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# Spectral properties and stability of a nonselfadjoint Euler-Bernoulli beam

### Abstract

In this note we study the spectral properties of an Euler-Bernoulli beam model with damping and elastic forces applying both at the boundaries as well as along the beam. We present results on completeness, minimality, and Riesz basis properties of the system of eigen- and associated vectors arising from the nonselfadjoint spectral problem. Within the semigroup formalism it is shown that the eigenvectors have the property of forming a Riesz basis, which in turn enables us to prove the uniform exponential decay of solutions of the particular system considered.

Key words: Euler-Bernoulli beam, nonselfadjoint operator, operator pencil, completeness, minimality, Riesz basis, series expansion, exponential stability.

### Article Information

 Title Spectral properties and stability of a nonselfadjoint Euler-Bernoulli beam Source Methods Funct. Anal. Topology, Vol. 23 (2017), no. 4, 346-366 MathSciNet MR3745186 Milestones Received 02/05/2017; Revised 27/06/2017 Copyright The Author(s) 2017 (CC BY-SA)

### Authors Information

Mahyar Mahinzaeim
School of Mechanical and Systems Engineering, Newcastle University, Stephenson Building, Newcastle upon Tyne, NE1 7RU, United Kingdom

### Citation Example

Mahyar Mahinzaeim, Spectral properties and stability of a nonselfadjoint Euler-Bernoulli beam, Methods Funct. Anal. Topology 23 (2017), no. 4, 346-366.

### BibTex

@article {MFAT1003,
AUTHOR = {Mahyar Mahinzaeim},
TITLE = {Spectral properties and stability of a nonselfadjoint Euler-Bernoulli beam},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {23},
YEAR = {2017},
NUMBER = {4},
PAGES = {346-366},
ISSN = {1029-3531},
MRNUMBER = {MR3745186},
URL = {http://mfat.imath.kiev.ua/article/?id=1003},
}

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