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Error estimate in calculating natural frequencies of a vibrating shaft by changing number of segments using lumped parameter model and transfer matrix method

Kargarnovin, M. H ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. Publisher: University of Southampton, Institute of Sound Vibration and Research , 2008
  3. Abstract:
  4. In this paper using classical beam theory, the dynamical governing differential equations of a vibrating shaft are derived then by using lumped parameter technique and method of transfer matrix (TM) the induced eigen value problem is solved. In calculating natural frequencies of a vibrating shaft under different boundary conditions, primarily the shaft was divided into number of segments. In each segment different number of lumped properties like mass, damping and flexibility on overall massless elastic or rigid shaft were applied. One of the aims of this study was to find out the optimum value for number of segments under different aforementioned conditions. In order to estimate the natural frequency error, the number of segments has been changed from 5 to 20. Moreover, the considered boundary conditions are; fixed-fixed, simply support-simply support, fixed-free, simply support-fixed. In each segment the position of the lumped mass was changed along the segment and its effect has been studied on the natural frequencies. Following to this study the first and second mode of lateral vibration of a clamped shaft using lumped flexibility and lumped mass techniques were investigated. By approaching the number of segments to infinity, the results of a continuous model are obtained hence the appropriateness of the method is verified
  5. Keywords:
  6. Boundary conditions ; Differential equations ; Matrix algebra ; Natural frequencies ; Structural dynamics ; Classical beam theory ; Different boundary condition ; Eigen-value problems ; Governing differential equations ; Lumped flexibility ; Lumped mass ; Lumped parameter ; Lumped parameter modeling ; Transfer matrix method
  7. Source: 7th European Conference on Structural Dynamics, EURODYN 2008, 7 July 2008 through 9 July 2008 ; 2008 ; 9780854328826 (ISBN)