Accurate modal superposition method for harmonic frequency response sensitivity of non-classically damped systems with lower-higher-modal truncation

摘要

Frequency response and their sensitivities analysis are of fundamental importance. Due to the fact that the mode truncation errors of frequency response functions (FRFs) are introduced for two times, the errors of frequency response sensitivities may be larger than other dynamic analysis. Many modal correction approaches (such as modal acceleration methods, dynamic correction methods, force derivation methods and accurate modal superposition methods) have been presented to eliminate the modal-truncation error. However, these approaches are just suitable to the case of un-damped or classically damped systems. The state-space equation based approaches can extend these approaches to non-classically damped systems, but it may be not only computationally expensive, but also lack physical insight provided by the superposition of the complex modes of the equation of motion with original space. This paper is aimed at dealing with the lower-higher-modal truncation problem of harmonic frequency response sensitivity of non-classically damped systems. Based on the Neumann expansion and the frequency shifting technique, the contribution of the truncated lower and higher modes to the harmonic frequency response sensitivity is explicitly expressed only by the available middle modes and system matrices. An extended hybrid expansion method (EHEM) is then proposed by expressing harmonic frequency response sensitivity as the explicit expression of the middle modes and system matrices. The EHEM maintains original-space without having to involve the state-space equation of motion such that it is efficient in computational effort and storage capacity. Finally, a rail specimen is used to illustrate the effectiveness of the proposed method.