Geodesic
Another approach to vibration analysis of stepped structures
Electronic transactions on numerical analysis, Tome 24 (2006), pp. 66-73
In this paper a model of an -stepped bar with variable Cross-sections coupled with foundation by $\sterling $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.
Classification : 35B34, 35R05, 34B27, 34L16
Keywords: PDE with discontinuous coefficients, numerical approximation of eigenvalues, stepped structure, transducers, waveguide, variable cross-section, non-classical boundary conditions, Green function, resonance 
@article{ETNA_2006__24__a6,
     author = {Fedotov,  Igor and Joubert,  Steve and Marais,  Julian and Shatalov,  Michael},
     title = {Another approach to vibration analysis of stepped structures},
     journal = {Electronic transactions on numerical analysis},
     pages = {66--73},
     year = {2006},
     volume = {24},
     zbl = {1122.35147},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__24__a6/}
}
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%A Shatalov,  Michael
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%J Electronic transactions on numerical analysis
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Fedotov,  Igor; Joubert,  Steve; Marais,  Julian; Shatalov,  Michael. Another approach to vibration analysis of stepped structures. Electronic transactions on numerical analysis, Tome 24 (2006), pp. 66-73. http://geodesic.mathdoc.fr/item/ETNA_2006__24__a6/