Original scientific paper

A family of isospectral fourth order Sturm Liouville problems and equivalent beam equations Hanif Mirzaei

Hanif Mirzaei ; Department of Mathematics, Sahand University of Technology, Tabriz, Iran

Abstract

In this paper, we consider the class of fourth order Sturm- Liouville equation of the form $y^{(4)}(z)-2(q(z)y^{\prime})^{\prime}+(q^2(z)-q^{\prime\prime}(z))y(z)=\lambda^2y(z),\ 0\leq z \leq L$, with boundary conditions $y(z)=y^{\prime\prime}(z)=0$ at $z=0,L$. We prove that this class is equivalent to a second order Sturm Liouville problem. Using Darboux Lemma we obtain the closed form of fourth order Sturm-Liouville equations that is isospectral to a given one. Also we obtain the Euler Bernoulli beam equation equivalent to this class.

Keywords

Isospectral; fourth order Sturm-Liouville equation; Euler-Bernoulli beam equation

Hrčak ID:

192105

URI

https://hrcak.srce.hr/192105

Publication date:

30.5.2018.

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