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Longitudinal Vibrations of Cantilever Rods: Determination of Mechanical Quantities

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Abstract

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

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    N. P. Plakhtienko

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  1. N. P. Plakhtienko
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Translated from Prikladnaya Mekhanika,Vol. 41, No. 5, pp.131–140, May 2005.

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Plakhtienko, N.P. Longitudinal Vibrations of Cantilever Rods: Determination of Mechanical Quantities. Int Appl Mech 41, 573–581 (2005). https://doi.org/10.1007/s10778-005-0126-0

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  • DOI: https://doi.org/10.1007/s10778-005-0126-0

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