Free Vibration of Spinning Stepped Timoshenko Beams Using Finite Element Method

2000 ◽  
Author(s):  
Z. C. Wang ◽  
W. L. Cleghorn ◽  
S. D. Yu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Work Piece ◽  
Stepped Shaft ◽  
Lateral Displacements ◽  
Element Method

Abstract Free lateral vibration of stepped shafts is investigated in this paper using the Timoshenko beam theory and the finite element method. Beam finite elements having two nodes and 16 degrees of freedom were employed to model flexural vibration of a stepped shaft for a total four field variables — two lateral displacements and two bending angles. Within each uniform segment, the stepped shaft is modeled as a substructure for which a system of equations of motion may be easily formulated using the Galerkin method. The global equations of motion for the entire stepped shaft are subsequently formulated by enforcing the displacement continuity and force equilibrium conditions across the interfaces between two adjacent substructures. The second order governing differential equations for a non self-adjoint dynamic system are then reduced to the equivalent first order differential equations for which eigenvalue problem is formulated and solved using the Matlab® program. Values of natural frequencies are in excellent agreement with those available in the literature. Effects of rotational springs attached to the end of a stepped shaft, used to simulate the non-classical boundary constraints of chuck on a work piece in a typical turning process, are also investigated. The bi-orthogonal conditions for modal vectors, which are useful in chatter analysis during turning processes, are given in this paper.

In-Plane Free Vibration of Curved Beams Using Finite Element Method

2007 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
E. Esmailzadeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Central Line ◽  
Circular Ring ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Element Method

Curved beam-type structures have many applications in engineering area. Due to the initial curvature of the central line, it is complicated to develop and solve the equations of motion by taking into account the extensibility of the curve axis and the influences of the shear deformation and the rotary inertia. In this study the finite element method is utilized to study the curved beam with arbitrary geometry. The curved beam is modeled using the Timoshenko beam theory and the circular ring model. The governing equation of motion is derived using the Extended-Hamilton principle and numerically solved by the finite element method. A parametric sensitive study for the natural frequencies has been performed and compared with those reported in the literature in order to demonstrate the accuracy of the 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.

scholarly journals A recommendation of computation of normal streeses in single point incremental forming technology

2014 ◽  
Vol 17 (1) ◽  
pp. 21-28
Author(s):  
Dien Khanh Le ◽  
Nam Thanh Nguyen ◽  
Binh Thien Nguyen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Incremental Forming ◽  
Single Point ◽  
Finite Element Method Simulation ◽  
Recent Decade ◽  
Work Piece ◽  
Single Point Incremental Forming ◽  
Forming Technology ◽  
Element Method

Single Point Incremental Forming (SPIF) has become popular for metal sheet forming technology in industry in many advanced countries. In the recent decade, there were lots of related studies that have concentrated on this new technology by Finite Element Method as well as by empirical practice. There have had very rare studies by pure analytical theory and almost all these researches were based on the formula of ISEKI. However, we consider that this formula does not reflect yet the mechanics of destruction of the sheet work piece as well as the behavior of the sheet in reality. The main aim of this paper is to examine ISEKI’s formula and to suggest a new analytical computation of three elements of stresses at any random point on the sheet work piece. The suggested formula is carefully verified by the results of Finite Element Method simulation.

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