柯西-麦克斯韦方程：耦合电磁学与弹性力学的统一场论
Cauchy-Maxwell equations: A unified field theory for coupled electromagnetism and elasticity
AI总结：
该研究利用共形规范理论首次推导了统一弹性动力学与电磁学的柯西-麦克斯韦方程，通过半解析研究验证了其在压电、压磁场景的应用，为能量收集等领域研究提供了新理论基础。
摘要：
本文采用共形规范理论来描述并统一固体连续介质中观测到的多种机电与磁机耦合效应。通过在有限变形框架下使用时空伪黎曼度规，并利用拉格朗日量的局部共形对称性，我们首次推导得出柯西-麦克斯韦（CM）方程，该方程将柯西弹性动力学方程与电磁学麦克斯韦方程无缝结合。我们的模型可还原真空麦克斯韦方程，这本身也构成了这些方程的一种新推导方式。由于拉格朗日密度中耦合了变形梯度与物质速度，欧拉-拉格朗日方程中会出现各种赝力。这些力无法通过经典连续介质力学识别，在特定几何或载荷条件下可能具有重要意义。作为CM方程应用的有限示例，我们开展了半解析研究，即针对经受等容变形的无限体，以及同时承受拉伸与横向载荷的有限薄膜，研究中考虑了压电效应与压磁效应。结果表明，在特定载荷频率与张力下，薄膜部分区域的电势与磁势可能快速升高，这对未来高效能量收集研究具有参考价值。
英文摘要：
A conformal gauge theory is used to describe and unify myriad electromechanical and magnetomechanical coupling effects observed in solid continua. Using a space-time pseudo-Riemannian metric in a finite-deformation setup and exploiting the local conformal symmetry of the Lagrangian, we derive Cauchy-Maxwell (CM) equations that seamlessly combine, for the first time, Cauchy's elasto-dynamic equations with Maxwell's equations for electromagnetism. Maxwell's equations for vacuum are recoverable from our model, which in itself also constitutes a new derivation of these equations. With deformation gradient and material velocity coupled in the Lagrange density, various pseudo-forces appear in the Euler-Lagrange equations. These forces, not identifiable through classical continuum mechanics, may have significance under specific geometric or loading conditions. As a limited illustration on how the CM equations work, we carry out semi-analytical studies, viz. on an infinite body subject to isochoric deformation and a finite membrane under both tensile and transverse loading, considering piezoelectricity and piezomagnetism. Our results show that under specific loading frequencies and tension, electric and magnetic potentials may increase rapidly in some regions of the membrane. This may have significance in future studies on efficient energy harvesting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
