A new approach to compute natural frequencies and mode shapes of one-Dimensional continuous structures with arbitrary nonuniformities

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Abstract

One-dimensional continuous structures include longitudinal vibration of bars, torsional vibration of circular shafts, and transverse vibration of beams. Using the linear time-varying system theory, algorithms are developed in this paper to compute natural frequencies and mode shapes of these structures with nonuniform spatial parameters (mass distributions, material properties and cross-sectional areas) which can have jump discontinuities. A general numerical approach has been presented to include Dirac-delta functions and their spatial derivatives due to jump discontinuities. Numerical results are presented to illustrate the application of these techniques to the solution of different types of spatial variations of parameters and boundary conditions.

Original languageEnglish (US)
Article number111004
JournalJournal of Computational and Nonlinear Dynamics
Volume15
Issue number11
DOIs
StatePublished - Nov 2020

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics

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