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.

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.

Finite Element Analysis of Vibration of Toroidal Field Coils Coupled With Laplace Transform

1982 ◽  
Vol 49 (3) ◽  
pp. 594-600 ◽  
Author(s):  
K. Miya ◽  
M. Uesaka ◽  
F. C. Moon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Laplace Transform ◽  
Equations Of Motion ◽  
Toroidal Field ◽  
Inverse Laplace Transform ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Original Domain ◽  
Element Method

A numerical analysis of a vibration of toroidal field coils in a magnetic fusion reactor is shown here on the basis of the finite element method coupled with Laplace transform. Lagrangian consisting of kinetic, elastic strain, and magnetic energies was utilized to deduce equations of motion of the coils. The equations were solved numerically by applying the Laplace transform to a formulation with respect to time and the finite element method to one with respect to space. The Fast Fourier Transform algorithm was utilized for a calculation of the inverse Laplace transform to obtain a nodal vector of the coil’s displacement in the original domain. Numerical results reasonably explain a dependency of the coil current on a frequency of the coil.

scholarly journals Vibration Analysis of Collecting Electrodes by means of the Hybrid Finite Element Method

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
I. Adamiec-Wójcik ◽  
J. Awrejcewicz ◽  
A. Nowak ◽  
S. Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electrostatic Precipitator ◽  
Equations Of Motion ◽  
The Body ◽  
The Finite Element Method ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Rigid Finite Element Method ◽  
Element Method

The paper presents a hybrid finite element method of shell modeling in order to model collecting electrodes of electrostatic precipitators. The method uses the finite element method to reflect elastic features and the rigid finite element method in order to model mass features of the body. A model of dust removal systems of an electrostatic precipitator is presented. The system consists of two beams which are modeled by means of the rigid finite element method and a system of collecting shells modeled by means of the hybrid finite element method. The paper discusses both the procedure of deriving the equations of motion and the results of numerical simulations carried out in order to analyze vibrations of the whole system. Experimental verification of the model is also presented.

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.

scholarly journals Finite element modelling of moving loads on structures

2021 ◽  
Author(s):  
Gareth Forbes
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Moving Load ◽  
Equations Of Motion ◽  
Moving Loads ◽  
The Finite Element Method ◽  
Structure Development ◽  
Simply Supported ◽  
Ansys Apdl ◽  
Element Method

This paper provides a breif description of the moving load problem (force or mass) across a structure. Development of a matlab script to solve the analytical equations of motion is provided. The method of implementation to solve this type of structural dynamics, using the Finite Element Method is then described with a matlab script for a simply supported beam provided. Additionally, a script and method for implementing the Finite Element Method using ANSYS APDL is also given.

Modeling Continuum Multibody Systems Using the Finite Element Method and Element Convected Frames

1994 ◽  
Author(s):  
Tamer M. Wasfy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Deformation Gradient ◽  
New Method ◽  
Integration Scheme ◽  
The Finite Element Method ◽  
Applied Forces ◽  
Element Method

Abstract A new method for predicting the dynamic response of flexible multibody systems is developed. The method can account for large rigid-body motion and large deflections. The method is based on the Finite Element Method and the use of a new type of element convected frames. Continuum type elements are used to model the multibody system. The motion of the “nodes” is referred to a global inertial reference frame. D’Alembert principle is used to derive the system’s equations of motion, by invoking the equilibrium, at the nodes, of inertia forces, structural (internal) forces and externally applied forces. Structural forces on a node are calculated from the state of deformation of the elements surrounding that node. Each element has a convected frame which translates and rotates with it. This frame is used to extract the flexible deformation of the element from the total element motion. The orientation of a convected frame is found using the deformation gradient tensor and the Polar decomposition theorem. The equations of motion are solved along with constraint equations using a direct implicit iterative integration scheme. A numerical example is solved to demonstrate some of the features of the new method.

scholarly journals Free vibrations of circular curved beams

2018 ◽  
Vol 211 ◽  
pp. 04006
Author(s):  
Ajinkya Baxy ◽  
Abhijit Sarkar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fem Simulation ◽  
Free Vibrations ◽  
Opening Angle ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Governing Equations ◽  
Simulation Results

The study of free vibrations of curved beams has relevance in engineering applications like modeling turbo machinery blades, propellers, arch design, etc. Vibration characteristics of structures are generally evaluated using the Finite Element Method. The governing equations for the curved beam using the inextensional theory are available in the literature. These equations are solved analytically for two different boundary conditions, namely (a) simplysupported, (b) cantilever. The results obtained for all the cases are compared against the FEM simulation results. It is found that the present solutions are in agreement with the FEM solutions up to an opening angle of 40°.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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