Abstract
In the article [1], is considered a classic method for analyze the dynamics of the loaded beam, as a result leading to the solution of a system of transcendental equations for the eigenvalues. In this paper, shall show that perhaps the solution using functions Tymoshenko arising in the analysis of the free beam vibrations. As a result, the problem will be reduced to infinite dimensional system of differential equations satisfying the conditions for the approximate solution.
Highlights
The study of the beam vibrations continues to be actual over the years and finds wide application in engineering practice
The authors [4,5,6] studied this problem is performed analysis to find eigenfrequencies and eigenmodes. This approach is useful when considering the free vibrations of the beam
The formula is clearly seen the main difference of this method from the classic separation of variables - additional load is taken into account in the Fourier coefficients, rather than in orthogonal conditions eigenfunctions
Summary
The study of the beam vibrations continues to be actual over the years and finds wide application in engineering practice. The authors [4,5,6] studied this problem is performed analysis to find eigenfrequencies and eigenmodes. This approach is useful when considering the free vibrations of the beam. If mass or spring-mass attach to a beam, having difficulty with the calculation of eigenfrequencies. We will show how, without changing the system of eigenfunctions, explore the fluctuations in the beam with a system of mass-spring-damper
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