scholarly journals Kane’s Formalism Used to the Vibration Analysis of a Wind Water Pump

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1030
Author(s):  
Gabriel Leonard Mitu ◽  
Eliza Chircan ◽  
Maria Luminita Scutaru ◽  
Sorin Vlase
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Element ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Transmission Mechanism ◽  
Water Pump ◽  
The Finite Element Method ◽  
Lagrange’S Equation ◽  
Elastic Elements

The paper uses Kane’s formalism to study two degrees of freedom (DOF) mechanisms with elastic elements = employed in a wind water pump. This formalism represents an alternative, in our opinion, that is simpler and more economical to Lagrange’s equation, used mainly by researchers in this type of application. In the problems where the finite element method (FEM) is applied, Kane’s equations were not used at all. The automated computation causes it to be reconsidered in the case of mechanical systems with a high DOF. Analyzing the planar transmission mechanism, these equations were applied for the study of an elastic element. An analysis was then made of the results obtained for this type of water pump. The matrices coefficients of the obtained equations were symmetric or skew-symmetric.

Force Vibration Analysis of Thick Beams on Two Parameter Elastic Foundation by Finite Element Method

2002 ◽  
Author(s):  
Ali Bahcivan ◽  
Vedat Karadag
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Cross Section ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Beam Element ◽  
Thick Beam ◽  
Two Parameter

In the present work, the free vibration analysis of rectangular cross-section uniform beams on two-parameter elastic foundation, considering shear deformation and rotatory inertia is made by the finite element method. In this analysis, two different thick beam elements are used. The first 4 degrees of freedom thick beam element has two nodes with two degrees of freedom at each node such as transverse displacements and cross-section rotations. In the second beam element, the nodal variables are the transverse displacement, the cross-section rotation and shear deformation. The elastic foundation is idealized as a constant two-parameter model characterized by two moduli, i.e., the Winkler foundation modulus k and the shear foundation modulus kG. In the case kG = 0, this model reduces to the Winkler model, i.e., the elastic foundation is idealized as a constant one-parameter model. Axial displacement of the beam is also considered. Three kinds of end conditions, i.e., simply-supported, clamped-clamped and clamped-free ends are considered in this study. The effects of axial force, foundation stiffness parameters and partial elastic foundation on the natural frequencies of the beam are examined. In this analysis, the vibration calculation results are presented in the tables and their importance in design are discussed. The numerical results obtained from this analysis are compared with the exact or available solutions, wherever possible. Numerical results and comparisons show the effectiveness of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document