The Research On Nonsingular Solution Of The Sylvester Equation Based On Quadratic System Decoupling

Quadratic differential systems are used extensively in many applications, such as applied mechanics, electronic vibration, vibrational acoustics, and hydromechanics. In certain conditions, because many high-order systems can be simplified into quadratic systems, it has an important practical significance to study on and analyze the characteristics of quadratic systems deeply. It is often necessary to study on the system decouplings to analyze the characteristics. The quadratic system decoupling means that based on the appropriate transformations or other methods, the multi-degree-of-freedom quadratic system can be linked with multiple totally independent single-degree-of-freedom quadratic subsystems.For decoupling of second order system, the nonlinear problem to solve decoupling transformations of system can be translated to solution about nonsingular solution of the Sylvester equation. However, as a solution method to this equation by using linear equation groups, it easily gives birth to experiment error and don't even to obtain completely equivalent decoupling system. In this paper, the nonsingular solution of the Sylvester equation is solved, according to a constitution method of that equation solution, i.e. first, the formation of general solution is constructed by using the same spectrum information, which is achieved between pre-and post-system decoupling; second, the nonsingular solution was searched by estimation of parameters. The results of numerical experiments show this constitution method is feasible, which supply a simple approach for nonsingular solution of the Sylvester equation. In this paper, it found a relatively simple method for quadratic system decoupling, which has a vital significance to analyze the quadratic differential systems.