Kazem Ghanbari
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
,
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 Tabriz, Iran email: kghanbari@sut.ac.ir |
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