EFFICIENT SOLUTION METHOD OF EIGENPROBLEMS FOR DAMPED STRUCTURAL SYSTEMS USING MODIFIED NEWTON-RAPHSON TECHNIQUE

An efficient solution method is presented to solve the eigenvalue prob lem arising in the dynamic analysis of nonproportionally damped struct ural systems. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenve ctors to the linear eigenproblem through matrix augmentation of the qu adratic eigenvalue problem. In the iteration methods, such as the vect or inverse iteration and subspace iteration methods, singularity may o ccur during the factorizing process when the shift value is close to a n eigenvalue of the system. However, even though the shift value is an eigenvalue of the system, the proposed method provides nonsingularity , if the desired eigenvalue is not multiple, and this is analytically proved. Because the modified Newton-Raphson technique is adapted to th e proposed method, initial values are needed. The initial values of th e proposed method can be obtained by the intermediate results of itera tion methods or results of approximate methods. Because the Lanczos me thod effectively produces better initial values than other methods the results of the Lanczos method are taken as the initial values of the proposed method. Two numerical examples are presented to demonstrate t he effectiveness of the proposed method.