2004 Conference on Diff. Eqns. and Appl. in Math. Biology, Nanaimo,
BC, Canada.
Electronic Journal of Differential Equations,
Conference 12, 2005, pp. 57-64.
Title: On the isospectral beams
Author: Kazem Ghanbari (Sahand Univ. of Technology, Tabriz, Iran)
Abstract:
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