Volume 24, pp. 66-73, 2006.
Another approach to vibration analysis of stepped structures
Igor Fedotov, Steve Joubert, Julian Marais, and Michael Shatalov
Abstract
In this paper a model of an –stepped bar with variable Cross-sections
coupled with foundation by means of lumped masses and springs is studied.
It is assumed that the process of vibrations in each section of the bar is
described by a wave equation. The analytical tools of vibration analysis
are based on finding eigenfunctions with piecewise continuous derivatives,
which are orthogonal with respect to a generalized weight function.
These eigenfunctions automatically satisfy the boundary conditions at the
end points as well as the non-classical boundary conditions at the junctions.
The solution of the problems is formulated in terms of Green function.
By means of the proposed algorithm a problem of arbitrary complexity could
be considered in the same terms as a single homogeneous bar. This algorithm
is efficient in design of low frequency transducers. An example is given to
show the practical application of the algorithm to a two-stepped transducer.
Full Text (PDF) [212 KB],
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Key words
PDE with discontinuous coefficients, numerical approximation of eigenvalues, stepped structure, transducers, waveguide, variable cross-section, non-classical boundary conditions, Green function, resonance
AMS subject classifications
35B34, 35R05, 34B27, 34L16
