Accurate modal superposition method for harmonic frequency response sensitivity of non-classically damped systems with lower-higher-modal truncation. (15th February 2017)

• Record Type: Journal Article
• Authors: Xiao, Weiwei; Li, Li; Lei, Sheng
• Is Part Of: Mechanical systems and signal processing. Volume 85(2017)
• Page Start: 204
• Page End: 217
• Publication Date: 2017-02-15
• Subjects: Frequency response sensitivity -- Frequency shifting -- Non-classical damping -- Modal superposition method -- Modal truncation error -- Harmonic response; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2016.08.017
• Languages: English
• ISSNs: 0888-3270

Abstract

Abstract: 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. Highlights: Harmonic frequency response sensitivity of non-classically damped systems is studied. The contribution of the lower and higher modes is expressed explicitly. The lower-higher-modal truncation error is eliminated. The method deals with the truncation error of FRF which is introduced for two times. The method maintains original-space resulting in efficient in computational source.