An efficient method of solving for the eigenvalues in a dynamic transfer matrix analysis of beams, shafts and rotors

Abstract

The eigenvalues in a dynamic transfer matrix analysis have usually been obtained by trial-and-error searching for values which set a characteristic determinant to zero. Such a procedure requires an initial value, a step size, and a range over which the eigenvalues are sought. To be sure that an eigenvalue has not been missed by the search, it may be necessary to find all eigenvalues. To do so may require new starting values, search increments, and ranges. The authors develop an efficient procedure for finding the eigenvalues in a dynamic transfer matrix analysis. All eigenvalues are obtained simultaneously by the convergence of a matrix equation. The convergence does not depend upon the initial eigenvalue estimates, which may be arbitrary, and the need for search increments and range estimates is eliminated.<>