弹性杆和弹性旋转环作为引力波探测器
Elastic rods and elastic spinning rings as gravitational wave detectors
AI总结：
本文研究弹性杆和旋转环作为引力波探测器的理论，通过线性化相对论弹性方程求解共振频率，并发现可通过调整旋转环角速度调谐共振频率。
摘要：
本文考虑了弹性杆和旋转环在遭遇引力波时的线性化相对论弹性运动方程。对于杆的情况，方程在适当的边界条件下简化为波动方程。利用傅里叶变换，求出了共振频率，并给出了对于加极化和叉极化引力波的显式分布解。对于旋转环的情况，方程是具有周期边界条件的耦合波动方程。通过傅里叶级数展开，波动方程组被改写为关于傅里叶系数的一族常微分方程，然后通过傅里叶变换求解。求出了共振频率，包括缓慢旋转环的简单近似表达式，并在非旋转环的情况下获得了显式分布解。有趣的是，可以通过调整旋转环的角速度来调谐共振频率。
英文摘要：
Linearised relativistic elasticity equations of motion are considered for a rod and a spinning ring encountering a gravitational wave. In the case of the rod, the equations reduce to a wave equation with appropriate boundary conditions. Using Fourier transforms, the resonant frequencies are found and an explicit distributional solution is given, both for a plus- and a cross-polarised gravitational wave. In the case of the spinning ring, the equations are coupled wave equations with periodic boundary conditions. Using a Fourier series expansion, the system of wave equations is recast as a family of ordinary differential equations for the Fourier coefficients, which are then solved via Fourier transforms. The resonant frequencies are found, including simple approximate expressions for slowly rotating rings, and an explicit distributional solution is obtained in the case of the non-spinning ring. Interestingly, it is possible to tune the resonant frequencies by adjusting the angular velocity of the spinning ring.
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。
