# On the stability of the stretched Euler-Bernoulli beam on a star-shaped graph

@inproceedings{Mahinzaeim2021OnTS, title={On the stability of the stretched Euler-Bernoulli beam on a star-shaped graph}, author={Mahyar Mahinzaeim and Genqi Xu and Hai Zhang}, year={2021} }

We deal with the as yet unresolved exponential stability problem for a stretched Euler–Bernoulli beam on a star-shaped geometric graph with three edges. The edges are hinged with respect to the boundary vertices. The inner vertex is capable of both translation and rotation, the latter of which is subject to a combination of elastic and frictional effects. We present detailed results on the properties of the linear monic operator pencil associated with the spectral problem in Hilbert space… Expand

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SHOWING 1-10 OF 28 REFERENCES

Spectral properties and stability of a nonselfadjoint Euler–Bernoulli beam

- Methods of Functional Analysis and Topology, 23:346–366
- 2017

Introduction To Infinite Dimensional Linear Systems Theory

- Computer Science
- 2016

This introduction to infinite dimensional linear systems theory helps people to enjoy a good book with a cup of tea in the afternoon, instead they juggled with some harmful bugs inside their laptop. Expand

Modeling Analysis And Control Of Dynamic Elastic Multi Link Structures

- Computer Science
- 2016

Thank you very much for reading modeling analysis and control of dynamic elastic multi link structures, and maybe you have knowledge that, people have look hundreds of times for their favorite readings, but end up in malicious downloads. Expand

On the Riesz basis property of root vectors system for $2 \times 2$ Dirac type operators

- Mathematics
- 2015

The paper is concerned with the Riesz basis property of a boundary value problem associated in $L^2[0,1] \otimes \mathbb{C}^2$ with the following $2 \times 2$ Dirac type equation $$ L y = -i B^{-1}… Expand

Spectral Theory of Operator Pencils

- Hermite–Biehler Functions, and their Applications. Birkhäuser
- 2015

On the completeness and Riesz basis property of root subspaces of boundary value problems for first order systems and applications

- Mathematics
- 2014

The paper is concerned with the completeness property of root functions of general boundary value problems for $n \times n$ first order systems of ordinary differential equations on a finite… Expand

Introduction to the Spectral Theory of Polynomial Operator Pencils

- Mathematics
- 2012

Operators with compact resolvent which are close to being normal Keldysh pencils Factorization of pencils Selfadjoint pencils.

On the completeness of root subspaces of boundary value problems for first order systems of ordinary differential equations

- Mathematics
- 2012

The paper is concerned with the completeness problem of root functions of general boundary value problems for first order systems of ordinary differential equations. We introduce and investigate the… Expand

Differential Equations on Metric Graph

- WSEAS Press
- 2010

Spectral Properties of a Fourth Order Differential Equation

- Mathematics
- 2006

The eigenvalue problem y(4)(λ, x) − (gy′)′(λ, x) = λ2y(λ, x) with boundary conditions y(λ, 0) = 0, y′′(λ, 0) = 0, y(λ, a) = 0, y′′(λ, a) + iαλy′(λ, a) = 0 is considered, where g ∈ C1[0, a] and α > 0.… Expand