Minimising the energy consumption associated with periodic motion is a priority common to a wide range of technologies and organisms - among them, many species of flying insect, for which flapping-wing flight is a life-essential mode of locomotion. In pursuit of this priority, the following problem often manifests: how to introduce elasticity into an actuated, oscillating, system in order to minimise actuator power consumption? Here, we explore this question in a range of general systems, and find some surprising answers. For instance, it is widely assumed that, if the system dynamics are linear, then linear resonant elasticity is the only optimal choice. We show, to the contrary, that there exist nonlinear elasticities with equivalent optimality, and provide an elegant method for constructing these elasticities in general systems. This is a new principle of linear and nonlinear dynamics, fundamentally altering how questions of energetic optimality in a wide range of dynamical systems must be approached. Furthermore, we show how this principle enables new forms of optimal system design, including optimal unidirectional actuation in nonlinear systems; new tools for the design of optimal biomimetic propulsion systems; and new insights into the role of structural elasticity in a range of different organisms.
翻译:与周期运动相关的能源消耗最小化是一系列广泛的技术和生物 — — 其中很多是飞行昆虫的物种 — — 常见的一个优先事项,它们中有许多飞虫物种,拍翼飞行是生命必需的移动模式。在追求这一优先事项时,以下问题往往表现为:如何将弹性引入一个已经激活的、振动的系统,以尽量减少动力消耗?在这里,我们在一系列一般系统中探索这一问题,并找到一些令人惊讶的答案。例如,人们广泛认为,如果系统动态是线性,那么线性共振弹性是唯一的最佳选择。相反,我们显示存在着非线性弹性,具有同等的最佳性,并为在一般系统中构建这些弹性提供了一种优雅的方法。这是一个线性和非线性动态的新原则,从根本上改变了如何在广泛的动态系统中处理高能最佳性的问题。此外,我们展示了这一原则如何促成新式的最佳系统设计形式,包括最佳单向振动弹性弹性弹性弹性弹性,在非线性动力化结构智能系统中提供了一种新型的系统;在非线性动力化结构感化系统中,一种新型的动力化结构动力学工具。