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