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Minimization of the lowest eigenvalue for a vibrating beam

The third author is supported by the National Natural Science Foundation of China (Grant No. 11671378) and the Fund of UCAS. The fourth author is supported by the National Natural Science Foundation of China (Grants No. 11371047 and No. 11422111)

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  • In this paper we solve the minimization problem of the lowest eigenvalue for a vibrating beam. Firstly, based on the variational method, we establish the basic theory of the lowest eigenvalue for the fourth order measure differential equation (MDE). Secondly, we build the relationship between the minimization problem of the lowest eigenvalue for the ODE and the one for the MDE. Finally, with the help of this built relationship, we find the explicit optimal bound of the lowest eigenvalue for a vibrating beam.

    Mathematics Subject Classification: Primary: 34L15; Secondary: 34L40.

    Citation:

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  • Figure 1.  Function $\mathbf{L}(r)$ of $r$

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