Li Kai, Chen Zengfu, Wang Zhijian, Cai Shengqiang
Department of Civil Engineering, Anhui Jianzhu University, Hefei, Anhui 230601, China.
Materials Science and Engineering Program, University of California, San Diego, La Jolla, California 92093, USA.
Phys Rev E. 2021 Mar;103(3-1):033004. doi: 10.1103/PhysRevE.103.033004.
When a cylindrical rod is placed on a flat and hot surface with a constant temperature, it can reach a steady state after certain time. In the steady state, though the temperature field inside the rod is inhomogeneous, it does not change with time. The inhomogeneous temperature change in the rod may induce inhomogeneous thermal expansion in it. Recent experiments have determined that if the rod is slightly curved, the inhomogeneous thermal expansion in the rod can drive its continuous and self-sustained rolling on a hot surface. It has been further shown that if the rod is bent to a closed torus and placed on a hot surface, the torus everts or inverts continuously due to the cross-coupling between the thermal field and the cyclic rotation. Such cyclic eversion or inversion of a torus can be regarded as a zero-elastic-energy mode because both the elastic energy and the shape of the torus remain unchanged during the rotation. In this article, we develop a coupled mechanics theory to model the continuous self-sustained eversion or inversion of a viscoelastic torus on a hot surface. We hope our modeling will inspire more novel designs of elastic motors being capable of zero-energy mode motion and help to quantitatively predict their performance.
当将一根圆柱形杆放置在温度恒定的平坦且热的表面上时，经过一定时间它能达到稳态。在稳态下，尽管杆内部的温度场是不均匀的，但它不随时间变化。杆内不均匀的温度变化可能会在其中引起不均匀的热膨胀。最近的实验已经确定，如果杆稍微弯曲，杆内不均匀的热膨胀会驱动它在热表面上持续且自我维持地滚动。进一步表明，如果将杆弯曲成一个封闭的圆环并放置在热表面上，由于热场和循环旋转之间的交叉耦合，圆环会持续外翻或内翻。圆环的这种循环外翻或内翻可被视为一种零弹性能模式，因为在旋转过程中圆环的弹性能和形状都保持不变。在本文中，我们建立了一个耦合力学理论来模拟粘弹性圆环在热表面上持续的自我维持外翻或内翻。我们希望我们的建模能够激发更多能够实现零能量模式运动的弹性马达的新颖设计，并有助于定量预测它们的性能。
