Showing papers on "Thermoelastic damping published in 2010"

Thermal Stresses -- Advanced Theory and Applications

Abstract: 1 Basic Laws of Thermoelasticity 1 Introduction 2 Stresses and Tractions 3 Equations of Motion 4 Coordinate Transformation. Principal Axes 5 Principal Stresses and Stress Invariants 6 Displacement and Strain Tensor 7 Compatibility Equations. Simply Connected Region 8 Compatibility Conditions. Multiply Connected Regions 9 Constitutive Laws of Linear Thermoelasticity 10 Displacement Formulation of Thermoelasticity 11 Stress Formulation of Thermoelasticity 12 Two-Dimensional Thermoelasticity 13 Michell conditions 2 Thermodynamics of Elastic Continuum 1 Introduction 2 Thermodynamics Definitions 3 First Law of Thermodynamics 4 Second Law of Thermodynamics 5 Variational Formulation of Thermodynamics 6 Thermodynamics of Elastic Continuum 7 General Theory of Thermoelasticity 8 Free Energy Function of Hookean Materials 9 Fourier's Law and Heat Conduction Equation 10 Generalized Thermoelasticity. Second Sound 11 Thermoelasticity without Energy Dissipation 12 Uniqueness Theorem 13 Variational Principle of Thermoelasticity 14 Reciprocity Theorem 15 Initial and Boundary Conditions 3 Basic Problems of Thermoelasticity 1 Introduction 2 Temperature Distribution for Zero Thermal Stress 3 Analogy of Thermal Gradient with Body Forces 4 General Solution of Thermoelastic Problems 5 General Solution in Cylindrical Coordinates 6 Solution of Two-Dimensional Navier Equations 7 Solution of Problems in Spherical Coordinates 4 Heat Conduction Problems 1 Introduction 2 Problems in Rectangular Cartesian Coordinates 2.1 Steady State One-Dimensional Problems 2.2 Steady Two-Dimensional Problems. Separation of Variables 2.3 Fourier Series 2.4 Double Fourier Series 2.5 Bessel Functions and Fourier-Bessel series 2.6 Nonhomogeneous Differential Equations and Boundary Condition 2.7 Lumped Formulation 2.8 Steady State Three-Dimensional Problems 2.9.Transient Problems 3 Problems in Cylindrical coordinates 3.1 Steady-State One-Dimensional Problems (Radial Flow) 3.2. Steady -State Two-Dimensional Problems 3.3 Steady-State Three-Dimensional Problems 3.4 Transient Problems 4 Problems in Spherical Coordinates 4.1 Steady-State One-Dimensional Problems 4.2 Steady-State Two- and Three-Dimensional Problems 4.3 Transient Problems 5 Thermal Stresses in Beams 1 Introduction 2 Elementary Theory of Thermal Stresses in Beams 3 Deflection Equation of Beams 4 Boundary Conditions 5 Shear Stress in a Beam 6 Beams of Rectangular Cross Section 7 Transient Thermal Stresses in Rectangular Beams 8 . Beam with Internal Heat Generation 9 Bimetallic Beam 10 Functionally Graded Beams 11 Transient Thermal Stresses in Functionally Graded Beams 12 Thermal Stresses in Thin Curved Beams and Rings 13 Deflection of Thin Curved Beams and Rings 6 Disks, Cylinders, and Spheres 1 Introduction 2 . Cylinders with Radial Temperature Variation 3 Thermal Stresses in Disks 4 Thick Spheres 5 Thermal Stresses in a Rotating Disk 6 Non-Axisymmetrically Heated cylinders 7 Method of Complex Variables 8 Functionally Graded Thick Cylinders 9 Axisymmetric Thermal Stresses in FGM Cylinders 10.Transient Thermal Stresses in Thick Spheres 11 Functionality Graded Spheres 7 Thermal Expansion in Piping Systems 1 Introduction 2 Definition of the Elastic Center 3 . Piping Systems in Two Dimensions 4 Piping Systems in Three-dimensions 5 Pipelines with Large Radius Elbows 8 Coupled and Generalized Thermoelasticity 1 Introduction 2 Governing Equations of Coupled Thermoelasticity 3 Coupled Thermoelasticity for Infinite Space 4 Variable Heat Source 5 One-Dimensional Coupled Problem 6 Propagation of Discontinuities 7 Half-Space Subjected to a Harmonic Temperature 8 Coupled Thermoelasticity of Thick Cylinders 9 Green-Naghdi Model of a Layer 10 Generalized Thermoelasticity of Layers 11 Generalized Thermoelasticity of Spheres and Cylinders

Anisotropic Elastic Plates

Abstract: Linear Anisotropic Elastic Materials.- Lekhnitskii Formalism.- Stroh Formalism.- Infinite Space, Half-Space, and Bimaterials.- Wedges and Interface Corners.- Holes.- Cracks.- Inclusions.- Contact Problems.- Thermoelastic Problems.- Piezoelectric Materials.- Plate Bending Analysis.- Coupled Stretching-Bending Analysis.- Holes/Cracks/Inclusions in Laminates.- Boundary Element Analysis.

Band structure of phononic crystals with general damping

Abstract: In this paper, we present theoretical formalisms for the study of wave dispersion in damped elastic periodic materials. We adopt the well known structural dynamics techniques of modal analysis and state-space transformation and formulate them for the Bloch wave propagation problem. First, we consider a one-dimensional lumped parameter model of a phononic crystal consisting of two masses in the unit cell whereby the masses are connected by springs and dashpot viscous dampers. We then extend our analysis to the study of a two-dimensional phononic crystal, modeled as a dissipative elastic continuum, and consisting of a periodic arrangement of square inclusions distributed in a matrix base material. For our damping model, we consider both proportional damping and general damping. Our results demonstrate the effects of damping on the frequency band structure for various types and levels of damping. In particular, we reveal two intriguing phenomena: branch overtaking and branch cut-off. The former may result in an abrupt drop in the relative band gap size, and the latter implies an opening of full or partial wavenumber (wave vector) band gaps. Following our frequency band structure analysis, we illustrate the concept of a damping ratio band structure.

Electromagnetic Field Matter Interactions in Thermoelastic Solids and Viscous Fluids

Abstract: This book in two parts delivers a thorough derivation of nonrelativistic interaction models of electromagnetic field theories with thermoelastic solids and viscous fluids, the intention being to derive unique representations for the observable field quantities. Part I, a revised and updated version of LNP 88 "Field Matter Interactions in Thermoelastic Solids," investigates the foundations and the equivalence of various formulations of the interaction of the electromagnetic field with thermoelastic solids in the classical continuum physics limit, while Part II extensively surveys two major fields of applications, namely, magnetoelastic instabilities and vibrations, and electrorheological fluids. This volume is intended for and will be useful to students and researchers working on all aspects of electromagneto-mechanical interactions in the materials sciences of complex solids and fluids. Keywords: complex fluids, electromechanics, electrorheology, thermoelastic materials

Acceleration waves and ellipticity in thermoelastic micropolar media

Abstract: Acceleration waves in nonlinear thermoelastic micropolar media are considered. We establish the kinematic and dynamic compatibility relations for a singular surface of order 2 in the media. An analogy to the Fresnel–Hadamard–Duhem theorem and an expression for the acoustic tensor are derived. The condition for acceleration wave’s propagation is formulated as an algebraic spectral problem. It is shown that the condition coincides with the strong ellipticity of equilibrium equations. As an example, a quadratic form for the specific free energy is considered and the solutions of the corresponding spectral problem are presented.

Thermoelastic stress analysis of damage mechanisms in composite materials

Abstract: A methodology for the application of Thermoelastic Stress Analysis (TSA) in damage studies of glass reinforced polymers is established. Test specimens have been designed to promote certain damage types and the methodology applied to each. It is shown that a TSA approach can evaluate fibre breakage, matrix cracking and delamination damage. Metrics are established based on calibrated strain data obtained from the TSA. It is shown that these can be used to assess the condition of a component throughout its fatigue life.

The FEM-Modeling of the Frictional Heating Phenomenon in the Pad/Disc Tribosystem (A Review)

Abstract: This article is concerned with frictional heating phenomenon playing a central role in disc brake (clutch) systems performance. It was of great interest to carry the description of existing numerical solutions of the problem. The level of the calculations was categorized into three problems. The first is a common approach, drawn primarily on the assumption that the heat flow rate generated at the disc/pad interface is a known quantity. Heat generation was substituted by the intensity of heat flux depending on contact pressure, coefficient of friction and evolution of angular velocity, and radius of the disc product. A more complex description of the braking action was given by the assumption of mutual relation between mating parts of the disc brake system. In this case, the thermoelasticity theory was applied to the model. The facts of existing critical speed is established, in which hot spots caused mainly by contact pressure variations frictionally-excited thermoelastic instability phenomenon entered co...

Harmonic Vibrations in Thermoelasticity of Microstretch Materials

Abstract: Consider a cylinder made of a microstretch thermoelastic material for which one plane end is subjected to plane boundary data varying harmonically in time. On the lateral surface and other base, we have zero body force and heat supply. By using a Toupin type measure associated with the corresponding steady-state vibration, and by assuming that the angular frequency of oscillations is lower than a certain critical frequency, we show that the amplitude of the vibrations decays exponentially with the distance to the base. This decay estimate is similar to that of the Saint-Venant type.

Simulations and experiments of hardening and softening resonances in a clamped-clamped beam MEMS resonator

Abstract: By means of a combined analytical-numerical and experimental approach, the nonlinear dynamic behavior of a clamped–clamped beam MEMS resonator has been investigated. A good qualitative correspondence between simulations and experiments has been obtained. First-principles based multiphysics modeling is applied to derive a reduced-order model of the resonator. The model includes nonlinear geometric and electrostatic effects as well as thermoelastic damping. Both simulations and experiments show hardening and softening nonlinear dynamic behavior depending on the excitation parameters. The model captures the observed nonlinear behavior qualitatively and allows for design optimization with respect to nonlinear effects.

Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylinder under the hyperbolic heat conduction model

Abstract: In this paper, we proposed a model of generalized magneto-thermoelastic for orthotropic hollow cylinder whose surfaces are subjected to a thermal relaxation under the effect of rotation with one relaxation time. The system of fundamental equations is solved by using an implicit finite-difference scheme. A numerical method is used to calculate the temperature, displacement and the components of stresses with time and through the radial of the cylinder. Numerical results are given and illustrated graphically for each case considered. The results indicate that the effect of rotation, inhomogeneity and magnetic field are very pronounced. Comparison made with the results predicted by the theory of generalized magneto-thermoelasticity with one relaxation time in the absence of rotation.

A partition of energy in thermoelasticity of microstretch bodies

Abstract: This paper is concerned with microstretch thermoelastic materials. For the mixed initial boundary value problem defined in this context, we prove that the Cesaro means of the kinetic and strain energies of a solution with finite energy become asymptotic equal as time tends to infinity.

A theory of thermoelastic diffusion materials with voids

Abstract: In the first part of this paper, we derive the equations of the linear theory of thermoelastic diffusion in porous media based on the concept of volume fraction. Then, we establish a reciprocal relation which leads to reciprocity, uniqueness and continuous dependence theorems for anisotropic materials. Finally, we prove the existence of a generalized solution by means of the semigroup of linear operators theory.

Higher order tip enrichment of eXtended Finite Element Method in thermoelasticity

Abstract: An eXtended Finite Element Method (XFEM) is presented that can accurately predict the stress intensity factors (SIFs) for thermoelastic cracks. The method uses higher order terms of the thermoelastic asymptotic crack tip fields to enrich the approximation space of the temperature and displacement fields in the vicinity of crack tips—away from the crack tip the step function is used. It is shown that improved accuracy is obtained by using the higher order crack tip enrichments and that the benefit of including such terms is greater for thermoelastic problems than for either purely elastic or steady state heat transfer problems. The computation of SIFs directly from the XFEM degrees of freedom and using the interaction integral is studied. Directly computed SIFs are shown to be significantly less accurate than those computed using the interaction integral. Furthermore, the numerical examples suggest that the directly computed SIFs do not converge to the exact SIFs values, but converge roughly to values near the exact result. Numerical simulations of straight cracks show that with the higher order enrichment scheme, the energy norm converges monotonically with increasing number of asymptotic enrichment terms and with decreasing element size. For curved crack there is no further increase in accuracy when more than four asymptotic enrichment terms are used and the numerical simulations indicate that the SIFs obtained directly from the XFEM degrees of freedom are inaccurate, while those obtained using the interaction integral remain accurate for small integration domains. It is recommended in general that at least four higher order terms of the asymptotic solution be used to enrich the temperature and displacement fields near the crack tips and that the J- or interaction integral should always be used to compute the SIFs.

Strength optimized designs of thermoelastic structures

Abstract: For thermoelastic structures the same optimal design does not simultaneously lead to minimum compliance and maximum strength. Compliance may be a questionable objective and focus for the present paper is on the important aspect of strength, quantified as minimization of the maximum von Mises stress. With compliance defined as the product of resulting displacements and their corresponding total loads, then for thermoelastic problems compliance is different from total elastic energy. An explicit formula for this difference is derived and numerically illustrated in the optimized examples. As an alternative to mathematical programming, which with a large number of both design variables and strength constraints, is found non-practical, we choose simple recursive iterations to obtain uniform energy density and find by examples that the obtained designs are close to fulfilling also strength maximization. In compliance minimization it may be advantageous to decrease the total volume, but for strength maximization it is argued that it is advantageous to keep the total permissible volume. With the thermoelastic analysis presented directly in a finite element formulation, simple explicit formulas for equivalent thermoelastic loads are appended.

Some Estimates on Vibrations in Thermoelasticity of Dipolar Bodies

Abstract: We consider a right cylinder composed of a physically dipolar thermoelastic material for which one plane end is subjected to an excitation which is harmonic in time. By using a measure of Toupin type associated with the corresponding steady-state vibration and assuming that the exciting frequency is lower than a certain critical frequency, we obtain a spatial decay estimate, similar to that of Saint-Venant type.