Fan Yu, Collet Manuel, Ichchou Mohamed, Bareille Olivier, Li Lin
School of Energy and Power Engineering, Beihang University, Beijing 100191, China.
Beijing Key Laboratory of Aero-Engine Structure and Strength, Beijing 100191, China.
Materials (Basel). 2018 Aug 11;11(8):1406. doi: 10.3390/ma11081406.
A novel metrics termed the 'wave electromechanical coupling factor' (WEMCF) is proposed in this paper, to quantify the coupling strength between the mechanical and electric fields during the passage of a wave in piezoelectric composites. Two definitions of WEMCF are proposed, leading to a frequency formula and two energy formulas for the calculation of such a factor. The frequency formula is naturally consistent with the conventional modal electromechanical coupling factor (MEMCF) but the implementation is difficult. The energy formulas do not need the complicated wave matching required in the frequency formula, therefore are suitable for computing. We demonstrated that the WEMCF based on the energy formula is consistent with the MEMCF, provided that an appropriate indicator is chosen for the electric energy. In this way, both the theoretical closure and the computational feasibility are achieved. A numerical tool based on the wave and finite element method (WFEM) is developed to implement the energy formulas, and it allows the calculation of WEMCF for complex one-dimensional piezoelectric composites. A reduced model is proposed to accelerate the computing of the wave modes and the energies. The analytical findings and the reduced model are numerically validated against two piezoelectric composites with different complexity. Eventually an application is given, concerning the use of the shunted piezoelectric composite for vibration isolation. A strong correlation among the WEMCF, the geometric parameters and the energy transmission loss are observed. These results confirm that the proposed WEMCF captures the physics of the electromechanical coupling phenomenon associated with the guided waves, and can be used to understand, evaluate and design the piezoelectric composites for a variety of applications.
本文提出了一种名为“波动机电耦合因子”（WEMCF）的新指标，用于量化波在压电复合材料中传播时机械场与电场之间的耦合强度。提出了WEMCF的两种定义，由此得到了计算该因子的一个频率公式和两个能量公式。频率公式与传统的模态机电耦合因子（MEMCF）自然一致，但实现起来较为困难。能量公式不需要频率公式中所需的复杂波匹配，因此适合计算。我们证明，只要为电能选择合适的指标，基于能量公式的WEMCF与MEMCF是一致的。通过这种方式，实现了理论上的封闭性和计算上的可行性。开发了一种基于波动和有限元方法（WFEM）的数值工具来实现能量公式，它可以计算复杂一维压电复合材料的WEMCF。提出了一个简化模型以加速波动模式和能量的计算。针对两种不同复杂度的压电复合材料，对分析结果和简化模型进行了数值验证。最后给出了一个应用实例，涉及并联压电复合材料在隔振中的应用。观察到WEMCF、几何参数和能量传输损耗之间存在很强的相关性。这些结果证实，所提出的WEMCF捕捉到了与导波相关的机电耦合现象的物理本质，可用于理解、评估和设计用于各种应用的压电复合材料。
