Non-dimensional analysis of the elastic beam having periodic linear spring mass resonators

Band gaps appear in the frequency spectra of an elastic beam having periodic spring-mass attachment, acronymed as metabeam. Two widely used beam theories, i.e. Euler-Bernoulli and Timoshenko, are non-dimensionalized in order to obtain the dimensionless periodicity parameters. In this paper, the location and width of band-gaps are investigated due to the variation of these periodicity parameters of a metabeam. Implementing transfer matrix method in conjunction with Bloch-Floquet theorem, a unified methodology has been adopted to estimate the propagation and attenuation bands in a metabeam. This paper provides a guideline towards the designing of wide-band metabeam by tunning the non-dimensional parameters.