Bloch mode synthesis (BMS) is a model order reduction method that was originally formulated to accelerate band-structure calculations of periodic elastic materials. In this paper, the BMS framework is expanded to offer a platform suitable for analysis of electroelastic metamaterials with piezoelectric resonant shunt damping. First, a transformation of coordinates formed by a set of dominant fixed-interface modes and a set of static-constraint modes is used in combination with Bloch periodicity boundary conditions to derive the classical BMS method in the context of electroelastic metamaterials. Then, a set of residual modes that is simply truncated in the classical BMS, is augmented into the reduction process, leading to an enhanced BMS method, denoted RMH-BMS.

Currently available model order reduction techniques for electroelastic metamaterials adopt a reduction basis obtained from one of the limiting eigenvalue problems associated with short-circuit (SC) and open-circuit (OC) boundary conditions. In either case, the electrical circuit parameters are ignored during modal reduction. In this paper, it is shown that such approximation leads to inaccurate band-structure predictions for electroelastic metamaterials equipped with periodic array of resonant shunt circuits. To this end, two versions of the proposed BMS methods are evaluated and compared. In the first version, the reduced order model is constructed following the widely used OC basis approach. The second version, on the other hand, exploits a coupled basis approach, which requires knowledge of the electrical circuit parameters prior to the interior modal reduction step. A comprehensive error analysis is conducted to assess the computational performances of the BMS methods, and the results revealed that whether the classical BMS or the RMH-BMS is employed to construct the reduced order model, the coupled basis approach produces significantly more accurate results compared to the OC basis approach. The results presented in this work expose the limitations of implementing the OC basis approach in wave propagation analysis of electroelastic metamaterials with piezoelectric resonant shunt damping and shed light on the associated consequences in predicting the bandgap properties of such metamaterials.

布洛赫模式合成 (BMS) 是一种模型降阶方法，最初是为了加速周期性弹性材料的能带结构计算而制定的。在本文中，扩展了 BMS 框架，以提供一个适用于分析具有压电谐振分流阻尼的电弹性超材料的平台。首先，由一组主要的固定界面模式和一组静态约束模式形成的坐标变换与布洛赫周期性边界条件相结合，在电弹性超材料的背景下推导出经典的 BMS 方法。然后，在经典 BMS 中简单截断的一组残差模式被扩充到减少过程中，从而产生增强的 BMS 方法，表示为 RMH-BMS。

目前可用的电弹性超材料模型降阶技术采用从与短路 (SC) 和开路 (OC) 边界条件相关的限制特征值问题之一获得的还原基础。在任何一种情况下，在模态缩减期间都会忽略电路参数。在本文中，表明这种近似会导致对配备周期性谐振分流电路阵列的电弹性超材料的能带结构预测不准确。为此，对所提出的 BMS 方法的两个版本进行了评估和比较。在第一个版本中，降阶模型是按照广泛使用的 OC 基方法构建的。另一方面，第二个版本利用耦合基方法，这需要在内部模态减少步骤之前了解电路参数。进行了全面的误差分析以评估 BMS 方法的计算性能，结果表明，无论是使用经典 BMS 还是 RMH-BMS 来构建降阶模型，耦合基方法产生的结果明显更准确。 OC基础方法。这项工作中提出的结果揭示了在具有压电谐振分流阻尼的电弹性超材料的波传播分析中实施 OC 基础方法的局限性，并揭示了预测此类超材料的带隙特性的相关后果。进行了全面的误差分析以评估 BMS 方法的计算性能，结果表明，无论是使用经典 BMS 还是 RMH-BMS 来构建降阶模型，耦合基方法产生的结果明显更准确。 OC基础方法。这项工作中提出的结果揭示了在具有压电谐振分流阻尼的电弹性超材料的波传播分析中实施 OC 基础方法的局限性，并揭示了预测此类超材料的带隙特性的相关后果。进行了全面的误差分析以评估 BMS 方法的计算性能，结果表明，无论是使用经典 BMS 还是 RMH-BMS 来构建降阶模型，耦合基方法产生的结果明显更准确。 OC基础方法。这项工作中提出的结果揭示了在具有压电谐振分流阻尼的电弹性超材料的波传播分析中实施 OC 基础方法的局限性，并揭示了预测此类超材料的带隙特性的相关后果。与 OC 基础方法相比，耦合基础方法产生的结果要准确得多。这项工作中提出的结果揭示了在具有压电谐振分流阻尼的电弹性超材料的波传播分析中实施 OC 基础方法的局限性，并揭示了预测此类超材料的带隙特性的相关后果。与 OC 基础方法相比，耦合基础方法产生的结果要准确得多。这项工作中提出的结果揭示了在具有压电谐振分流阻尼的电弹性超材料的波传播分析中实施 OC 基础方法的局限性，并揭示了预测此类超材料的带隙特性的相关后果。