In this paper a model of an N-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.
Reference:
Fedotov, I, et al. 2006. Another approach to vibrational analysis of stepped structures. Electronic Transactions on Numerical Analysis, Vol. 24, pp 66-73
Fedotov, I., Joubert, S., Marais, J., & Shatalov, M. (2006). Another approach to vibrational analysis of stepped structures. http://hdl.handle.net/10204/972
Fedotov, I, S Joubert, J Marais, and M Shatalov "Another approach to vibrational analysis of stepped structures." (2006) http://hdl.handle.net/10204/972
Fedotov I, Joubert S, Marais J, Shatalov M. Another approach to vibrational analysis of stepped structures. 2006; http://hdl.handle.net/10204/972.