<p>The dynamics of material particle chains exhibit the interesting property of sub-dynamics interaction. This paper discusses identical synchronization as a potential interaction of these sub-dynamics within the externally excited dynamics of an orthogonal lattice of chained material particles. The coupling elements between the particles possess viscous, linear and/or nonlinear elastic characteristics. One or more particles in the chain are subjected to periodic excitation. The extent of the synchronization effect varies based on the properties of the coupling elements, as well as the position and frequency of the excitations. A multi-parameter analysis was conducted through numerical simulations in the phase space of the output variables of the coupled particles, accompanied by diagrams illustrating synchronization errors. The analysis of signal propagation and delays was derived from the synchronization capabilities of adjacent particles under different external excitation positions and for different lengths of the chains. The time delay of signals was estimated from the synchronization error diagrams by measuring the duration required for transient changes prior to achieving identical and phase synchronization. The time taken for signal travel and delay is influenced by other system parameters. As the values of coupling parameters increase, the time for signal travel also increases. Also, shorter chains achieve faster synchronization, which is crucial for detecting signal transmission speed and delay in lattice of orthogonal chains of material points.</p>

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The signal delay in the synchronization of nonlinear chains of material particles

  • Julijana Simonovic

摘要

The dynamics of material particle chains exhibit the interesting property of sub-dynamics interaction. This paper discusses identical synchronization as a potential interaction of these sub-dynamics within the externally excited dynamics of an orthogonal lattice of chained material particles. The coupling elements between the particles possess viscous, linear and/or nonlinear elastic characteristics. One or more particles in the chain are subjected to periodic excitation. The extent of the synchronization effect varies based on the properties of the coupling elements, as well as the position and frequency of the excitations. A multi-parameter analysis was conducted through numerical simulations in the phase space of the output variables of the coupled particles, accompanied by diagrams illustrating synchronization errors. The analysis of signal propagation and delays was derived from the synchronization capabilities of adjacent particles under different external excitation positions and for different lengths of the chains. The time delay of signals was estimated from the synchronization error diagrams by measuring the duration required for transient changes prior to achieving identical and phase synchronization. The time taken for signal travel and delay is influenced by other system parameters. As the values of coupling parameters increase, the time for signal travel also increases. Also, shorter chains achieve faster synchronization, which is crucial for detecting signal transmission speed and delay in lattice of orthogonal chains of material points.