scholarly journals Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110609
Author(s):  
Hossein Talebi Rostami ◽  
Maryam Fallah Najafabadi ◽  
Davood Domiri Ganji
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Variable Properties ◽  
The Third ◽  
Koch Snowflake

This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it.

Natural Frequencies of Rectangular Membrane With Boundary Perturbation

1995 ◽  
Vol 1 (2) ◽  
pp. 139-144 ◽  
Author(s):  
Jamal A. Masad
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Perturbation Approach ◽  
Boundary Perturbation ◽  
The Finite Element Method ◽  
Analytic Expression ◽  
Element Method

A perturbation approach, coupled with the adjoint concept, is used to derive an analytic expression for the natural frequencies of a nearly rectangular membrane. The method is applied for a rectangular membrane with a semicircle at one of the boundaries. The fundamental natural frequency results for this configuration are presented and compared with results from a finite-element method and results from an approximate Galerkin method. The agreement between the fundamental natural frequencies calculated with the perturbation approach and those calculated with the finite-element method improves as the radius of the semicircle decreases and as the semicircle location becomes more eccentric.

APPLICATION OF FINITE ELEMENT METHOD TO SOLVE 2D PROBLEMS RELATED TO NEMATIC SURFACE PROPERTIES

1999 ◽  
Vol 10 (02n03) ◽  
pp. 485-500
Author(s):  
R. BARBERI ◽  
M. IOVANE ◽  
C. FERRERO ◽  
V. MOCELLA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Surface Properties ◽  
Periodic Boundary Conditions ◽  
The Third ◽  
Numerical Studies ◽  
Nematic Director ◽  
Macroscopic Orientation ◽  
Element Method

This paper is devoted to numerical studies of two-dimensional problems concerning surface properties of nematic liquid crystals. We use a finite element method, based essentially on the classic variational approach, to find an approximate solution minimizing the Gibbs free energy of the nematic material under given boundary conditions. Three examples illustrate the performance and versatility of this analysis. Two cases are related to the macroscopic orientation induced by periodic boundary conditions: the first is a saw-toothed substrate in the micrometric range and the second is a microtextured surface. We analyze the bulk planar–homeotropic transition conditions for both of them. In the third case, we study the coupling between the spatial variation of the nematic director and that of the order parameter in the presence of surface-induced distortion.

Influence Analysis of Hull Deformation on Dynamic Behavior of Propulsion Shafting

2014 ◽  
Vol 904 ◽  
pp. 432-436
Author(s):  
Feng Bao An ◽  
Ping Yang ◽  
Xin Ping Yan ◽  
Ming Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequency ◽  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Container Ship ◽  
Structure Model ◽  
The Finite Element Method ◽  
Ship Structure ◽  
Ship Propulsion

The aim of this paper is to study the influence of hull deformation on dynamic behavior of ship propulsion shafting. Taking an 8530TEU container ship as an objective and using the finite element method, a global ship structure model is built up to evaluate the hull deformations under typical loading cases. Then the hull bottom-propulsion shafting integrated model is adopted to analyze the effect of hull deformation on shafting natural frequency under dry and wet mode. The results show that the natural frequencies of the shafting will increase due to the effect of hull deformation. Consequently, it is necessary to consider the effect of ship deformation when dealing with the dynamic behavior of ship propulsion shafting.

scholarly journals Vibration-based damage identification for ship sandwich plate using finite element method

2020 ◽  
Vol 10 (1) ◽  
pp. 744-752
Author(s):  
Abdi Ismail ◽  
Achmad Zubaydi ◽  
Bambang Piscesa ◽  
Rizky Chandra Ariesta ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Damage Identification ◽  
Identification System ◽  
Structural Failure ◽  
Hull Structure ◽  
Element Method

AbstractThe sandwich plate can be used to replace the conventional steel stiffened plates on the ship’s hull structure. By using the sandwich plate, not only the stiffness of the plate can be increased but also the overall ship weight can be reduced, as well as the ship payload can be increased. The sandwich plate should be accompanied by the damage identification system to prevent ship structural failure. In this paper, the global damage identification method, which is based on the vibration analysis, is investigated. For that purpose, the vibration-based damage identification using the Finite Element Method (FEM) is explored. The variables being investigated are the damage sizes, damage locations, and the boundary conditions which affect the natural frequencies of the structures. The sandwich plate considered in this study consisted of steel faceplates with the polyurethane elastomer core, which has been checked to meet Lloyd’s register, an international maritime standard. From the analysis, it is found that the fully clamped boundary conditions accompanied by high vibration modes are more sensitive to the presence of artificial damage. The changes in the natural frequencies can be used as a reference to identify the size and location of damage in the sandwich plate.

scholarly journals Modification of boundary condition for the optimization of natural frequencies of plate structures with fluid loading

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879600 ◽  
Author(s):  
Dayi Ou ◽  
Cheuk Ming Mak
Keyword(s):  
Genetic Algorithm ◽  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Natural Frequencies ◽  
Fluid Loading ◽  
Loaded Plate ◽  
Element Method

A finite element method, boundary element method, and genetic algorithm combined method is developed for the optimization of natural frequencies of fluid-loaded plates. In this method, the coupled finite element method–boundary element method is used for the free flexural vibration analysis of plates with arbitrary fluid loading effects and arbitrary elastic boundary conditions, and the genetic algorithm method is combined with the finite element method–boundary element method for searching the optimal values of plate’s boundary parameters. By using this method, multiple natural frequencies of a given fluid-loaded plate can be optimized simultaneously to different target values. The coupled finite element method–boundary element method is first validated by comparing with earlier published results. The proposed optimization method is then applied to the optimal boundary condition design of four different cases. The results show natural frequencies of a fluid-loaded plate are sensitive to its boundary conditions. The possibility of optimizing the natural frequencies of a fluid-loaded plate by modifying boundary conditions is demonstrated, as well as the effectiveness of the proposed method as a structural optimization tool. According to the authors’ knowledge, this study is the first attempt of optimizing fluid-loaded plate natural frequencies by considering arbitrary boundary conditions as optimization variables.

On the Mechanism of Bandgap Formation in Beams With Periodic Arrangement of Beam-Like Resonators

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Ó. Serrano ◽  
R. Zaera ◽  
J. Fernández-Sáez
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Band Structure ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Numerical Procedure ◽  
The Finite Element Method ◽  
Horizontal Beam ◽  
Bloch’S Theorem ◽  
Periodic Arrangement

Abstract Metastructures made of spring-mass resonators present a bandgap at the natural frequency of the resonator. This rule cannot be generalized for more complex resonators. This work analyzes the case of a metastructure composed of a periodic arrangement of vertical beams rigidly joined to a horizontal beam. The vertical beams work as resonators, and their natural frequencies play a strong role on the band structure of the whole system, however, different than the case with spring-mass resonators. Since this metastructure can be considered a lattice, Bloch’s theorem is applied to the unit cell and a numerical procedure based on the finite element method permits to obtain the dispersion curves. Illustrative results show the influence of the natural frequencies of the horizontal and vertical beams on the band structure.

scholarly journals Modal Analysis of a Thick-Disk Rotor with Interference Fit Using Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Yuhua Fan ◽  
Hongchang Ding ◽  
Maoyuan Li ◽  
Jiacheng Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Modal Analysis ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Bending Stiffness ◽  
Thick Disk ◽  
Interference Fit ◽  
Motion Equations ◽  
Ansys Workbench

This paper is concerned with the modal analysis of a thick-disk rotor, which consists of an elastic shaft with a rigid thick disk assembled by interference fit, and the width of the thick disk is not negligible. Firstly, the friction moment on the contact surface of disk and shaft is deduced in terms of elastic theory, and a new enhanced coefficient of bending stiffness of assembly body is proposed and calculated for the first time. Secondly, the effect of the width of thick disk on diametrical moment of inertia, as well as the enhanced coefficient of bending stiffness of interference-fit part between disk and shaft, is included in the motion equations of thick-disk rotor, which are established based on finite element method, and the natural frequencies of rotor are obtained by solving the motion equations. Then the modal analysis is performed to get the natural frequencies in ANSYS Workbench, in which the friction coefficient and interference fit are set to be the same as those of the finite element calculation method. At last the modal experiment is done to verify the accuracy of calculation and simulation. The results show that the calculation values using enhanced stiffness of assembly part are in good agreement with those of ANSYS Workbench and experiment, and the percent errors of the first natural frequency and the second natural frequency are down to about 0.32% and 0.83%, respectively.

Natural Frequencies of Out-of-Plane Vibration of Arcs

1982 ◽  
Vol 49 (4) ◽  
pp. 910-913 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
K. Tanaka
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Plane Vibration ◽  
Out Of Plane

The natural frequencies of out-of-plane vibration based on the Timoshenko beam theory are calculated numerically for uniform arcs of circular cross section under all combination of boundary conditions, and the results are presented in some figures.

Dynamic Analysis of a Hyperbolic Composite Coupling

2005 ◽  
Author(s):  
H. Ghoneim ◽  
D. J. Lawrie
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Composite Materials ◽  
Timoshenko Beam ◽  
Single Unit ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Discrete Equation ◽  
The Finite Element Method

A novel hyperbolic composite coupling is proposed. In addition to enjoying the advantages of composite materials, the proposed coupling can be readily integrated with composite drive shaft into a single unit. A mathematical model of the coupling is developed based on the Timoshenko beam theory using the energy approach and the extended Lagrange’s equations. The corresponding discrete equation of vibration is obtained using the finite element method and solved for the natural frequencies using MATLAB. The dynamic characteristics of the coupling (Axial, torsional and bending natural frequencies) are studied in order to assess the merits and potential of the proposed coupling.

scholarly journals ON THE SIMULATION OF THE FIRST NATURAL FREQUENCY OF A TUNED MASS DISC DAMPER

2021 ◽  
Vol 2021 (4) ◽  
pp. 4924-4929
Author(s):  
CHRISTIAN BRECHER ◽  
◽  
GUIFENG ZHAO ◽  
MARCEL FEY ◽  
◽  
...  
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Machine Tools ◽  
Natural Frequencies ◽  
Finite Element Models ◽  
Acceptable Error ◽  
The Third

The tuned mass disc damper (TMDD) can be applied to avoid chatter of machine tools. The effectiveness of the TMDD depends mostly on the tuning accuracy of the natural frequency. In this paper, three finite element models are presented to simulate the vibrations of the TMDDs. The simulated natural frequencies are compared with measured results. The third model solves the problems of the first and the second model and can predict the natural frequencies of the TMDDs with an acceptable error.

Sign in / Sign up

Export Citation Format

Share Document