Minimization of the lowest eigenvalue for a vibrating beam

Quanyi Liang; Kairong Liu; Gang Meng; Zhikun She

doi:10.3934/dcds.2018085

Minimization of the lowest eigenvalue for a vibrating beam

Quanyi Liang
, Kairong Liu
, Gang Meng
, Zhikun She^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Chinese Academy of Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	2079-2092
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	38
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2018085
State	Published - Apr 2018

Keywords

Eigenvalue
Minimization problem
The fourth order equation

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10.3934/dcds.2018085

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abstract = "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.",

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N2 - 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.

AB - 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.

KW - Eigenvalue

KW - Minimization problem

KW - The fourth order equation

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M3 - 文章

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 4

ER -

Minimization of the lowest eigenvalue for a vibrating beam

Abstract

Keywords

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