Study of a bi-mass chain with a band gap, and an engineering implementation based on tensegrity prisms

In this communication a Maxwell-Rayleigh model is outlined, describing a unidimensional elastic system with hosting and resonant masses [1]. Despite its simplicity this discrete model allows one to deduce, through Piola heuristic homogenization and a variational approach based on Hamilton least action principle, a dispersion relation, revealing the existence of a band gap, in which the propagation of harmonic perturbations is inhibited. Figure 1 illustrates the harmonic perturbations admissible for this system, in terms of nondimensional angular frequency and wavenumber, specified by the so-called acoustic and optical branches, which constitute lower and upper bounds for the band gap. The band frequency range can be tuned controlling the features (mass, stiffness, characteristic length) of the original system. As a meaningful engineering application, reference is made to tensegrity prisms, including compressed bars and tensioned cables, for which it is possible to tune the overall tangent stiffness by governing the cable pre-tensioning, see e.g. [2] and [3]. The preliminary design of a unidimensional chain with hosting and resonant masses, whose mutual elastic connections are constituted indeed of tensegrity prisms, is hence proposed, inhibiting harmonic perturbations in the frequency range of 1-10 Hz, typical of surface seismic waves, see also [4] and [5].