Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin-Shtrikman type
Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin-Shtrikman type
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DOI：
10.1098/rspa.2010.0006
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发表时间：
2010-10-08
影响因子：
3.5
通讯作者：
Willis, John R.
中科院分区：
文献类型：
--
作者：
Milton, Graeme W.;Willis, John R.
米尔顿等人获得了耗散介质中的线性弹性动力学、声学或电磁时间谐波的最小化变分原理（米尔顿等人，2009年，Proc. R. Soc. A 465，367-396（doi：10.1098/rspa.2008.0195）），推广了Cherkaev和Gibiansky的准静态变分原理（Cherkaev & Gibiansky 1994 J.Math.Phys.35，127-145（doi：10.1063/1.530782））。在这里，进一步的推广是允许更广泛的各种边界条件，特别是狄利克雷和诺依曼边界条件。此外，最小化或最大化原则的Hashin-Shtrikman类型，纳入“偏振场”，开发。静态问题的相应原理在确定复合材料的有效静态性能方面有着重要的应用。新的动力学原理为研究此类材料的有效动力学性质提供了前景。
Minimization variational principles for linear elastodynamic, acoustic or electromagnetic time-harmonic waves in dissipative media were obtained by Milton et al. (Milton et al. 2009 Proc. R. Soc. A 465, 367-396 (doi:10.1098/rspa.2008.0195)), generalizing the quasistatic variational principles of Cherkaev and Gibiansky (Cherkaev & Gibiansky 1994 J. Math. Phys. 35, 127-145 (doi:10.1063/1.530782)). Here, a further generalization is made to allow for a much wider variety of boundary conditions, and in particular Dirichlet and Neumann boundary conditions. In addition minimization or maximization principles of the Hashin-Shtrikman type, incorporating 'polarization fields', are developed. The corresponding principles for static problems have found substantial use in bounding the effective static properties of composite materials. The new dynamical principles offer the prospect of developing bounds on the effective dynamic properties of such materials.