Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts

Abstract

In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam. The boundary-condition configuration should be preserved under this transformation. We present the constraints under which the boundary configurations will remain unchanged. Frequency equivalence of the non-uniform beams and the uniform beam is confirmed by the finite-element method. For the considered cases, examples of beams having a rectangular cross section are presented to show the application of our analysis.

Correction to ‘Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts’

“…This correction concerns equation 2.17 and consequently figs. 1 and 2 of [ 1 ]. The correct equation, and figures 1 and 2 are as follows:

Figure 1.

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