2004 Conference on Diff. Eqns. and Appl. in Math. Biology, Nanaimo, BC, Canada.
Electron. J. Diff. Eqns., Conference 12, 2005, pp. 57-64.

On the isospectral beams

Kazem Ghanbari

The free undamped infinitesimal transverse vibrations of a thin straight beam are modelled by a forth-order differential equation. This paper investigates the families of fourth-order systems which have one spectrum in common, and correspond to four different sets of end-conditions. The analysis is based on the transformation of the beam operator into a fourth-order self-adjoint linear differential operator. This operator is factorized as a product $L=H^{*}H$, where $H$ is a second-order differential operator of the form $H=D^2+rD+s$, and $H^{*}$ is its adjoint operator.

Published April 20, 2005.
Math Subject Classifications: 34B05,34B10.
Key Words: Isospectral, Euler-Bernoulli equation for the vibrating beam, beam operator.

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Kazem Ghanbari
Department of Mathematics
Sahand University of Technology
Tabriz, Iran
email: kghanbari@sut.ac.ir

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