On the Dynamic Analysis of Curved and Twisted Cylinders Transporting Fluids

1976 ◽  
Vol 98 (2) ◽  
pp. 143-150 ◽  
Author(s):  
R. W. Doll ◽  
C. D. Mote
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
The Finite Element Method ◽  
Spectra Analysis ◽  
Variable Curvature ◽  
End Conditions ◽  
Linear Oscillation

The longitudinal, torsional and 2-transverse equations of motion are formulated for the titled problem through application of Hamilton’s Principle. Curvature-torsion conditions under which linear oscillation in a plane can exist are identified. The finite element method with isoparametric elements is used for discretization prior to spectra analysis. Natural frequency calculations over a range of mass transport velocities and cylinder end conditions were carried out for comparison with constant and variable curvature analyses and experiment. These results support the application of the constant curvature, inextensible centerline model for curved cylinder vibration analysis.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

2018 ◽  
Vol 18 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Łukasz Drąg ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
New Approach ◽  
Static And Dynamic Analysis ◽  
Rigid Finite Element Method ◽  
Longitudinal Flexibility ◽  
Element Method

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

Finite Element Models for Flexible Cosserat Solids

2020 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Minghe Shan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Displacement Vector ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Discrete Equations ◽  
Computation Efficiency ◽  
Elasticity Problems ◽  
Element Method

Abstract The application of the finite element method to the modeling of Cosserat solids is investigated in detail. In two- and three-dimensional elasticity problems, the nodal unknowns are the components of the displacement vector, which form a linear field. In contrast, when dealing with Cosserat solids, the nodal unknowns form the special Euclidean group SE(3), a nonlinear manifold. This observation has numerous implications on the implementation of the finite element method and raises numerous questions: (1) What is the most suitable representation of this nonlinear manifold? (2) How is it interpolated over one element? (3) How is the associated strain field interpolated? (4) What is the most efficient way to obtain the discrete equations of motion? All these questions are, of course intertwined. This paper shows that reliable schemes are available for the interpolation of the motion and curvature fields. The interpolated fields depend on relative nodal motions only, and hence, are both objective and tensorial. Because these schemes depend on relative nodal motions only, only local parameterization is required, thereby avoiding the occurrence of singularities. For Cosserat solids, it is preferable to perform the discretization operation first, followed by the variation operation. This approach leads to considerable computation efficiency and simplicity.

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.

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