| 摘要(英) |
Vibration of plate structures and the phenomenon of clustering and inversion of Chladni
patterns have been extensively studied by scientists in the past century. However, prior
investigations predominantly employed the Finite Element Method (FEM) to simulate plate
vibration characteristics and relied on physical experiments for chladni patterns. This study
pioneers the application of a bidirectional coupled Discrete Element Method (DEM) and Finite
Element Method (FEM) to simulate the dynamic behavior of particles on an elastic rectangular
plate. The proposed coupled model was validated against corresponding experimental
observations. The aggregation behavior of particles was explored under various dimensionless
accelerations (Γ). Particle area fraction, particle translational velocity, particle rotational
velocity, particle perturbation velocity, and granular temperature are employed to further
analyze the internal physical behavior of particles on the rectangular plate. Various parameters
are considered in this study to understand their impact on the patterns of particle aggregation,
including the influence of gravity on the rectangular plate, particle Young′s modulus, and
particle restitution coefficient. The main findings are summarized below
(1) Disregarding the effect of gravity on the rectangular plate, when the dimensionless
acceleration (Γ) is less than 1, particles aggregate towards the nodal lines, forming an
inverse Chladni patterns. When Γ is greater than or equal to 1, particles aggregate towards
the anti-nodal line, forming a Chladni patterns. Moreover, as Γ significantly exceeds 1, the
time required to form a Chladni patterns substantially decreases. Larger values of Γ reduce
formation time for Chladni patterns.
(2) Considering the gravitational effect on the rectangular plate, its susceptibility to gravity
leads to pre-deformation, causing particles to roll towards areas with higher deformation,
and making it difficult to form an inverse Chladni patterns. However, when the
dimensionless acceleration (Γ) exceeds a certain threshold, a Chladni pattern still emerges.
iii
(3) As the dimensionless acceleration (Γ) increases, the rate of increase in particle translational
velocity is faster, resulting in a shorter formation time for the Chladni patterns.
(4) When forming the inverse Chladni patterns, particles roll towards the anti-nodal regions,
while when forming the Chladni patterns, particles roll towards the nodal regions.
(5) When forming the inverse Chladni patterns patterns, there is a weaker occurrence of particle
collisions, while during the formation of the Chladni pattern, particle collisions are more
intense, concentrated largely around the nodal points. Moreover, with larger values of the
dimensionless acceleration (Γ), the tendency for collisions becomes more pronounced.
Keywords: Chladni patterns, inverse Chladni patterns, bidirectional coupled DEM and FEM,
dimensionless acceleration, internal physical properties of particles |
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