Realizable response matrices of multi-terminal electrical, acoustic and elastodynamic networks at a given frequency

被引:10
作者
Milton, Graeme W. [1 ]
Seppecher, Pierre [2 ]
机构
[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA
[2] Univ Toulon & Var, Lab Anal Non Lineare Appl & Modelisat, La Garde, France
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2008年 / 464卷 / 2092期
关键词
networks; circuits; multi-terminal;
D O I
10.1098/rspa.2007.0345
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
We give a complete characterization of the possible response matrices at a fixed frequency of n-terminal electrical networks of inductors, capacitors, resistors and grounds, and of n-terminal discrete linear elastodynamic networks of springs and point masses, both in three-dimensional and two-dimensional cases. Specifically, we construct networks that realize any response matrix that is compatible with the known symmetry properties and thermodynamic constraints of response matrices. Owing to a mathematical equivalence, we also obtain a characterization of the response matrices of discrete acoustic networks.
引用
收藏
页码:967 / 986
页数:20
相关论文
共 27 条
[1]   Truss modular beams with deformation energy depending on higher displacement gradients [J].
Alibert, JJ ;
Seppecher, P ;
Dell'Isola, F .
MATHEMATICS AND MECHANICS OF SOLIDS, 2003, 8 (01) :51-73
[2]  
[Anonymous], PORTUGALIAE MATH
[3]  
[Anonymous], RICERCHE MATEMATICA
[4]   Phononic band gaps in linearized elasticity. [J].
Avila, A ;
Griso, G ;
Miara, B .
COMPTES RENDUS MATHEMATIQUE, 2005, 340 (12) :933-938
[5]  
Bouchitté G, 2002, ASYMPTOTIC ANAL, V32, P153
[6]  
BRAINE M, 2007, COMMUN PART DIFF EQ, V32, P935, DOI DOI 10.1080/03605300600910423
[7]   Homogenization of non-uniformly bounded operators: Critical barrier for nonlocal effects [J].
Briane, M .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 164 (01) :73-101
[8]   Asymptotic behaviour of equicoercive diffusion energies in dimension two [J].
Briane, Marc ;
Casado-Diaz, Juan .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2007, 29 (04) :455-479
[9]   Determination of the closure of the set of elasticity functionals [J].
Camar-Eddine, M ;
Seppecher, P .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2003, 170 (03) :211-245
[10]   Closure of the set of diffusion functionals with respect to the mosco-convergence [J].
Camar-Eddine, M ;
Seppecher, P .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (08) :1153-1176