Altay Gülay, Dökmeci M Cengiz
Faculty of Enginering, Bogazici University, Bebek 34342, Istanbul, Turkey.
IEEE Trans Ultrason Ferroelectr Freq Control. 2005 Nov;52(11):2112-9.
The governing equations of a porous piezoelectric continuum are presented in variational form, though they were well established in differential form. Hamilton's principle is applied to the motions of a regular region of the continuum, and a three-field variational principle is obtained with some constraint conditions. By removing the constraint conditions that are usually undesirable in computation through an involutory transformation, a unified variational principle is presented for the region with a fixed internal surface of discontinuity. The unified principle leads, as its Euler-Lagrange equations, to all the governing equations of the region, including the jump conditions but excluding the initial conditions. Certain special cases and reciprocal variational principles are recorded, and they are shown to recover some of the earlier ones.
多孔压电连续介质的控制方程以变分形式给出，尽管它们在微分形式中已得到充分确立。哈密顿原理应用于连续介质规则区域的运动，并在一些约束条件下得到了一个三场变分原理。通过对合变换消除计算中通常不希望出现的约束条件，为具有固定内部间断面的区域提出了一个统一的变分原理。该统一原理作为其欧拉 - 拉格朗日方程，可导出该区域的所有控制方程，包括跳跃条件，但不包括初始条件。记录了某些特殊情况和互易变分原理，并表明它们恢复了一些早期的原理。
