International Applied Mechanics

, Volume 41, Issue 5, pp 573–581 | Cite as

Longitudinal Vibrations of Cantilever Rods: Determination of Mechanical Quantities

  • N. P. Plakhtienko


Mechanical vibrating systems described by a one-dimensional wave equation are considered. Solutions are found in the form of Fourier series with terms decreasing at a certain rate. A relationship between the rate of convergence of the series and the intensity of the initial statical load is established. An approach is proposed to estimate the necessary number of terms, which is consistent with the degree of validity of the mathematical model. A method to minimize the error due to the Gibbs phenomenon for discontinuous periodic processes is justified


cantilever rod wave motion degree of validity error minimization 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • N. P. Plakhtienko
    • 1
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKievUkraine

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