Finite Element Analysis of Thermoelastic Damping in Contour-Mode Vibrations of Micro- and Nanoscale Ring, Disk, and Elliptical Plate Resonators

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Yun-Bo Yi
Keyword(s):  
Finite Element ◽  
Dominant Frequency ◽  
Element Formulation ◽  
Thermoelastic Damping ◽  
Q Value ◽  
Element Analysis ◽  
Quadratic Interpolation ◽  
Leading Mode ◽  
Quality Factor Q ◽  
Contour Mode

Thermoelastic damping in contour-mode in-plane vibrations of rings, disks, and elliptical plates is investigated on various size scales, using a reduced finite element formulation. The Fourier scheme is applied to the axisymmetric geometries including circular rings and disks, and is found to be remarkably efficient in searching solutions. The numerical accuracy is further improved by the implementation of quadratic interpolation functions. The computational results are validated by comparing with the commercial software packages as well as the existing analytical solutions in literature. For resonators of elliptical shapes, the dominant frequency has a weak dependence on the geometric aspect ratio γ, whereas the effect of γ on the quality factor (Q value) is much stronger and the peak Q value of the leading mode consistently occurs in the vicinity of γ=1.42.

Eigenvalue Solution of Thermoelastic Damping in Beam Resonators Using a Finite Element Analysis

2007 ◽  
Vol 129 (4) ◽  
pp. 478-483 ◽  
Author(s):  
Yun-Bo Yi ◽  
Mohammad A. Matin
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Thermoelastic Damping ◽  
Element Analysis ◽  
Beam Resonator ◽  
Various Boundary Conditions ◽  
Parametric Studies ◽  
Analytical Approaches

A finite element formulation is developed for solving the problem related to thermoelastic damping in beam resonator systems. The perturbation analysis on the governing equations of heat conduction, thermoleasticity, and dynamic motion leads to a linear eigenvalue equation for the exponential growth rate of temperature, displacement, and velocity. The numerical solutions for a simply supported beam have been obtained and shown in agreement with the analytical solutions found in the literature. Parametric studies on a variety of geometrical and material properties demonstrate their effects on the frequency and the quality factor of resonance. The finite element formulation presented in this work has advantages over the existing analytical approaches in that the method can be easily extended to general geometries without extensive computations associated with the numerical iterations and the analytical expressions of the solution under various boundary conditions.

Design and Analysis of Viscoelastic Seismic Dampers

2002 ◽  
Author(s):  
N. Shimizu ◽  
H. Nasuno ◽  
T. Yazaki ◽  
K. Sunakoda
Keyword(s):  
Finite Element ◽  
Constitutive Relation ◽  
Time Domain ◽  
Dynamic Properties ◽  
Design Procedure ◽  
Fe Analysis ◽  
Damping Capacity ◽  
Element Formulation ◽  
Element Analysis ◽  
Equivalent Viscous Damping

This paper describes a methodology of design and analysis of viscoelastic seismic dampers by means of the time domain finite element analysis. The viscoelastic constitutive relation of material incorporating with the fractional calculus has been derived and the finite element formulation based on the constitutive relation has been developed to analyze the dynamic property of seismic damper. A time domain computer program was developed by using the formulation. Dynamic properties of hysteresis loop, damping capacity, equivalent viscous damping coefficient, and equivalent spring constant are calculated and compared with the experimental results. Remarkable correlation between the FE analysis and the experiment is gained, and consequently the design procedure with the help of the FE analysis has been established.

FINITE ELEMENT ANALYSIS OF PIEZOELECTRIC ELASTICITY WITH SINGULAR INPLANE ELECTROELASTIC FIELDS

2006 ◽  
Vol 03 (01) ◽  
pp. 115-135 ◽  
Author(s):  
MENG-CHENG CHEN ◽  
JIAN-JUN ZHU ◽  
K. Y. SZE
Keyword(s):  
Finite Element ◽  
Ad Hoc ◽  
Wedge Angle ◽  
Electric Displacement ◽  
Weak Form ◽  
Efficient Solutions ◽  
Element Formulation ◽  
Displacement Fields ◽  
Element Analysis ◽  
Electroelastic Fields

An ad hoc one-dimensional finite element formulation is developed for the eigenanalysis of inplane singular electroelastic fields at material and geometric discontinuities in piezoelectric elastic materials by using the eigenfunction expansion procedure and the weak form of the governing equations for prismatic sectorial domains composed of piezoelectrics, composites or air. The order of the electroelastic singularities and the angular variation of the stress and electric displacement fields are obtained with the formulation. The influence of wedge angle, polarization orientation, material types, and boundary and interface conditions on the singular electroelastic fields and the order of their singularity are also examined. The simplicity and accuracy of the formulation are demonstrated by comparison to several analytical solutions for piezoelectric and composite multi-material wedges. The nature and speed of convergence suggests that the present eigensolution could be used in developing hybrid elements for use along with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries leading to singular electroelastic states.

Failure Analysis of Bamboo Bolt Connection in Uniaxial Tension by FEM by Considering Fiber Direction

2021 ◽  
Vol 71 (1) ◽  
pp. 58-64
Author(s):  
Raviduth Ramful
Keyword(s):  
Finite Element ◽  
Uniaxial Tension ◽  
Failure Modes ◽  
Damage Mechanism ◽  
Field Analysis ◽  
Fiber Direction ◽  
Element Formulation ◽  
Element Analysis ◽  
Test Standards ◽  
Lack Of Information

Abstract Full-culm bamboo has been used for millennia in construction. Specific connections are normally required to suit its unique morphology and nonuniform structure. Presently, the use of full-culm bamboo is limited in the construction industry as a result of a lack of information and test standards about the use and evaluation of full-culm connections. This study aims to further explore this area by investigating the failure modes in bamboo bolt connections in uniaxial tension by considering fiber direction in finite element analysis. Three types of bolt configurations of varying permutations, namely, single, dual, and orthogonal, were investigated. An orthotropic material was used as a constitutive model in finite element formulation to capture the inhomogeneity prevailing in bamboo culm. From the strain-field analysis of a hollow-inhomogeneous model representing bamboo, shear-out failure was dominant, as a localized area equivalent to the bolt diameter was affected due to high material orthotropy with high axial strength but weak radial and tangential strength. Bearing failure is assumed to precede shear-out failure at the bolt–bamboo contact interface, as the embedding strength was affected by localized strain concentration. The strain distribution in various bolt arrangements was found to vary between bolted connections of inhomogeneous-hollow geometry of bamboo and the ones of inhomogeneous-solid geometry representing timber. The observation in this study highlights the need for alternative design criteria to specifically assess the damage mechanism in bamboo connections.

The Finite Element Analysis of Dynamic Interaction of High-Speed Shinkansen, the Rail, and Bridge

1993 ◽  
Author(s):  
Makoto Tanabe ◽  
Hajime Wakui ◽  
Nobuyuki Matsumoto
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
High Speed ◽  
Response Analysis ◽  
Element Formulation ◽  
Element Analysis ◽  
Finite Element Program ◽  
The Finite Element Analysis ◽  
Element Program ◽  
The Impact

Abstract A finite element formulation to solve the dynamic behavior of high-speed Shinkansen cars, rail, and bridge is given. A mechanical model to express the interaction between wheel and rail is described, in which the impact of the rail on the flange of wheel is also considered. The bridge is modeled by using various finite elements such as shell, beam, solid, spring, and mass. The equations of motions of bridge and Shinkansen cars are solved under the constitutive and constraint equations to express the interaction between rail and wheel. Numerical method based on a modal transformation to get the dynamic response effectively is discussed. A finite element program for the dynamic response analysis of Shinkansen cars, rail, and bridge at the high-speed running has been developed. Numerical examples are also demonstrated.

scholarly journals Mathematical Optimization Problems for Particle Finite Element Analysis Applied to 2D Landslide Modeling

2019 ◽  
Author(s):  
Liang Wang ◽  
Xue Zhang ◽  
Filippo Zaniboni ◽  
Eugenio Oñate ◽  
Stefano Tinti
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Optimization Problems ◽  
Mathematical Optimization ◽  
Element Formulation ◽  
Numerical Implementation ◽  
Element Analysis ◽  
Landslide Modeling ◽  
Element Method

AbstractNotwithstanding its complexity in terms of numerical implementation and limitations in coping with problems involving extreme deformation, the finite element method (FEM) offers the advantage of solving complicated mathematical problems with diverse boundary conditions. Recently, a version of the particle finite element method (PFEM) was proposed for analyzing large-deformation problems. In this version of the PFEM, the finite element formulation, which was recast as a standard optimization problem and resolved efficiently using advanced optimization engines, was adopted for incremental analysis whilst the idea of particle approaches was employed to tackle mesh issues resulting from the large deformations. In this paper, the numerical implementation of this version of PFEM is detailed, revealing some key numerical aspects that are distinct from the conventional FEM, such as the solution strategy, imposition of displacement boundary conditions, and treatment of contacts. Additionally, the correctness and robustness of this version of PFEM in conducting failure and post-failure analyses of landslides are demonstrated via a stability analysis of a typical slope and a case study on the 2008 Tangjiashan landslide, China. Comparative studies between the results of the PFEM simulations and available data are performed qualitatively as well as quantitatively.

Dynamic Finite Element Analysis of the Position Control System of a Two-Link Horizontal Flexible Robot

1990 ◽  
Vol 2 (2) ◽  
pp. 83-90
Author(s):  
Hiroyuki Kojima ◽  
Keyword(s):  
Finite Element ◽  
Control System ◽  
Position Control ◽  
Velocity Curve ◽  
Element Formulation ◽  
Robot Arm ◽  
Flexible Robot ◽  
Element Analysis ◽  
Flexible Arm ◽  
Position Control System

In this paper, a finite element formulation method for a horizontal flexible robot arm with two links is first presented. In the analysis, the kinetic energy of the flexible arm is represented in brief compared with previous methods, and the matrix equation of motion in consideration of the nonlinear forces, such as the Coriolis force, is derived by the finite element method and the variational theorem. Then, the state equation of the mechatronics system consisting of the flexible arm and the position control system is obtained. Secondly, numerical simulations in the case of applying path control based on the trapezoidal velocity curve are carried out by use of the Wilson-<I>θ</I> method, and the effects of the bending rigidity and the shape of the trapezoidal velocity curve on the dynamic characteristics of the mechatronics system are demonstrated.

Mixed Finite Element Analysis of Elastomeric Butt-Joints

2005 ◽  
Vol 129 (1) ◽  
pp. 11-18 ◽  
Author(s):  
P. A. Kakavas ◽  
G. I. Giannopoulos ◽  
N. K. Anifantis
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Poisson Ratio ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Butt Joint ◽  
Element Formulation ◽  
Butt Joints ◽  
Element Analysis ◽  
Strain Energy Density Function

This paper presents a mixed finite element formulation approximating large deformations observed in the analysis of elastomeric butt-joints. The rubber has been considered as nearly incompressible continuum obeying the Mooney/Rivlin (M/R) strain energy density function. The parameters of the model were determined by fitting the available from the literature uniaxial tension experimental data with the constitutive equation derived from the M/R model. The optimum value of the Poisson ratio is adjusted by comparing the experimentally observed diametral contraction of the model with that numerically obtained using the finite element method. The solution of the problem has been obtained utilizing the mixed finite element procedure on the basis of displacement/pressure mixed interpolation and enhanced strain energy mixed formulation. For comparison purposes, an axisymmetric with two-parameter M/R model and a three-dimensional (3D) with nine-parameters M/R model of the butt-joint are formulated and numerical results are illustrated concerning axisymmetric or general loading. For small strains the stress and/or strain distribution in the 2D axisymmetric butt-joint problem was compared with derived analytical solutions. Stress distributions along critical paths are evaluated and discussed.

Modal Reduction Technique for Predicting the Onset of Chaotic Behavior due to Lateral Vibrations in Drillstrings

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Kathira Mongkolcheep ◽  
Annie Ruimi ◽  
Alan Palazzolo
Keyword(s):  
Finite Element ◽  
Oil And Gas ◽  
Chaotic Behavior ◽  
Large Diameter ◽  
Operating Conditions ◽  
Dynamical Analysis ◽  
Computational Time ◽  
Element Formulation ◽  
Element Analysis ◽  
Lateral Vibrations

Drillstrings used for oil and gas exploration and extraction consist of a drillpipe (slender columns on the order of 3–5 km long), drill collars (DCs) (thick-walled large-diameter pipes), stabilizers (cylindrical elements with short sections and diameter near that of the borehole), and a rock-cutting tool that uses rotational energy to penetrate the soil. Several types of vibrations ensue from these motions and play a major role in added costs resulting from unforeseen events such as abandoning holes, replacing bits, and fishing severed bottom-hole assemblies (BHAs). It is thus of critical importance to understand, predict, and mitigate the severe vibrations experienced by drillstrings and BHA to optimize drilling time while lowering fuel consumption and related emissions of NOX and/or other pollutants. In this paper, we present a dynamical analysis of the behavior of drillstrings due to the violent lateral vibrations (LVs) DCs may experience as a result of rotating drillstrings. The behavior is represented by a system of two coupled nonlinear ordinary equations that are integrated numerically with a finite element analysis based on Timoshenko beam (TB) formulation combined to a modal condensation technique to reduce the computational time. Various nonlinear dynamical analysis tools, such as frequency spectrum, Poincaré maps, bifurcation diagrams, and Lyapunov exponents (LE), are used to characterizing the response. The DC section between two stabilizers is essentially modeled as a Jeffcott rotor with nonlinearity effects included. The model builds on two earlier models for the finite element formulation and the treatment of chaotic vibrations. Nonlinearity appears in the form of drillstring/borehole contact force, friction, and quadratic damping. The DC flexibility is included to allow investigation of bending modes. The analysis takes into account the length of time to steady state, number of subintervals, presence of rigid body modes, number of finite elements, and modal coordinates. Simulations results indicate that by varying operating conditions, a spectrum of behaviors from periodic to chaotic may be observed.

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