Benchmark for three-dimensional explicit asynchronous absorbing layers for ground wave propagation and wave barriers

Oscillating Nonlinear Acoustic Waves in a Mooney–Rivlin Rod

“…It should also be emphasized that the discussed phenomena can be used in creating a new type of non-reflecting boundary elements without viscous dissipation [45], compared with more traditional elastic-viscous elements [46,47] used for non-reflecting boundaries. Another area for possible application resides in the development of seismic barriers [48,49] used for protection from Rayleigh and Rayleigh-Lamb seismic waves, along with various applications in vibration protection [50][51][52][53][54][55][56]. Actually, the analyzed non-linear elastic media modeled by the Mooney-Rivlin equation of state and exhibiting the mechanical energy dissipation at the acoustic wave propagation open up a new approach in creating seismic and vibration isolation devices.…”

Dirac cones in three-layered plates

“…Originally, the term Dirac cone was referred to the unusual electron properties arising in the vicinity of Fermi level, where the valence and conduction bands form a conical surface with an apex known as the Dirac point 1 and the first theoretical prediction of Dirac cones in graphene. 2 In this respect see also theoretical studies [3][4][5] and works on experimental observation of Dirac cones appearing in graphene. [6][7][8] It was shown that Lamb waves propagating in a traction-free homogeneous isotropic and linearly elastic plate at some specific values of Poisson's ratio ( ν ), may exhibit a phenomenon, known as the Dirac cone, [9][10][11][12][13][14][15] associated with (i) the coincidence of two higher symmetric or asymmetric branches of Lamb waves at a phase velocity ( c ) approaching infinity; (ii) the non-vanishing angle between coinciding branches, considered as a function of the phase slowness ( s=c -1 ) or wave number ( r=ωs ), at s→0 or r→0; see Figure 1.…”

“…Originally, the term Dirac cone was referred to the unusual electron properties arising in the vicinity of Fermi level, where the valence and conduction bands form a conical surface with an apex known as the Dirac point 1 and the first theoretical prediction of Dirac cones in graphene. 2 In this respect see also theoretical studies 3–5 and works on experimental observation of Dirac cones appearing in graphene. 6–8…”

Convergence results of a heterogeneous asynchronous newmark time integrators

“…The introduction of the mixed time integration methods with/without different time steps (commonly known as heterogeneous asynchronous time integrators) for dynamic problems [2-4, 6, 8, 10, 12, 13, 16, 17, 19, 21, 27, 29, 31, 31, 32] are of considerable interest to many applications involving subdomains decomposition techniques (wave propagation [9,20,31], fluid-structure interaction problems [24], non-smooth contact problems [13]). The principle of heterogeneous asynchronous time integrators (HATI), for transient dynamic problems, consists on splitting the global problem into several subdomains, each one integrated by its own time scheme and/or its own time step.…”