Inverted Slider-Crank Mechanism Driven by Hydraulic Cylinder: Transfer Functions and Approximations
Issue:
Volume 6, Issue 1, June 2022
Pages:
1-5
Received:
22 March 2022
Accepted:
15 April 2022
Published:
26 April 2022
Abstract: Inverted slider-crank mechanisms driven by hydraulic cylinder have highly non-linear transfer functions, which in this form complicate kinematic and dynamic researches. A central slider-crank mechanism scheme is used with the specific small parameter equal to the ratio of the lengths of both links of the revolute pair of the mechanism (λ=R/L<1). The present study considers the two main transfer functions of the mechanism. In the first case the angle of the revolute pair as an independent parameter is accepted and in the second case the linear motion of the hydraulic cylinder as an independent parameter is accepted. The exact transfer functions of the mechanism are described and approximate representations of the transfer functions are found. In the first case we use a binomial order of the degrees of the small parameter calculated up to 4-th degree and very high accuracy of approximate function has been achieved (maximal error less than 1.6%). In the second case we use a trigonometric function, which corresponds to the exact transfer function up to second derivative, and the accuracy is also high (error less than 2%) in the main operating range. The power characteristics of the inverted slider-crank mechanism driven by hydraulic cylinder are determined using the transfer functions. All main conclusions are interpreted by geometrical representations.
Abstract: Inverted slider-crank mechanisms driven by hydraulic cylinder have highly non-linear transfer functions, which in this form complicate kinematic and dynamic researches. A central slider-crank mechanism scheme is used with the specific small parameter equal to the ratio of the lengths of both links of the revolute pair of the mechanism (λ=R/L<1). The ...
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A Weak Galerkin Finite Element Method for the Incompressible Viscous Magneto-hydrodynamic Equations
Su Sung Om,
Kwang Jin Kim,
Thae Gun Oh,
Nam Chol Yu
Issue:
Volume 6, Issue 1, June 2022
Pages:
6-17
Received:
10 August 2022
Accepted:
17 September 2022
Published:
18 October 2022
DOI:
10.11648/j.engmath.20220601.12
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Abstract: In this paper, we are studied the weak Galerkin finite element method for the incompressible viscous Magneto-hydrodynamic (MHD) equations. There have been the several numerical methods for the incompressible viscous Magneto-hydrodynamic equations: the continuous Galerkin finite element methods, the discontinuous Galerkin finite element methods, and the mixed Galerkin finite element methods et al. These numerical methods are converted to large-scale system of linear or nonlinear equations, which are solved by direct or iterative method. Besides accuracy, efficiency, and robustness of numerical methods, physical properties such as local conservation and flux continuity are very important in practical applications. And these numerical methods have following properties. (1) The continuous Galerkin finite element methods are known as lacking of ‘‘local conservation’’. (2) The discontinuous Galerkin finite element methods are locally conservative but there is no continuity. Also the discontinuous Galerkin finite element methods increase in numbers of unknowns. (3) The mixed Galerkin finite element methods approximate the two variables that satisfy the inf-sup condition. Therefore the obtained saddle point problems are difficult to solve. A weak Galerkin finite element methods are locally conservative well, continuous across element interfaces, less unknowns than discontinuous Galerkin finite element methods, and definite discrete linear systems. A weak Galerkin finite element methods are based on new concept called discrete weak gradient, discrete weak divergence and discrete weak rotation, which are expected to play an important role in numerical methods for magneto-hydrodynamic equation. This article intends to provide a general framework for managing differential, divergence, rotation operators on generalized functions. With the proposed method, solving the magneto-hydrodynamic (MHD) equation is that the classical gradient, divergence, vortex operators are replaced by the discrete weak gradient, divergence, rotation and apply the Galerkin finite element method. It can be seen that the solution of the weak Galerkin finite element method is not only continuous function but also totally discontinuous function. For the proposed method, optimal order error estimates are established in Hilbert space.
Abstract: In this paper, we are studied the weak Galerkin finite element method for the incompressible viscous Magneto-hydrodynamic (MHD) equations. There have been the several numerical methods for the incompressible viscous Magneto-hydrodynamic equations: the continuous Galerkin finite element methods, the discontinuous Galerkin finite element methods, and...
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