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Numerical Study of the Natural Oscillations of Perforated Vibrating Surfaces with Holes of Complex Geometry

Kharchenko Serhii, Samborski Sylwester, Kharchenko Farida, Paśnik Jakub

Advances in Science and Technology. Research Journal

2023

Vol. 17, no 6

73--87

The widespread use of perforated vibrating surfaces in various industries requires maximum productivity and construction reliability. The research task is to determine the significant factors and their degree of influence on the natural oscillations of vibrating surfaces with multiple holes of complex geometry. For this purpose, studies were carried out for three samples of plates: non-perforated, with basic round holes and holes of complex geometry in the form of a five-petal epicycloid. Studies of the natural oscillations of perforated vibrating surfaces have been conducted using the finite element method in Abaqus, which has proved sufficient accuracy of calculations. The dependencies of the natural oscillation frequency of perforated surface samples on their thickness, partition width between the holes, material type, and fixing method have been obtained. In addition, the analysis involved the study of eight modes of oscillation common in practice. The dependencies of the natural oscillation frequency of perforated surface on the relative parameters of ligament efficiency and stiffness coefficient have also been obtained. These parameters take into account the ratios of the partition width between the holes to the plate thickness and the dimensions of the holes. The research results allow to obtain levels of influence of the perforated vibrating surface parameters on their natural oscillations frequency. The obtained research results make it possible to further determine the absence of damage between the holes and predict the durability of perforated vibration surfaces in the presence of holes of complex geometry.

Finite element modeling of laminar flow of a third grade fluid in a Darcy-Forcheimmer porous medium with suction effects

Takhar H. S., Bhargava R., Rawat S., Beg T. A., Beg O. A.

International Journal of Applied Mechanics and Engineering

2007

Vol. 12, no 1

215-233

A mathematical model to simulate the steady laminar flow of an incompressible, third grade, non-Newtonian fluid past an infinite porous plate embedded in a Darcy-Forcheimmer porous medium is presented. A number of special cases are examined for the governing nonlinear differential equation. The model is solved with appropriate boundary conditions using the finite element method. Velocity and velocity gradient are plotted graphically for variation in permeability (k), Forcheimmer parameter (b), third grade materiaI parameter (f3 3 ) , and suction effect (Vo). It is shown that velocities are generally decreased transverse to the plate surface with increasing Forcheimmer parameter; increasing permeability conversely boosts the velocities, as this corresponds to an increasingly fluid (Le., progressively less porous) regime. The third grade material parameter is also seen to substantially increase the velocities in the direction normal to the plate surface. The special case of a second order viscoelastic flow is also studied. The flow scenario finds applications in polymer extrusion processes, and other important industrial rheology systems.