Wyznaczanie Częstości Drgań Własnych i Amplitud Układu o Skończonej Liczbie Stopni Swobody

Abstract

To determine the natural frequencies and amplitudes of a system with a finite number of degrees of freedom (and in many numerical problems of mechanics and physics) it is necessary to find the eigenvalues and eigenvectors of a matrix. The present paper proposes a method for determining the coefficients of the characteristic (secular) equation of matrix based on certain properties of almost triangular matrices. After determining the roots of the characteristic equation (the eigen-values) the eigenvectors of the matrix can be determined by this method in a simple manner. The method is characterized by a simple computation scheme and the fact that a smaller number of multiplications and divisions must be done than in the well-known methods of Krylov, Danilevsky and Le Verrier.