its transformation to higher degrees' algebraic characteristic equations. The vibration of the system is then described by frequencies obtained from solution of characteristic equations. The proposed method follows Bezout's factor theorem, Bairstow-Hitchcock's method, method of synthetic division and other presuppositions given in the article. The solution is based on the determination of the complex zeros of polynomials.