A new method for band gap analysis of periodic structures using virtual spring model and energy functional variational principle

2022 ◽  
Vol 168 ◽  
pp. 108634
Author(s):  
Wenjie Guo ◽  
Zhou Yang ◽  
Qingsong Feng ◽  
Chengxin Dai ◽  
Jian Yang ◽  
...  
Keyword(s):  
Variational Principle ◽  
Band Gap ◽  
Gap Analysis ◽  
Periodic Structures ◽  
Energy Functional ◽  
New Method ◽  
Spring Model

A Hybrid Solution for Band-Gap Analysis of Vertical Vibration for Periodic Beam-Plate Coupled Systems Based on Variation Principle

2021 ◽  
pp. 2150173
Author(s):  
Qingsong Feng ◽  
Chengxin Dai ◽  
Wenjie Guo ◽  
Zhou Yang ◽  
Jianfei Lu
Keyword(s):  
Boundary Conditions ◽  
Band Gap ◽  
Composite Structures ◽  
Gap Analysis ◽  
Periodic Structures ◽  
Ritz Method ◽  
Coupled Systems ◽  
Variation Principle ◽  
Arbitrary Boundary ◽  
Hybrid Solution

The variation principle widely used in structural dynamics analysis allows us to transform the differential equation of the boundary value problem into a functional with extreme value. In recent years, it has been applied to the band-gap analysis of periodic structures. However, for periodic beam-plate composite structures with periodic and ordinary boundaries, it is relatively difficult for the traditional energy methods, such as the Rayleigh–Ritz method, to construct the displacement functions that satisfy boundary conditions. Hence, a hybrid solution is proposed in this paper to account for various boundary conditions of the periodic beam-plate composite structure. Specifically, the displacement functions constructed by the plane wave series can automatically satisfy the periodic boundary conditions. With the ordinary boundaries modeled by artificial springs, the spectral functions conforming to arbitrary boundary conditions are used to represent the displacement functions. The proposed solution is used to solve the band-gap problems of CRTS-III and CRTS-II slab ballastless tracks in China, and the accuracy of the solution is verified by comparing the calculated results with numerical simulations. In addition, through band-gap formation mechanism analysis, the frequency range of propagating flexural waves in each track component is accurately evaluated, which provides a theoretical basis for refined structural vibration reduction in the future. The solution proposed in this paper is flexible and convenient, which can be extended to a more complex band-gap analysis of periodic structures.

scholarly journals The effective mass problem for the Landau-Pekar equations

2021 ◽  
Author(s):  
Dario Feliciangeli ◽  
Simone Rademacher ◽  
Robert Seiringer
Keyword(s):  
Variational Principle ◽  
Effective Mass ◽  
Initial Velocity ◽  
Energy Functional ◽  
Mass Problem ◽  
Definition Of

Abstract We provide a definition of the effective mass for the classical polaron described by the Landau-Pekar equations. It is based on a novel variational principle, minimizing the energy functional over states with given (initial) velocity. The resulting formula for the polaron's effective mass agrees with the prediction by Landau and Pekar.

New method for determination of energy distribution of surface states in the semiconductor band-gap: XPS measurements under biases

1994 ◽  
Vol 92 (3) ◽  
pp. 249-254 ◽  
Author(s):  
Hikaru Kobayashi ◽  
Toshio Mori ◽  
Kenji Namba ◽  
Yoshihiro Nakato
Keyword(s):  
Energy Distribution ◽  
Band Gap ◽  
Surface States ◽  
New Method

Parametric Study on Rectangular Sonic Crystal

2012 ◽  
Vol 152-154 ◽  
pp. 281-286 ◽  
Author(s):  
Arpan Gupta ◽  
Kian Meng Lim ◽  
Chye Heng Chew
Keyword(s):  
Band Gap ◽  
Periodic Structure ◽  
Parametric Study ◽  
Sound Propagation ◽  
Periodic Structures ◽  
Sound Attenuation ◽  
Experimental Results ◽  
Center Frequency ◽  
Sonic Crystal ◽  
Sonic Crystals

Sonic crystals are periodic structures made of sound hard scatterers which attenuate sound in a range of frequencies. For an infinite periodic structure, this range of frequencies is known as band gap, and is determined by the geometric arrangement of the scatterers. In this paper, a parametric study on rectangular sonic crystal is presented. It is found that geometric spacing between the scatterers in the direction of sound propagation affects the center frequency of the band gap. Reducing the geometric spacing between the scatterers in the direction perpendicular to the sound propagation helps in better sound attenuation. Such rectangular arrangement of scatterers gives better sound attenuation than the regular square arrangement of scatterers. The model for parametric study is also supported by some experimental results.

Sign in / Sign up

Export Citation Format

Share Document