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.

Finite Element Analysis of Sloshing in Horizontal-Cylindrical Industrial Vessels Under Earthquake Loading

2005 ◽  
Author(s):  
M. A. Platyrrachos ◽  
S. A. Karamanos
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Solutions ◽  
Fluid Motion ◽  
Element Formulation ◽  
Element Analysis ◽  
Seismic Force ◽  
Current Design ◽  
Cylindrical Tanks ◽  
Horizontal Cylinders

The present paper presents a finite-element formulation for earthquake-induced sloshing in horizontal-cylindrical industrial vessels. Assuming small-amplitude free-surface elevation, a linearized sloshing problem is obtained, which provides very good results in comparison with other analytical or numerical solutions, and available experimental data. The paper is aimed at calculating sloshing frequencies, as well as sloshing transient response under horizontal seismic excitation. Based on an “impulsive-convective” decomposition of the container-fluid motion, an efficient methodology is proposed for the calculation of the total seismic force, through the corresponding sloshing masses. The results from the present finite element analysis offers an efficient tool for predicting the total seismic force in horizontal cylinders and extends the current design practice for vertical cylindrical tanks stated in existing seismic design specifications.

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.

A Discontinuous Finite Element Analysis of Transient Temperature Response in Semi-Transparent Media Induced by Pulsing Lasers

2004 ◽  
Author(s):  
X. Ai ◽  
X. Cui ◽  
B. Q. Li
Keyword(s):  
Finite Element ◽  
Temperature Response ◽  
Finite Element Formulation ◽  
Transient Temperature ◽  
Hyperbolic Heat Conduction ◽  
Element Formulation ◽  
Element Analysis ◽  
Coupled Equations ◽  
Discontinuous Finite Element ◽  
Transient Temperature Response

A discontinuous Galerkin finite element formulation is presented for the simulation of the transient temperature distribution in a semi-transparent medium heated by an extra-fast pulsing laser. For this problem, the classic Fourier law breaks down and the thermal effects are described by a hyperbolic heat conduction equation coupled with internal radiative heat transfer. These coupled equations are solved using the discontinuous finite element method, which is particularly suited for problems of the hyperbolic type. In the paper, the discontinuous finite element formulation is presented and numerical fluxes are determined by enforcing the stability of the numerical method. Numerical analysis of the transient temperature response induced by a laser pulse is conducted for a one-dimensional semi-transparent slab with black boundaries. The numerical simulation demonstrates the non-Fourier characteristic of thermal wave behaviors in the slab, and the results from radiation-conduction coupling calculations show that the internal radiation helps to reduce the non-Fourier effects in the media.

p-Version Finite Element Analysis of Gas Bearings of Finite Width

1991 ◽  
Vol 113 (3) ◽  
pp. 417-420 ◽  
Author(s):  
S. H. Nguyen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Solutions ◽  
Element Formulation ◽  
Finite Width ◽  
Coarse Mesh ◽  
Element Analysis ◽  
Newton Raphson ◽  
Bearing Number ◽  
Raphson Iteration

Steady-state compressible isothermal lubrication problems are analyzed by the p-version finite element formulation in conjunction with the Newton-Raphson iteration procedure. Test examples confirm that this is an effective formulation for solving finite width bearing problems, and that, even for high bearing number (Λx > 1000) and coarse mesh situations, numerical solutions are accurate and converge rapidly.

scholarly journals Free vibration of bidirectional functionally graded sandwich beams using a first-order shear deformation finite element formulation

2020 ◽  
Vol 14 (3) ◽  
pp. 136-150
Author(s):  
Le Thi Ngoc Anh ◽  
Vu Thi An Ninh ◽  
Tran Van Lang ◽  
Nguyen Dinh Kien
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Shear Deformation ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
First Order ◽  
Various Boundary Conditions

Free vibration of bidirectional functionally graded sandwich (BFGSW) beams is studied by using a first-order shear deformation finite element formulation. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in both the longitudinal and thickness directions by power gradation laws. The finite element formulation with the stiffness and mass matrices evaluated explicitly is efficient, and it is capable of giving accurate frequencies by using a small number of elements. Vibration characteristics are evaluated for the beams with various boundary conditions. The effects of the power-law indexes, the layer thickness ratio, and the aspect ratio on the frequencies are investigated in detail and highlighted. The influence of the aspect ratio on the frequencies is also examined and discussed. Keywords: BFGSW beam; first-order shear deformation theory; free vibration; finite element method.

p-Version Incompressible Lubrication Finite Element Analysis of Large Width Bearings

1991 ◽  
Vol 113 (1) ◽  
pp. 116-119 ◽  
Author(s):  
S. H. Nguyen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Pressure Field ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Element Analysis ◽  
Numerical Examples ◽  
Arbitrary Polynomial ◽  
Large Width

This paper presents a p-version finite element formulation for incompressible lubrication analyses where the pressure field can be of any arbitrary polynomial of order p. The formulation ensures the C° continuity between mating element boundaries. Numerical examples are provided to demonstrate the simplicity of modeling and the accuracy of the formulation.

Numerical simulation of EPS geofoam behaviour in triaxial tests

2015 ◽  
Vol 32 (5) ◽  
pp. 1372-1390 ◽  
Author(s):  
Sanka Dilshan Ekanayake ◽  
D.S. Liyanapathirana ◽  
Chin Jian Leo
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Constitutive Model ◽  
Finite Element Formulation ◽  
Triaxial Tests ◽  
Element Formulation ◽  
Short Term ◽  
Element Analysis ◽  
Eps Geofoam ◽  
Content Type

Purpose – EPS geofoam has been widely used in embankment construction, slope stabilisation, retaining walls, bridge approaches and abutments. Nevertheless, the potential of EPS geofoam as an engineering material in geotechnical applications has not been fully realised yet. The purpose of this paper is to present the finite element formulation of a constitutive model based on the hardening plasticity, which has the ability to simulate short-term behaviour of EPS geofoam, to predict the mechanical behaviour of EPS geofoam and it is implemented in the finite element programme ABAQUS. Design/methodology/approach – Finite element formulation is presented based on the explicit integration scheme. Findings – The finite element formulation is verified using triaxial test data found in the literature (Wong and Leo, 2006 and Chun et al., 2004) for two varieties of EPS geofoam. Performance of the constitute model is compared with four other models found in the literature and results confirm that the constitutive model used in this study has the ability to simulate the short-term EPS geofoam behaviour with sufficient accuracy. Research limitations/implications – This research is focused only on the short-term behaviour of EPS geofoam. Experimental studies will be carried out in future to incorporate effects of temperature and creep on the material behaviour. Practical implications – This formulation will be applicable to finite element analysis of boundary value problems involving EPS geofoam (e.g. application of EPS geofoam in ground vibration isolation, retaining structures as compressible inclusions and stabilisation of slopes). Originality/value – Finite element analysis of EPS geofoam applications are available in the literature using elastic perfectly plastic constitutive models. However, this is the first paper presenting a finite element application utilising a constitutive model specifically developed for EPS geofoam.

Structural-Acoustic Vibration Reduction Using Switched Shunt Piezoelectric Patches: A Finite Element Analysis

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Walid Larbi ◽  
Jean-François Deü ◽  
Monica Ciminello ◽  
Roger Ohayon
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Vibration Reduction ◽  
Coupled System ◽  
Acoustic Vibration ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Element Analysis ◽  
Acoustic Cavity ◽  
Acoustic Fluid

In this paper, we present a finite element formulation for vibration reduction in structural-acoustic systems using passive or semipassive shunt techniques. The coupled system consists of an elastic structure (with surface-mounted piezoelectric patches) filled with an inviscid linear acoustic fluid. An appropriate finite element formulation is derived. Numerical results for an elastic plate coupled to a parallelipedic air-filled interior acoustic cavity are presented, showing the performances of both the inductive shunt and the synchronized switch shunt techniques.

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