Dynamic Analysis of Tapered Plates Based on Higher Order Beam Theory

2014 ◽  
Vol 919-921 ◽  
pp. 79-82
Author(s):  
S.M. Ibrahim ◽  
Y.A. Al-Salloum ◽  
H. Abbas
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Beam Theory ◽  
Longitudinal Axis ◽  
Vibration Modes ◽  
Bending Vibration ◽  
3D Finite Element ◽  
Different Types ◽  
Tapered Plates ◽  
Good Agreement

Modal solutions of plates with uniformly varying cross section using unified beam theory are presented. The results are given in the form of Euler-Bernoulli, Timoshenko and quasi 3D solutions. Numerical results for cantilever and CFCF supported rectangular planform plates are presented. Different types of modes, i.e. axial, bending and torsional modes are observed. The frequency values are in good agreement with 3D finite element results as well as published literature. Due to uniform taper in plate cross section, bending vibration modes become asymmetric along the longitudinal axis of the structure. Further, it can also be noticed that the vibration behavior of thick tapered plates is characterized by the appearance of significant number of axial and torsional modes at lower frequency values.

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

Vibration Response of a Thin-Walled Cylindrical Pipe with Liquid

2012 ◽  
Vol 189 ◽  
pp. 345-349
Author(s):  
Yu Lan Wei ◽  
Bing Li ◽  
Li Gao ◽  
Ying Jun Dai
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Beam Model ◽  
Vibration Modes ◽  
Timoshenko Beam Model ◽  
Cylindrical Pipe ◽  
Bending Vibration ◽  
Beam Bending ◽  
Thin Walled

Vibration characteristics of the thin-walled cylindrical pipe are affected by the liquid within the pipe. The natural frequencies and vibration modes of the pipe without liquid are analyzed by the theory of beam bending vibration and finite element model, which is based on the Timoshenko beam model. The first three natural frequencies and vibration modes of the pipe with or without liquid are acquired by experiments. As shown in the experiment results, the natural frequencies of the containing liquid pipe are lower than the natural frequencies of the pipe without liquid.

Displacement Properties of Newly Developed 3-Dimensional Piezoelectric Actuator at Various AC Frequencies

2007 ◽  
Vol 534-536 ◽  
pp. 1441-1444 ◽  
Author(s):  
Man Soon Yoon ◽  
Y.G. Choi ◽  
Soon Chul Ur
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Piezoelectric Actuator ◽  
Element Model ◽  
Vibration Modes ◽  
Maximum Strain ◽  
Electromechanical Properties ◽  
3 Dimensional ◽  
The Finite Element Model ◽  
Good Agreement

The electromechanical properties of a newly proposed 3-dimensional piezoelectric actuator have been investigated. Especially, the effects of 3-dimensional geometry on the maximum tip displacement were carefully investigated. As a result, it was found that the maximum strain of the 3-dimensional piezoelectric device was significantly enhanced up to 4.5 times higher than that of a disk shape device. This data was in good agreement with the finite element model analysis of strains and vibration modes. Moreover, the field -induced displacement stability of dome-shaped 3- dimensional piezoelectric actuator at various ac freguencies was superior to Rainbow actuator.

scholarly journals On the Finite Element Free Vibration Analysis of Delaminated Layered Beams: A New Assembly Technique

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Bending Vibration ◽  
Natural Frequencies And Modes ◽  
Layered Beams ◽  
Assembly Technique ◽  
Free Mode ◽  
Element Free

The dynamic analysis of flexible delaminated layered beams is revisited. Exploiting Boolean vectors, a novel assembly scheme is developed which can be used to enforce the continuity requirements at the edges of delamination region, leading to a delamination stiffness term. The proposed assembly technique can be used to form various beam configurations with through width delaminations, irrespective of the formulation used to model each beam segment. The proposed assembly system and the Galerkin Finite Element Method (FEM) formulation are subsequently used to investigate the natural frequencies and modes of 2- and 3-layer beam configurations. Using the Euler-Bernoulli bending beam theory and free mode delamination, the governing differential equations are exploited and two beam finite elements are developed. The free bending vibration of three illustrative example problems, characterized by delamination zones of variable length, is investigated. The intact and defective beam natural frequencies and modes obtained from the proposed assembly/FEM beam formulations are presented along with the analytical results and those available in the literature

Homogenization of multi-turn coil with elliptic cross-section using complex permeability

2019 ◽  
Vol 38 (3) ◽  
pp. 999-1008 ◽  
Author(s):  
Shogo Fujita ◽  
Hajime Igarashi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Cross Section ◽  
Fe Analysis ◽  
Complex Permeability ◽  
Elliptic Cross Section ◽  
Content Type ◽  
Elliptic Cross ◽  
Good Agreement

Purpose The tensor complex permeability of a multi-turn coil with elliptic cross-section is analytically expressed. In field analysis, a multi-turn coil can be modeled by the uniform material that has the present tensor complex permeability. It is shown that the frequency characteristic of the present tensor complex permeability is in good agreement with that evaluated by finite element method applied to a unit cell of the multi-turn coil region. Design/methodology/approach The authors introduce a new method to evaluate the complex permeability of a multi-turn rectangular coil. To obtain the complex permeability of a rectangular coil in a closed form, it is approximated as an elliptic coil. Because the rectangular coil has different complex permeabilities in the vertical and horizontal directions, the complex permeability have to be defined in a tensor form. It suffices to discretize the coil region into rather coarse finite elements without considering the skin depth in contrast to the conventional finite element method. Findings The proposed method is shown to give the impedance of multi-turn coils which is in good agreement with results obtained by the conventional finite element (FE) analysis. By extending the proposed approach, the authors can easily perform 3D FE analysis without difficulty in discretization of the coil region with fairly fine finite elements. Moreover, they found that the approximation of rectangular coils as the elliptic coils is valid for analysis of quasi-static fields using this homogenization method. Originality/value The novelty of this study is in the approximation of the rectangular coils with elliptic coils, and the complex permeability for them is formulated here in a closed form. The proposed formula includes that for the round coils. Using the present method, the authors analyze the rectangular coils without fine discretization.

SCALED BOUNDARY FINITE ELEMENT METHOD FOR SEMI-INFINITE RESERVOIR WITH UNIFORM CROSS SECTION

2012 ◽  
Vol 09 (01) ◽  
pp. 1240006 ◽  
Author(s):  
SHANGMING LI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cross Section ◽  
Uniform Cross Section ◽  
Vertical Ground ◽  
Part Modeling ◽  
Infinite Reservoir ◽  
Scaled Boundary Finite Element ◽  
Good Agreement ◽  
Element Method

A unified scaled boundary finite element method (SBFEM) in the frequency domain was proposed for a semi-infinite reservoir with uniform cross section subjected to horizontal and vertical ground excitations, and a methodology was presented to solve the unified SBFEM through decomposing the unified SBFEM into two parts; one part modeling the reservoir subjected to horizontal excitations and the other part modeling the whole reservoir subjected to vertical excitations. The accuracy of the unified SBFEM and its solving methodology was validated through analyzing numerical examples. The SBFEM solutions were in good agreement with analytical or other numerical method's solutions.

Stent vs Stent Study by Means of Finite Element Method

2014 ◽  
Author(s):  
Misagh Imani ◽  
A. M. Goudarzi ◽  
D. D. Ganji ◽  
M. Barzegar Gerdroodbary
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Randomized Trials ◽  
Interventional Procedure ◽  
Clinical Results ◽  
Regulatory Agencies ◽  
Stent Design ◽  
Different Types ◽  
Good Agreement ◽  
Element Method

It is well known that the stent design plays an important role in the outcome of the stenting interventional procedure. Thus, analyzing and comparing the behavior of different types of stent is essential to select the most appropriate stent design to use. Furthermore, assessing the behavior of stent is one of the components of the process in which new biomedical stent devices are designed and approved. Indeed, new stent designs have to be proved to be equivalent to an approved stent to be confirmed from the regulatory agencies. This sets the stage for a series of “stent versus stent” randomized trials designed to show that each newer stent design was not inferior to the prior approved stent. In this paper, finite element method is used to assess the behavior of stents. The objective of this work is to present a numerical alternative for “stent versus stent” complicated clinical studies. Three commercially available stents (the Palmaz–Schatz, Multi–Link and NIR stents) are modeled and their behaviors are compared. According to the findings, the possibility of restenosis is lower for Multi–Link and NIR stents in comparison with Palmaz–Schatz stent which is in good agreement with clinical results.

Assessment of Overlapped Internal and External Volumetric Flaws in p-M Diagram

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Shinji Konosu ◽  
Hikaru Miyata
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Pressure Vessel ◽  
Effective Cross Section ◽  
Finite Element Analyses ◽  
Diagram Method ◽  
Reference Stress ◽  
Common Problems ◽  
Good Agreement

Assessment of overlapped internal and external volumetric flaws is one of the most common problems related to pressure vessel and piping components. Under the current fitness for service rules, such as those provided in ASME, BS, and so on, the procedures for the assessment of these flaws have not yet been defined. In this paper, a reference stress, incorporating the decrease in the effective cross section as a function of flaw depth and flaw angle in a cylinder, has been proposed in order to assess the flaws using the simple p-M (pressure-moment) diagram method. Numerous finite element analyses for a cylinder with overlapped internal and external flaws were conducted to verify the proposed procedure. There is good agreement among them.

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