We develop a complete framework for modeling general electromechanical systems in the quasi-electrostatic regime. The equations are applicable to a broad range of electrostatic problems and offer the advantage of being theoretically tractable for scaling arguments. Additionally, we show how the formalism can be used together with finite element simulations to obtain estimates for non-stationary effects such as charge accumulation in insulators. As a demonstration, we combined the formalism with measurements from Advanced LIGO to give an updated estimate for the Johnson noise coupling to the gravitational-wave channel. The induced signal was determined to be 10 times lower than the instrument’s design sensitivity in the detection band and scaling as f ⁻².

我们为在准静电状态下的通用机电系统建模开发了一个完整的框架。该方程式适用于范围广泛的静电问题，并具有从理论上讲可用于换算参数的优点。此外，我们展示了形式主义如何与有限元模拟一起使用，以获取对非平稳效应（例如绝缘子中电荷积累）的估计。作为演示，我们将形式主义与Advanced LIGO的测量结果相结合，以提供对约翰逊噪声耦合到引力波通道的最新估计。确定感应信号比仪器在检测频带中的设计灵敏度低10倍，并缩放为f ^-2。