摘要：AbstractThis paper aims to characterize and classify the synchronization phenomena in the system consisting of multiple identical metronomes placed on an elastically fixed cart by using describing function (DF) method, which deals with a discontinuous model of the torque driving the metronome in terms of its angle and angular velocity. Different from a previous study on the uniform amplitude synchronization of all metronomes in the system, this paper analyzes uniform and non-uniform amplitude synchronization. By investigating and using the relation between the motion of the cart (common base) and the multiple metronomes which was not studied in the previous study, this paper presents a new DF solution of the system to characterize and classify the synchronization phenomena in the system by the following two types of synchronization: One is the inherent synchronization, for which the cart is still. The frequency and amplitudes of all synchronized metronomes are the same as those of a single metronome hanging from a fixed base. The other is the non-inherent synchronization, for which the cart moves in synchronization with all metronomes. It includes in-phase uniform amplitude synchronization and non-uniform amplitude synchronization. The new characterization and classification of the synchronization is validated via numerical investigation to the system with two, three, and four metronomes.
关键词：KeywordsSynchronizationmetronomespendulum clocksdescribing functionphasor representationcomplex system
