带有静电假设的电荷或电流激励的主动约束层（ACL）梁模型的建模和稳定化结果
Modeling and stabilization results for a charge or current-actuated active constrained layer (ACL) beam model with the electrostatic assumption
摘要：
采用彻底变分法，在固定-自由边界条件下，建立了三层主动约束层（ACL）梁模型的无限维模型，该模型由顶部的压电弹性层和底部的弹性宿主层组成，中间约束粘弹层。采用Rao-Nakra薄柔性层近似来模拟夹层结构，并假设压电层为静电方法（忽略磁效应）。代替压电层的电压致动，压电层被提议由电荷（或电流）源激活。证明了具有机械反馈的闭环系统是一致指数稳定的。我们的结果是紧凑的扰动参数和一个独特的连续的结果依赖于乘子方法的谱问题的结果。最后，将本文的建模方法推广到多层ACL梁，建立了类似的一致指数稳定性结果。
英文摘要：
An infinite dimensional model for a three-layer active constrained layer (ACL) beam model, consisting of a piezoelectric elastic layer at the top and an elastic host layer at the bottom constraining a viscoelastic layer in the middle, is obtained for clamped-free boundary conditions by using a thorough variational approach. The Rao-Nakra thin compliant layer approximation is adopted to model the sandwich structure, and the electrostatic approach (magnetic effects are ignored) is assumed for the piezoelectric layer. Instead of the voltage actuation of the piezoelectric layer, the piezoelectric layer is proposed to be activated by a charge (or current) source. We show that, the closed-loop system with all mechanical feedback is shown to be uniformly exponentially stable. Our result is the outcome of the compact perturbation argument and a unique continuation result for the spectral problem which relies on the multipliers method. Finally, the modeling methodology of the paper is generalized to the multilayer ACL beams, and the uniform exponential stabilizability result is established analogously.
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