Active Cloaking for Finite Clusters of Pins in Kirchhoff Plates

Abstract

Abstract. This paper considers active cloaking of a square array of evenly spaced pins in a Kirchhoff plate in the presence 3 of flexural waves. Active sources, modelled as ideal point sources, are represented by the non-singular Green's function for 4 the two-dimensional biharmonic operator and have an arbitrary complex amplitude. These sources are distributed exterior to 5 the cluster and their complex amplitudes are found by solving an algebraic system of equations. This procedure ensures that 6 selected multipole orders of the scattered field are successfully annulled. For frequencies in the zero-frequency stop band, we 7 find that a small number of active sources located on a grid is sufficient for cloaking. For higher frequencies, we achieve efficient 8 cloaking with the active sources positioned on a circle surrounding the cluster. We demonstrate the cloaking efficiency with 9 several numerical illustrations, considering key frequencies from band diagrams and dispersion surfaces for a Kirchhoff plate 10 pinned in a doubly periodic fashion. 11

Platonic crystal with low-frequency locally-resonant spiral structures: wave trapping, transmission amplification, shielding and edge waves

“…From the comparisons between the dispersion diagrams of perforated and homogeneous plates in Figure 4, at β I I I it is evident that, at this frequency, the dispersion curves show similarities with the homogeneous case. The eigenmode reported in the Figure evidences that a plane wave propagate within the microstructure medium with low scattering, a behavior that can be linked to perfect transmission [10,42,43].…”

Active exterior cloaking of an inclusion with evanescent multipole devices for flexural waves in thin plates

“…A different approach, based on [8][9][10], using multipole devices was devised by Futhazar et al [14] to create a finite 'still' region and to ensure that only the incident field was present in the far field. O'Neill et al later extended their investigation to the cloaking of coated inclusions in thin plates for frequency ranges in which scattering resonances occur [15] and to the cloaking of finite clusters of pins in thin plates [16].…”

Active acoustic cloaking in a convected flow field

“…The last decade has seen a surge of interest in the field of cloaking, commencing when Pendry et al 1 detailed a method using transformation optics to guide electromagnetic waves around an object to render it invisible, thus signalling the beginning of passive cloaking. Cloaking in electromagnetics, [2][3][4][5][6] acoustics, and elastodynamics [36][37][38][39][40] was soon realized. Cloaking methods in acoustics can be broadly categorized into two types: passive and active.…”

“…The residual field, resulting from destructive interference between the primary and secondary fields, resembles the incident field. Interior cloaking has been applied to both acoustic [27][28][29][30][31][32][33][34][35] and elastic [38][39][40] domains. Bobrovnitskii 27,28 proposed a novel method where cloaking was achieved by covering the body with a smart skin containing structural actuators, structural sensors, and pressure sensors capable of inducing surface impedances such that the body becomes non-scattering.…”

“…This work was extended to further consider resonant coated inclusions 39 as well as a finite cluster of pins. 40 An advantage of active cloaking applicable to both exterior and interior approaches is that controller parameters can be updated in real time to adjust for variation in frequency and incident field behaviour.…”