该研究团队指出，在自然和人工环境中存在一类共振振荡，它们可被稳定的零频率力（如风、水、电场等）直接激发。这类振荡包括一个系统的两个通常独立的振荡模式，如建筑物或桥梁，它们单独无法被零频率力驱动。当同意合作条款时，这两种模式参与由稳定的零频率力驱动的联合振荡，其中一种是直接驱动，另一种是参数驱动。研究人员在一个家庭淋浴环境中观察到了属于这一类的双峰振动，其中两种模式是钟摆摆动和自由悬挂的莲蓬头的扭矩扭转，这两种模式在水流的阈值以上突然进入协同振动。
研究人员提出一个理论模型，用于预测和解释观察到的主要特征。这个模型扩展了1883年瑞利勋爵和迈克尔·法拉第提出的理论，通过在共振频率的两倍处调制系统参数来激发单个谐振模式。这一建议被认为是参量物理学的开端。该研究的实验部分由三个在家庭淋浴环境下拍摄的视频片段支持，这些视频片段证实了基本的理论假设。无所不在的零频率力，如风，以及它们直接转换为交变共振系统振动，赋予了这类具有放大的破坏潜力，对结构稳定性产生影响。
附：英文原文
Title: On a class of bimodal oscillations powered by a steady, zero-frequency force—Implications to energy conversion and structural stability
Author: Yariv, Amnon Zalman
Issue&Volume: 2023-9-11
Abstract: I propose that there exists in natural and artificial environments a class of resonant oscillations that can be excited directly by a steady, zero-frequency force such as that of wind, water, electric field. A member of this class comprises two normally independent oscillating modes of a system, for example, a building or bridge, which, separately, cannot be driven by a zero-frequency force. Agreeing on terms of collaboration, the two modes engage in a joint oscillation powered by the steady zero-frequency force in which they drive each other, one directly and the other parametrically. I observed a bimodal vibration belonging to this class in a home shower where the two modes are the pendulum excursion and the torsional twisting of a freely suspended showerhead which break into a joint oscillation above a threshold value of the water flow rate. I advance a theoretical model which predicts and explains the main features of the observations. The model constitutes an extension to two modes of a proposal and demonstration in 1883 by Lord Rayleigh and Michael Faraday for the excitation of a single resonant mode by modulating a system parameter at twice the resonance frequency. The proposal is credited with the launching of parametric physics. The Experiments section of this report consists of three linked video clips photographed in the home shower which support the basic theoretical assumptions. The ubiquity of zero-frequency forces, such as that of wind, and their direct conversion to alternating on-resonance system vibrations endows the class with an amplified destructive potential with implications for structural stability.
DOI: 10.1073/pnas.2311412120
Source: https://www.pnas.org/doi/10.1073/pnas.2311412120