Transfer matrix method for linear vibration analysis of flexible multibody systems

Hanjing Lu, Xiaoting Rui*, Xuping Zhang

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


Achieving high computational efficiency has been well recognized as a research challenge in the vibration analysis of flexible multibody systems. This paper presents a novel transfer matrix method to model and analyze the linear vibration of flexible multibody systems. The transfer equations, the transfer matrices, and the consistency equations of the general flexible body elements with multi-input ends are deduced for the first time. Subsequently, the automatic deduction theorem of the overall transfer equation is developed for flexible multibody systems. Based on the theorem, the overall transfer equation can be deducted automatically and the natural vibration characteristics can be obtained. The dynamic equations and augmented eigenvectors are formulated to solve the forced vibration response. Further, the proposed method is applied to study the dynamics of an ultra-precision machine tool with flexible body elements. The natural vibration characteristics and the forced vibration response are solved and validated with the data from the modal tests and the working conditions. The proposed method has the following advantages: easy deduction of the overall transfer equation, low order of system matrix, and high computational speed.

Original languageEnglish
Article number117565
JournalJournal of Sound and Vibration
Publication statusPublished - 14 Apr 2023


  • Flexible body elements
  • Forced vibration response
  • Natural vibration characteristics
  • Transfer matrix method for flexible multibody systems
  • Ultra-precision machine tool
  • Vibration analysis


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