Properties of Vibration Fields in a Two-Dimensional Lattice Structure Colliding with an Obstacle

2020 ◽  
pp. 473-485
Author(s):  
Vitaly Krupenin ◽  
Vladimir Astashev
Keyword(s):  
Lattice Structure ◽  
Two Dimensional ◽  
Dimensional Lattice

Study on bandgap and directional wave propagation of a two-dimensional lattice with nested core

2022 ◽  
Author(s):  
Jiahong Hou ◽  
Zhijun Zhang ◽  
Dong Li
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Group Velocity ◽  
Phase Structure ◽  
Single Phase ◽  
Lattice Structure ◽  
Two Dimensional ◽  
Practical Application ◽  
Dimensional Lattice ◽  
Directional Wave

Abstract This paper proposed a two-dimensional lattice structure with a nested core. The bandgap distribution and the anisotropy of phase velocity and group velocity were studied based on Bloch’s theorem and finite element method. The effects of eccentric ratio (e) and rotation angle (θ) of dual-phase structure on the bandgap distribution were investigated, and the anisotropy was studied via phase velocity and group velocity. The structure of (e) = 0.3 displayed the maximum total bandgap width. With (θ) increasing, the total bandgap widths of structures of different (e) all increased apparently and the low-frequency bandgap properties were improved. The phase velocity and group velocity of (e) = 0 displayed strong anisotropy, and the anisotropy was tuned by tuning (θ). Furthermore, the group velocity of the eighth mode displayed high directional wave propagation. For practical application, a single-phase structure was proposed and analyzed. Through additive manufacturing technology, the single-phase structure was prepared and tested by a low amplitude test setup. The experimental results displayed a good agreement with numerical results which demonstrated high directional propagation. This finding may pave the way for the practical application of the proposed lattice metamaterial in terms of wave filtering.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Sign in / Sign up

Export Citation Format

Share Document