Influence of Asymmetric Distribution of Defects on Dynamic Stability of Bernoulli-Euler Beam |
| W. Sochacki, J. Garus, S. Garus
Department of Mechanics and Fundamentals of Machinery Design, Faculty of Mechanical Engineering and Computer Science, Częstochowa University of Technology, J.H. Dąbrowskiego 73, 42-201 Częstochowa, Poland |
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| Defects of structural elements may have a significant impact on the dynamic stability of the systems in which these elements are used. A Bernoulli-Euler beam was taken as an example of a structural element with defects. The study analyzed the influence of the asymmetric distribution of defects modeled with rotating springs. The influence of the depth of damage on the dynamic stability of the beam was also investigated. The method of mode summation was used to solve the problem of dynamic stability. After using the orthogonality condition of the eigenfunctions, the equations of motion of the studied system were presented in the form of the Mathieu equations. The obtained coefficients a and b of the Mathieu equations allow to determine stable and unstable solutions to the equation on the Strutt card. On this basis, it is possible to determine the dynamic stability of the tested beam for specific physical and geometric parameters of the system. |
DOI:10.12693/APhysPolA.139.557 topics: cracked beam, dynamic stability, Mathieu equation |