Showing papers on "Thermoelastic damping published in 2002"

Composite Materials: Design and Applications

Abstract: PART ONE PRINCIPLES OF CONSTRUCTION COMPOSITE MATERIALS, INTEREST AND PROPERTIES What is Composite Material Fibers and Matrix What can be Made Using Composite Materials? Typical Examples of Interest on the Use of Composite Materials Examples on Replacing Conventional Solutions with Composites Principal Physical Properties FABRICATION PROCESSES Molding Processes Other Forming Processes Practical Hints in the Manufacturing Processes PLY PROPERTIES Isotropy and Anisotropy Characteristics of the Reinforcement-Matrix Mixture Unidirectional Ply Woven Fabrics Mats and Reinforced Matrices Multidimensional Fabrics Metal Matrix Composites Tests SANDWICH STRUCTURES: What is a Sandwich Structure? Simplified Flexure A Few Special Aspects Fabrication and Design Problems Nondestructive Quality Control CONCEPTION AND DESIGN Design of a Composite Piece The Laminate Failure of Laminates Sizing of Laminates JOINING AND ASSEMBLY Riveting and Bolting Bonding Inserts COMPOSITE MATERIALS AND AEROSPACE CONSTRUCTION Aircraft Helicopters Propeller Blades for Airplanes Turbine Blades in Composites Space Applications COMPOSITE MATERIALS FOR OTHER APPLICATIONS: Composite Materials and the Manufacturing of Automobiles Composites in Naval Construction Sports and Recreation Other Applications PART TWO: MECHANICAL BEHAVIOR OF LAMINATED MATERIALS ANISOTROPIC ELASTIC MEDIA: Review of Notations Orthotropic Materials Transversely Isotropic Materials ELASTIC CONSTANTS OF UNIDIRECTIONAL COMPOSITES: Longitudinal Modulus Poisson Coefficient Transverse Modulus Shear Modulus Thermoelastic Properties ELASTIC CONSTANTS OF A PLY ALONG AN ARBITRARY DIRECTION: Compliance Coefficients Stiffness Coefficients Case of Thermomechanical Loading MECHANICAL BEHAVIOR OF THIN LAMINATED PLATES: Laminate with Miplane Symmetry Laminate without Miplane Symmetry PART THREE: JUSTIFICATIONS, COMPOSITE BEAMS, THICK PLATES ELASTIC COEFFICIENTS Elastic Coefficients in an Orthotropic Material Elastic Coefficients for a Transversely Isotropic Material Case of a Ply THE HILL-TSAI FRACTURE CRITERION: Isotropic Material: Von Mises Criterion Orthotropic Material: Hill-Tsai Criterion Evaluation of the Resistance of a Unidirectional Ply with Respect to the Direction of Loading COMPOSITE BEAMS IN FLEXURE: Flexure of Symmetric Beams with Isotropic Phases The Case of any Cross Section (Asymmetric) COMPOSITE BEAMS IN TORSION: Uniform Torsion Location of the Torsion Center FLEXURE OF THICK COMPOSITE PLATES: Preliminary Remarks Displacement Field Strains Constitutive Relations Equilibrium Equations Technical Formulation for Bending Examples PART FOUR: APPLICATIONS LEVEL 1 Simply Supported Sandwich Beam Poisson Coefficient of a Unidirectional Layer Helicopter Blade Transmission Shaft for Trucks Flywheel in Carbon/Epoxy Wing Tip Made of Carbon/Epoxy Carbon Fibers Coated with Nickel Tube Made of Glass/Epoxy Under Pressure Filament Wound Reservoir, Winding Angle Filament Wound Reservoir, Taking into Account the Heads Determination of the Volume Fraction of Fibers by Pyrolysis Lever Arm Made of Carbon/Peek Unidirectionals and Short Fibers Telegraphic Mast in Glass/Resin Unidirectional Ply of HR Carbon Manipulator Arm of Space Shuttle LEVEL 2 Sandwich Beam: Simplified Calculations of the Shear Coefficient Procedure for Calculation of a Laminate Kevlar/Epoxy Laminates: Evolution of Stiffness Depending on the Direction of the Load Residual Thermal Stresses Due to Curing of the Laminate Thermoelastic Behavior of a Tube Made of Filament Wound Glass/Polyester Polymeric Tube Loaded by Thermal Load and Creep First Ply Fracture of a Laminate Ultimate Fracture Optimum Laminate for Isotropic Stress State Laminate Made of Identical Layers of Balanced Fabric Wing Spar in Carbon/Epoxy Determination of the Elastic Characteristics of a Carbon/Epoxy Unidirectional Layer from Tensile Test Sail Boat Shell in Glass/Polyester Determination of the in-Plane Shear Modulus of a Balanced Fabric Ply Quasi-Isotropic Laminate Orthotropic Plate in Pure Torsion Plate made by Resin Transfer Molding (RTM) Thermoelastic Behavior of a Balanced Fabric Ply LEVEL 3 Cylindrical Bonding Double Bonded Joint Composite Beam with Two Layers Buckling of a Sandwich Beam Shear Due to Bending in a Sandwich Beam Column Made of Stretched Polymer Cylindrical Bending of a Thick Orthotropic Plate under Uniform Loading Bending of a Sandwich Plate Bending Vibration of a Sandwich Beam Appendix 1: Stresses in the Plies of a Laminate of Carbon/Epoxy Loaded in its Plane Appendix 2: Buckling of Orthotropic Structures Bibliography

Modeling MEMS and NEMS

Abstract: INTRODUCTION MEMS and NEMS A Capsule History of MEMS and NEMS Dimensional Analysis and Scaling Exercises A REFRESHER ON CONTINUUM MECHANICS Introduction The Continuum Hypothesis Heat Conduction Elasticity Linear Thermoelasticity Fluid Dynamics Electromagnetism Numerical Methods for Continuum Mechanics SMALL IS DIFFERENT The Backyard Scaling Systems Exercises THERMALLY DRIVEN SYSTEMS Introduction Thermally Driven Devices From PDE to ODE: Lumped Models Joule Heating of a Cylinder Analysis of Thermal Data Storage Exercises MODELING ELASTIC STRUCTURES Introduction Examples of Elastic Structures in MEMS/NEMS The Mass on a Spring Membranes Beams Plates The Capacitive Pressure Sensor Exercises MODELING COUPLED THERMAL-ELASTIC SYSTEMS Introduction Devices and Phenomena in Thermal-Elastic Systems Modeling Thermopneumatic Systems The Thermoelastic Rod Revisited Modeling Thermoelastic V-Beam Actuators Modeling Thermal Bimorph Actuators Modeling Bimetallic Thermal Actuators Exercises MODELING ELECTROSTATIC-ELASTIC SYSTEMS Introduction Devices Using Electrostatic Actuation The Mass-Spring Model Modeling General Electrostatic-Elastic Systems Electrostatic-Elastic Systems - Membrane Theory Electrostatic-Elastic Systems - Beam and Plate Theory Analysis of Capacitive Control Schemes Exercises MODELING MAGNETICALLY ACTUATED SYSTEMS Introduction Magnetically Driven Devices Mass-Spring Models A Simple Membrane Micropump Model A Small-Aspect Ratio Model Exercises MICROFLUIDICS Introduction Microfluidic Devices More Fluidic Scaling Modeling Squeeze Film Damping Exercises BEYOND CONTINUUM THEORY Introduction Limits of Contiuum Mechanics Devices and Systems Beyond Continuum Theory Exercises REFERENCES APPENDICES Mathematical Results Physical Constants INDEX Each chapter also contains Related Reading and Notes sections.

Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates

Abstract: An exact solution is obtained for three-dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and/or bottom surfaces. Suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate, which are then solved by employing the power series method. The exact solution is applicable to both thick and thin plates. Results are presented for two-constituent metal‐ceramic functionally graded rectangular plates that have a power law through-the-thickness variation of the volume fractions of the constituents. The effective material properties at a point are estimated by either the Mori‐Tanaka or the self-consistentschemes. Exact displacementsand stressesatseveral locations for mechanical and thermal loads are used toassess theaccuracyof the classical plate theory, thee rst-ordershear deformation theory, and athird-order shear deformation theory for functionally graded plates. Results are alsocomputed for a functionally graded plate with material properties derived by the Mori‐Tanaka method, the self-consistent scheme, and a combination of these two methods.

Thermal Stresses in Functionally Graded Beams

Abstract: Thermoelastic equilibrium equations for a functionally graded beam are solved in closed-form to obtain the axial stress distribution. The thermoelastic constants of the beam and the temperature were assumed to vary exponentially through the thickness. The Poisson ratio was held constant. The exponential variation of the elastic constants and the temperature allow exact solution for the plane thermoelasticity equations. A simple Euler ‐ Bernoulli-type beam theory is also developed based on the assumption that plane sections remain plane and normal to the beam axis. The stresses were calculated for cases for which the elastic constants vary in the same manner as the temperature and vice versa. The residual thermal stresses are greatly reduced, when the variation of thermoelastic constants are opposite to that of the temperature distribution. When both elastic constants and temperature increasethrough the thickness in the samedirection, they causea signie cant raise in thermal stresses. For the case of nearly uniform temperature along the length of the beam, beam theory is adequate in predicting thermal residual stresses.

Thermoelasticity with second sound—exponential stability in linear and non‐linear 1‐d

Abstract: We consider linear and non-linear thermoelastic systems in one space dimension where thermal disturbances are modelled propagating as wave-like pulses travelling at finite speed. This removal of the physical paradox of infinite propagation speed in the classical theory of thermoelasticity within Fourier's law is achieved using Cattaneo's law for heat conduction. For different boundary conditions, in particular for those arising in pulsed laser heating of solids, the exponential stability of the now purely, but slightly damped, hyperbolic linear system is proved. A comparison with classical hyperbolic–parabolic thermoelasticity is given. For Dirichlet type boundary conditions—rigidly clamped, constant temperature—the global existence of small, smooth solutions and the exponential stability are proved for a non-linear system. Copyright © 2002 John Wiley & Sons, Ltd.

First-order-theory-based thermoelastic stability of functionally graded material circular plates

Abstract: Thermal buckling of circular plates made of functionally graded material is discussed. The nonlinear equilibrium and linear stability equations are derived using variational formulations. The thermal buckling of solid circular plates under uniform temperature rise, gradient through the thickness, and linear temperature variation along the radius are considered, and the buckling temperatures are derived. The buckling temperatures are derived for simply supported and clamped edges. The results are verified with known results in the literature.

Thermoelastic damping in fine-grained polysilicon flexural beam resonators

Abstract: The design and fabrication of polysilicon flexural beam resonators with very high mechanical quality factors (Q) is essential for many MEMS applications. Based on an extension of the well-established theory of thermoelastic damping in homogeneous beams, we present closed-form expressions to estimate an upper bound on the attainable quality factors of polycrystalline beam resonators with thickness (h) much larger than the average grain size (d). Associated with each of these length scales is an independent damping mechanism; we refer to them as Zener and intracrystalline thermoelastic damping, respectively. For representative polysilicon beam resonators (h = 2 /spl mu/m; d = 0.1 /spl mu/m) at 300 K, the predicted critical frequencies for these two mechanisms are /spl sim/7 MHz and /spl sim/14 GHz, respectively. The model is consistent with data from the literature in the sense that the measured values approach, but do not exceed, the calculated thermoelastic limit. From the viewpoint of the maximum attainable Q, our model suggests that single-crystal silicon, rather than fine-grained polysilicon, is the material of choice for the fabrication of flexural beam resonators for applications in the gigahertz frequency range.

Thermoelastic loss in microscale oscillators

Abstract: A simple model of thermoelastic dissipation is proposed for general, free standing microelectromechanical (MEMS) and nanoelectromechanical (NEMS) oscillators The theory defines a flexural modal participation factor, the fraction of potential energy stored in flexure, and approximates the internal friction by assuming the energy loss to occur solely via classical thermoelastic dissipation of this component of the motion The theory is compared to the measured internal friction of a high Q mode of a single-crystal silicon double paddle oscillator The loss at high temperature (above 150 K) is found to be in good agreement with the theoretical prediction The importance of this dissipation mechanism as a function of scale is briefly discussed We find that the relative importance of this mechanism scales with the size of the structure, and that for nanoscale structures it is less important than intrinsic phonon–phonon scattering

Thermoelastic wave in metal induced by ultrafast laser pulses

Abstract: In this work, an analytical solution for thermoelastic waves in a metal induced by an ultrafast laser pulse was formulated in the form of a Fourier series. The two-step heat transfer model was applied to account for the thermal nonequilibrium between electrons and the lattice during ultrafast pulsed laser heating. The coupling between the strain rate and the temperature field was also considered. Calculations were carried out to study generation, propagation, and attenuation of thermoelastic waves induced by a pico- and a femtosecond laser pulse. Results were compared with those obtained without considering the two-step heat transfer effect.

Green's function approach to unsteady thermal stresses in an infinite hollow cylinder of functionally graded material

Abstract: A Green's function approach based on the laminate theory is adopted for solving the two-dimensional unsteady temperature field (r, z) and the associated thermal stresses in an infinite hollow circular cylinder made of a functionally graded material (FGM) with radial-directionally dependent properties. The unsteady heat conduction equation is formulated as an eigenvalue problem by making use of the eigenfunction expansion theory and the laminate theory. The eigenvalues and the corresponding eigenfunctions obtained by solving an eigenvalue problem for each layer constitute the Green's function solution for analyzing the unsteady temperature. The associated thermoelastic field is analyzed by making use of the thermoclastic displacement potential function and Michell's function. Numerical results are carried out and shown in figures.

Lord-Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two-dimensional generalized thermoelasticity

Abstract: The model of the equations of generalized thermoelasticity based on Lord-Shulman theory in an isotropic elastic medium under the dependence of the modulus of elasticity on the reference temperature is established. The normal mode analysis is used to obtain the expressions for the temperature, the horizontal component of displacement, and thermal stress. The resulting formulation is applied to two different concrete problems. The first concerns the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space subject to appropriate boundary conditions. The second deals with a thick plate subject to a time-dependent heat source on each face. Numerical results are illustrated graphically for each problem considered. Comparisons are made with the results obtained in the case of temperature independence of the modulus of elasticity.

Luxemburg-Gorky Effect Retooled for Elastic Waves: A Mechanism and Experimental Evidence

Abstract: A new mechanism is proposed for the linear and amplitude-dependent dissipation due to elastic-wave-crack interaction. We have observed one of its strong manifestations in a direct elastic-wave analog of the Luxemburg-Gorky effect consisting of the cross modulation of radio waves at the dissipative nonlinearity of the ionosphere plasma. The counterpart acoustic mechanism implies, first, a drastic enhancement of the thermoelastic coupling at high-compliance microdefects, and, second, the high stress-sensitivity of the defects leads to a strong stress dependence of the resultant dissipation.

Free vibration analysis of homogeneous transversely isotropic thermoelastic cylindrical panel

Abstract: In this article, based on three-dimensional thermoelasticity, an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel is presented in the context of L ord-Shulman (L S), Green-L indsay (GL), and Green-Nagdhi (GN) theories of thermoelasticity. Three displacement potential functions are introduced so that the equations of motion and heat conduction are uncoupled and simplified. It is noticed that the purely transverse mode is independent of temperature change and rest of the motion. The equations for free vibration problems are further reduced to four second-order ordinary differential equations after expanding the potential and temperature functions with an orthogonal series. A modified Bessel function solution with complex arguments is then directly used for complex eigenvalues. Numerical examples are presented to clarify the developed method and compare the results to the existing one.

Deformation and structural stability of layered plate microstructures subjected to thermal loading

Abstract: We study the deformation and stability of gold-polysilicon MEMS plate microstructures fabricated by the MUMPS surface micromachining process and subjected to uniform temperature changes. We measured, using an interferometric microscope, full-field deformed shapes of a series of square and circular gold (0.5 /spl mu/m thick)/polysilicon (1.5 /spl mu/m thick) plate microstructures with characteristic lengths l (square side length and circle diameter) ranging from l=150 to 300 /spl mu/m. From these measurements we determined the pointwise and average curvature of the deformed plates. Although the curvature generally varies with position, the deformation response of the plates can be broadly characterized in terms of the spatial average curvature as a function of temperature change. In terms of this, three deformation regimes were observed: (i) linear thermoelastic response independent of plate size; (ii) geometrically nonlinear thermoelastic response that depends on plate size; and (iii) bifurcations in the curvature-temperature response that also depend on plate size. We modeled the deformation response both analytically and with the finite element method; in the former we assume spatially constant curvature, while in the latter, we relax this assumption. Good qualitative and quantitative agreement is obtained between predictions and measurements in all three deformation regimes, although the details of bifurcation are less accurately predicted than the linear and nonlinear response. This is attributed to their strong sensitivity to slight imperfections, which is discussed in some detail. Good agreement is also obtained between measurements and predictions of the spatial nonuniformity of the curvature across the plate. Although it is not the focus of this study, the predictions, when coupled with curvature measurements, can be used inversely to determine elastic and thermal expansion properties of the materials in a layered plate microstructure.

Finite element algorithms for thermoelastic wear problems

Abstract: In the present paper three algorithms are applied to a finite element model of two thermoelastic bodies in frictional wearing contact. All three algorithms utilize a modification of a Newton method for B-differentiable equations as non-linear equation solver. In the first algorithm the fully-coupled system of thermomechanical equations is solved directly using the modified method, while in the other two algorithms the equation system is decoupled in one mechanical part and another thermal part which are solved using an iterative strategy of Gauss–Seidel type. The two iterative algorithms differ in which order the parts are solved. The numerical performance of the algorithms are investigated for two two-dimensional examples. Based on these numerical results, the behaviour of the model is also discussed. It is found that the iterative approach where the thermal subproblem is solved first is slightly more efficient for both examples. Furthermore, it is shown numerically how the predicted wear gap is influenced by the bulk properties of the contacting bodies, in particular how it is influenced by thermal dilatation.

Effects of nonlinear thermoelastic damping in highly stressed fibers

Abstract: We present an analysis of thermoelastic damping in materials arising from the temperature dependence of the elastic moduli. We show that this form of damping can cancel thermoelastic damping arising from thermal expansion for a suitably chosen operating stress. For the case of the suspension fibers used in the gravitational wave detectors, this loss mechanism can be the dominant one.

A “quasi-elastic” affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites

Abstract: The derivation of the overall behaviour of nonlinear viscoelastic (or rate-dependent elastoplastic) heterogeneous materials requires a linearisation of the constitutive equations around uniform per phase stress (or strain) histories. The resulting Linear Comparison Material (LCM) has to be linear thermoviscoelastic to fully retain the viscoelastic nature of phase interactions. Instead of the exact treatment of this LCM (i.e., correspondence principle and inverse Laplace transforms) as proposed by the “classical” affine formulation, an approximate treatment is proposed here. First considering Maxwellian behaviour, comparisons for a single phase as well as for two-phase materials (with “parallel” and disordered morphologies) show that the “direct inversion method” of Laplace transforms, initially proposed by Schapery (1962), has to be adapted to fit correctly exact responses to creep loading while a more general method is proposed for other loading paths. When applied to nonlinear viscoelastic heterogeneous materials, this approximate inversion method gives rise to a new formulation which is consistent with the classical affine one for the steady-state regimes. In the transient regime, it leads to a significantly more efficient numerical resolution, the LCM associated to the step by step procedure being no more thermoviscoelastic but thermoelastic. Various comparisons for nonlinear viscoelastic polycrystals responses to creep as well as relaxation loadings show that this “quasi-elastic” formulation yields results very close to classical affine ones, even for high contrasts.

Determination of growth-induced strain and thermo-elastic properties of coatings by curvature measurements

Abstract: Determination of growth-induced strain and thermoelastic properties of coatings by curvature measurements

Null controllability of a thermoelastic plate

Abstract: Thermoelastic plate model with a control term in the thermal equation is considered. The main result in this paper is that with thermal control, locally distributed within the interior and square integrable in time and space, any finite energy solution can be driven to zero at the control time T.

Femtosecond-laser-produced low-density plasmas in transparent biological media: A tool for the creation of chemical, thermal and thermomechanical effects below the optical breakdown threshold

Abstract: The irradiance threshold for femtosecond optical breakdown in aqueous media is approximately equals 1.0x1013W cm-2. At the breakdown threshold, a plasma with a free electron density of about 1021cm-3 is generated, and the energy density in the breakdown region is sufficiently high to cause the formation of a bubble which can be experimentally observed. We found previously that plasmas with a free electron density <1021cm-3 are formed also in a fairly large irradiance range below the breakdown threshold. The present study investigates the chemical, thermal, and thermomechanical effects produced by these low-density plasmas. We use a rate equation model considering multiphoton ionization and produced by these low-density plasmas. We use a rate equation model considering multiphoton ionization and avalanche ionization to numerically simulate the temporal evolution of the free electron density during the laser pulse for a given irradiance, and to calculate the irradiance dependence of the free-electron density and volumetric energy density reached at the end of the laser pulse. The value of the energy density created by each laser pulse is then used to calculate the temperature distribution in the focal region after application of a single laser pulse and of series of pulses. The results of the temperature calculations yield, finally, the starting point for calculations of the thermoelastic stresses that are generated during the formation of the low-density plasmas. We found that, particularly for short wavelengths, a large 'tuning range' exists for the creation of spatially extremely confined chemical, thermal and mechanical effects via free electron generation through nonlinear absorption. Photochemical effects dominate at the lower end of this irradiance range, whereas at the upper end they are mixed with thermal effects and modified by thermoelastic stresses. Above the breakdown threshold, the spatial confinement is partly destroyed by cavitation bubble formation, and the laser-induced effects become more disruptive. Our simulations revealed that the highly localized ablation of intracellular structures and intranuclear chromosome dissection recently demonstrated by other researchers are probably mediated by free-electron- induced chemical bond breaking and not related to heating or thermoelastic stresses. We conclude that low density plasmas below the optical breakdown threshold can be a versatile tool for the manipulation of transparent biological media and other transparent materials. (enabling, e.g., the generation of optical waveguides in bulk glass). Low density plasmas may, however, also be a potential hazard in multiphoton microscopy and higher harmonic imaging.

Meshless approach to shape optimization of linear thermoelastic solids

Abstract: This paper presents a formulation for shape optimization in thermoelasticity using a meshless method, namely the element-free Galerkin method. Two examples are treated in detail and comparisons with previously published finite element analysis results demonstrate the excellent opportunities the EFG offers for solving these types of problems. Smoother stresses, no remeshing, and better accuracy than finite element solutions, permit answers to shape optimization problems in thermoelasticity that are practically unattainable with the classical FEM without remeshing. For the thermal fin example, the EFG finds finger shapes that are missed by the FEM analysis, and the objective value is greatly improved compared to the FEM solution. A study of the influence of the number of design parameters is performed and it is observed that the EFG can give better results with a smaller number of design parameters than is possible with traditional methods. Copyright © 2001 John Wiley & Sons, Ltd.