Cengiz Dokmeci M
Istanbul Tech. Univ., Istanbul.
IEEE Trans Ultrason Ferroelectr Freq Control. 1988;35(6):775-87. doi: 10.1109/58.9335.
Various forms of variational principles are developed and used to generate, as Euler-Lagrange equations, the fundamental differential equations of nonlinear piezoelectricity. First, Hamilton's principle is rigorously applied to the motion of an electroelastic solid with small piezoelectric coupling, and an associated variational principle is readily derived. Then, by use of the dislocation potentials and Lagrange undetermined multipliers (Friedrich's transformation), the variational principle is augmented for the motion of a piezoelectric solid region with an internal surface of discontinuity. To incorporate the constraints into the two-field variational principle, Friedrich's transformation is again applied, and a unified variational principle is systematically established. This unified variational principle is shown to produce the fundamental equations of an electroelastic solid with small piezoelectric coupling.
人们发展了各种形式的变分原理，并将其用于生成非线性压电性的基本微分方程，即欧拉 - 拉格朗日方程。首先，将哈密顿原理严格应用于具有小压电耦合的电弹性固体的运动，并且很容易推导出一个相关的变分原理。然后，通过使用位错势和拉格朗日待定乘数（弗里德里希变换），针对具有不连续内表面的压电固体区域的运动对变分原理进行了扩充。为了将约束纳入两场变分原理，再次应用弗里德里希变换，并系统地建立了一个统一的变分原理。结果表明，这个统一的变分原理能够给出具有小压电耦合的电弹性固体的基本方程。
