Free Vibrations of Multi-Degree Structures: Solving Quadratic Eigenvalue Problems with an Excitation and Fast Iterative Detection Method

For the free vibrations of multi-degree mechanical structures appeared in structural dynamics, we solve quadratic eigenvalue problem either by linearizing it to a generalized or directly treating developing iterative detection methods for real and complex eigenvalues. To problem, impose nonzero exciting vector into eigen-equation, nonhomogeneous linear system obtain response curve, which consists magnitudes n-vectors with respect eigen-parameters range. The n-dimensional eigenvector is supposed be superposition constant an m-vector, can obtained terms eigen-parameter solving projected eigen-equation. In doing so, save computational cost because curve generated from data acquired lower dimensional subspace. We develop fast method maximizing magnitude locate eigenvalue, appears as peak curve. Through zoom-in sequentially, very accurate obtained. reduce number eigen-equation n?1 find eigen-mode its certain component being normalized unit. eigenvalues eigen-modes determined simultaneously, quickly accurately proposed methods.