Abstract:In this paper we present an analytical model of Perfectly Matched Layers for flexural waves within elongated beam structures. The model is based on transformation optics techniques and it is shown to work both in time harmonic and transient regimes. A comparison between flexural and longitudinal waves is detailed and it is shown that the bending problem requires special interface conditions. A connection with transformation of eigenfrequencies and eigenmodes is given and the effect of the additional boundary c… Show more
“…The part of the structure with PML needs to be long enough to dissipate all the energy travelling through it. An alternative type of PML in a flexural system is discussed in [ 38 ]. Figure 6.…”
Section: Transmission Problem In a Multi-structure With Gyrobeamsmentioning
The paper presents a model of a chiral multi-structure incorporating gyro-elastic beams. Floquet–Bloch waves in periodic chiral systems are investigated in detail, with the emphasis on localization and the formation of standing waves. It is found that gyricity leads to low-frequency standing modes and generation of stop-bands. A design of an earthquake protection system is offered here, as an interesting application of vibration isolation. Theoretical results are accompanied by numerical simulations in the time-harmonic regime.
“…The part of the structure with PML needs to be long enough to dissipate all the energy travelling through it. An alternative type of PML in a flexural system is discussed in [ 38 ]. Figure 6.…”
Section: Transmission Problem In a Multi-structure With Gyrobeamsmentioning
The paper presents a model of a chiral multi-structure incorporating gyro-elastic beams. Floquet–Bloch waves in periodic chiral systems are investigated in detail, with the emphasis on localization and the formation of standing waves. It is found that gyricity leads to low-frequency standing modes and generation of stop-bands. A design of an earthquake protection system is offered here, as an interesting application of vibration isolation. Theoretical results are accompanied by numerical simulations in the time-harmonic regime.
“…Substituting (31) into the boundary conditions in (22), we obtain a linear system for the Fourier coefficients…”
Section: Tbc For the Pml Problemmentioning
confidence: 99%
“…It has found extensive applications in solving various wave scattering problems, including, for example, acoustic waves [23], electromagnetic waves [24][25][26], and elastic waves [27,28]. The PML method has also been utilized numerically in solving biharmonic wave scattering problems [29][30][31], highlighting its convenience and accuracy. However, to our knowledge, a comprehensive discussion regarding the well-posedness of the PML method and its convergence has not been documented in existing literature.…”
In this paper, we address exponential ergodicity for Lévy driven Langevin dynamics with singular potentials, which can be used to model the time evolution of a molecular system consisting of N particles moving in R d and subject to discontinuous stochastic forces. In particular, our results are applicable to the singular setups concerned with not only the Lennard-Jones-like interaction potentials but also the Coulomb potentials. In addition to Harris' theorem, the approach is based on novel constructions of proper Lyapunov functions (which are completely different from the setting for Langevin dynamics driven by Brownian motions), on invoking the Hörmander theorem for non-local operators and on solving the issue on an approximate controllability of the associated deterministic system as well as on exploiting the time-change idea.
“…An analytical model is considered in [17], which is ideally suited for layers of bending waves within elongated rod designs. The model is based on the methods of transformation of optics.…”
Section: Research Of Existing Solutions Of the Problemmentioning
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