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Considerable efforts had been devoted to investigating numerically the droplet impact dynamics on a superhydrophobic surface. Whereas most of these numerical simulations were restricted to the two-dimension (2-D) axisymmetric coordinate system with the one-dimension (1-D) substrate surface. In this work, a three-dimension (3-D) computational fluid dynamics (CFD) model, which intergrew a 2-D random rough surface, was proposed to investigate the droplet impact dynamics, and the multi-phase flow issue was solved by the Navier-Stokes equations. It is remarkable that the 3-D CFD model revealed several significant dynamic details that were not easily captured in a 2-D axisymmetric coordinate system or practical experiments. For instance, the 3-D CFD model provided a unique perspective to understand the varying dynamic behaviors of impinged droplet in terms of the velocity streamline and dynamic viscosity analyses. Herein, the dynamic viscosity diagram revealed that the sprawl droplet on the 2-D random rough surface was classified as Cassie state, while as Wenzel state for smooth surface, which also explained the better bouncing behaviors of droplet from the random rough surface. Accordingly, we suggested a visual way to evaluate the solid-liquid contact area surrounded by the triple-phase contact line. The effects of finger protrusion and central cavity growth from the sprawl droplet on the vortex generation were further analyzed on the ground of the velocity amplitude distribution and streamline data. The present work can provide early guidance to inquire into the impact dynamics of droplets on the random rough surface.

A cell-based smoothed finite element method (CS-FEM) is formulated for nonlinear free vibration analysis of a plate attached to a rigid rotating hub. The first-order shear deformation theory which is known as Mindlin plate theory is used to model the plate. In the process of formulating the system stiffness matrix, the discrete shear gap (DSG) method is used to construct the strains to overcome the shear locking issue. The effectiveness of the CS-FEM is first demonstrated in some static cases and then extended for free vibration analysis of a rotating plate considering the nonlinear effects arising from the coupling of vibration of the flexible structure with the undergoing large rotational motions. The nonlinear coupling dynamic equations of the system are derived via employing Lagrange’s equations of the second kind. The effects of different parameters including thickness ratio, aspect ratio, hub radius ratio and rotation speed on dimensionless natural frequencies are investigated. The dimensionless natural frequencies of CS-FEM are compared with those other existing method including the FEM and the assumed modes method (AMM). It is found that the CS-FEM based on Mindlin plate theory provides more accurate and “softer” solution compared with those of other methods even if using coarse meshes. In addition, the frequency loci veering phenomena associated with the mode shape interaction are examined in detail.

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