A new load-dependent Ritz vector method for structural dynamics analyses: quasi-static Ritz vectors

Abstract

Existing load-dependent Ritz vector (LDRV) methods employ static recurrence procedures to generate the Ritz vectors. As such, these vector methods are best suited for low-frequency problems. For higher-frequency problems, the existing methods may engender large sets of Ritz vectors, which significantly reduces the methods’ efficiency. A new algorithm is presented for LDRV generation using a quasi-static recurrence procedure, denoted as the quasi-static Ritz vector (QSRV) method. A tuning parameter, designated as the centering frequency, controls the behavior of the QSRV approach, enabling the new method to improve upon existing LDRV methods for particular frequency ranges of interest. Compared with existing LDRV methods, the QSRV method is more efficient (in terms of the number of Ritz vectors), more accurate (in terms of response errors), and more stable (in terms of orthogonality). Numerical examples are provided to illustrate the accuracy, efficiency and generality of the proposed method.