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 , where is a second-order differential operator of the form , and 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
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