Fig. 1 ( a ) Schematic of an acoustic monatomic lattice and its equivalent electrical circuit model. ( b ) Unit cell of the acoustic monatomic lattice detailing the geometrical properties of the chamber and channel. ( c ) Fundamental frequency of an isolated unit cell (acting as a Helmholtz resona... More about this image found in ( a ) Schematic of an acoustic monatomic lattice and its equivalent electri...

Fig. 2 Dispersion relations of acoustic monatomic lattices with different combinations of parameters and geometrical shapes. As shown in the rightmost panel, parameter d c ( d ) defines the necessary dimension to calculate the cross-sectional area of the different chamber (channel) shapes, wh... More about this image found in Dispersion relations of acoustic monatomic lattices with different combinat...

Fig. 3 Schematics of an acoustic diatomic lattice, its equivalent electrical circuit model, and its unit cell definition with detailed geometrical properties. Note that the chambers (channels) are of square cross-sectional area with sides d c ( d 1,2 ) and the chamber dimensions are identica... More about this image found in Schematics of an acoustic diatomic lattice, its equivalent electrical circu...

Fig. 4 ( a ) Dispersion relations for acoustic diatomic lattices with the following three combinations of the Helmholtz resonance frequencies: (i) ω 2 < ω 1 , (ii) ω 2 = ω 1 , and (iii) ω 2 > ω 1 , corresponding to Δ d being −1 mm, 0, and +1 mm, respectively. ( b ) Bandgap li... More about this image found in ( a ) Dispersion relations for acoustic diatomic lattices with the followin...

Fig. 5 ( a ) Natural-frequency spectrum for three different acoustic diatomic lattices with (i) ω 2 < ω 1 , (ii) ω 2 = ω 1 , and (iii) ω 2 > ω 1 , showing the emergence of edge states only when ω 2 > ω 1 in agreement with the nonzero winding number in Figs. 4( b ) a... More about this image found in ( a ) Natural-frequency spectrum for three different acoustic diatomic latt...

Fig. 6 ( a ) and ( b ) Schematics of an acoustic honeycomb lattice, the unit cell definition, and the equivalent circuit model of the unit cell. Note that the change in the chamber height occurs symmetrically such that the coupling square channels remain at the center of the chambers' height. ( c ... More about this image found in ( a ) and ( b ) Schematics of an acoustic honeycomb lattice, the unit cell ...

Fig. 7 ( a ) Supercell analysis for a honeycomb lattice, formed by merging two lattices with flipped order of chambers (i.e., sign of m D ) at an interface midway, with 25 chambers on each side. The spectrum based on the full-scale numerical model (circles) and analytical one (lines) are shown... More about this image found in ( a ) Supercell analysis for a honeycomb lattice, formed by merging two lat...

Fig. 8 A parallelogram-shaped honeycomb structure with embedded ( a ) L- and ( b ) Z-waveguides, which are made of type B interface, defined in Fig. 7 . An arbitrary input is imposed on the right end of the waveguides at a frequency of 2 kHz (around the center of the frequency bandgap). The numer... More about this image found in A parallelogram-shaped honeycomb structure with embedded ( a ) L- and ( b )...

Fig. 1 DSS schematic: the original structure is split into a numerical part and a physical part. The synchronization signal S s ( t ) is measured on the physical part and transmitted as input to the numerically simulated subsystem. The goal of a DSS controller is to control the actuator at the... More about this image found in DSS schematic: the original structure is split into a numerical part and a ...

Fig. 2 Schematic representation of the benchmark system considered initially in this paper More about this image found in Schematic representation of the benchmark system considered initially in th...

Fig. 3 Potential choices for the location of the substructuring interface: ( a ) type 1 decomposition where the interface is right after mass l and ( b ) type 2 decomposition where the interface is located after the spring-mass damper system connected to mass l More about this image found in Potential choices for the location of the substructuring interface: ( a ) t...

Fig. 4 Displacement of fourth mass with type 2 decomposition. The drift is due to its marginal stability. More about this image found in Displacement of fourth mass with type 2 decomposition. The drift is due to ...

Fig. 5 Results obtained for DSS with force control in the type 1 decomposition with physical subsystem A More about this image found in Results obtained for DSS with force control in the type 1 decomposition wit...

Fig. 6 Results obtained for DSS with position control in the type 1 decomposition with numerical subsystem A More about this image found in Results obtained for DSS with position control in the type 1 decomposition ...

Fig. 7 Results obtained for DSS with position control in the type 2 decomposition with physical subsystem A More about this image found in Results obtained for DSS with position control in the type 2 decomposition ...

Fig. 8 Complex frame structure: ( a ) real structure and ( b ) equivalent mathematical representation More about this image found in Complex frame structure: ( a ) real structure and ( b ) equivalent mathemat...

Fig. 9 Results obtained for the complex structure with force control in the type 1 decomposition More about this image found in Results obtained for the complex structure with force control in the type 1...