Occurrence of gradual resonance in a finite-length granular chain driven by harmonic vibration

Abstract

This study presents numerical simulations of the resonance of a finitelength granular chain of dissipative grains driven by a harmonically vibrated tube. Multiple gradual resonant modes, namely, non-resonance mode, partial-resonance mode, and complete-resonance mode, are identified. With a fixed vibration frequency, increased vibration acceleration leads to a one-by-one increase in the number of grains participating in resonance, which is equal to the number of grain-wall collisions in a vibration period. Compared with the characteristic time of the grain-grain and the grain-wall collisions, the time of free flight plays a dominant role in grain motion. This condition results in the occurrence of large opening gaps between the grains and independent grain-grain and gain-wall collisions. A general master equation that describes the dependence of the system energy on the length of the granular chain and the number of grain-wall collisions is established, and it is in good agreement with the simulation results. We observe a gradual step-jump increase in system energy when the vibration acceleration is continuously increased, which is dedicated to an individual energy injection. Moreover, two typical phase diagrams are discussed in the spaces of φ − Γ and N − Γ .

Asymmetric scattering effect of solitary wave in a two-section composite granular chain

“…In particular, Eqs. ( 5) (8) indicate that mass density and elastic coefficient have the same effects on the characteristic wave velocities c 0 and c mat . Thus, we can make the following arguments on the asymmetric scattering effect taken from the mismatched mass density and elastic coefficient by using classical acoustic theory in a linear medium.…”

“…[4][5][6] Nonlinear wave propagation has attracted the attention of physicists and engineers because of its technological applications, such as shock damper and mechanical logic elements. [7][8][9][10][11][12][13] A thorough understanding of nonlinear wave propagation dynamics in the ordered granular chain(GC) is often considered as the groundwork.…”

Asymmetric scattering effect of solitary wave in a two-section composite granular chain

“…[4][5][6] Nonlinear wave propagation has attracted the attention of physicists and engineers because of its technological applications, such as shock damper and mechanical logic elements. [7][8][9][10][11][12][13] A thorough understanding of nonlinear wave propagation dynamics in the ordered granular chain(GC) is often considered as the groundwork.…”