Transmission and localisation in ordered and randomly-perturbed structured flexural systems

Gyro-elastic beams for the vibration reduction of long flexural systems

“…The theoretical and practical challenge is to create, within the required frequency interval, ‘energy sinks’ where waves are channelled and thus diverted away from the main protected structure. Owing to their versatility, multi-scale high-contrast resonators can also be employed to protect randomly perturbed structures [ 14 ] from seismic waves. The incorporation of resonators into an elastic structure can lead to many interesting effects, such as generation of low-frequency standing waves [ 15 ], negative refraction [ 16 , 17 ], cloaking and filtering of seismic waves [ 18 , 19 ].…”

The generalized Floquet-Bloch spectrum for periodic thermodiffusive layered materials

“…In this case, being the wave number related to the Floquet multiplier by relation k 2 = ln(λ)/(i L), its real and imaginary parts are expressed in terms of λ = λ r + i λ i as 1/λ k is an eigenvalue. Such eigenvalues, in fact, are the roots of a palindromic characteristic polynomial, which is characterized by a reduced number of invariants (Hennig and Tsironis, 1999;Romeo and Luongo, 2002;Bronski and Rapti, 2005;Xiao et al, 2013;Carta and Brun, 2015;Carta et al, 2016). A procedure to compute the invariants of such characteristic polynomial is detailed in Appendix B.…”

Numerical investigations and experimental measurements on the structural dynamic behaviour of quasi-periodic meta-materials

“…According to the literature, there are numerous examples of disordered periodicities and/or uncertainties in real structures, like bridges with column spans, and array of fuel tanks interconnected with each other by flexural links. The issues of the non-perfect periodicity in real structures can also be attributed to errors in manufacturing processes [11]. The presence of defects and imperfections in geometric and constitutive properties of the structures is generally referred as disorder [12].…”