Showing papers on "Thermoelastic damping published in 2008"

Unintended Consequences of Modeling Damping in Structures

Abstract: This paper investigates the consequence of using Rayleigh proportional damping in the analysis of inelastic structural systems. The discussion is presented theoretically, as well as by example through the analysis of a simple five-story structure. It is shown that when the stiffness portion of the system damping matrix is based on the original system stiffness, artificial damping is generated when the structure yields. When the damping matrix is based on the tangent stiffness but the Rayleigh proportionality constants are based on the initial stiffness, a significant but reduced amplification of damping occurs. When the damping is based on the tangent stiffness and on updated frequencies based on this stiffness, virtually no artificial damping occurs. The paper also investigates the influence on effective damping when localized yielding occurs in areas of concentrated inelasticity. In such cases, it is possible to develop artificial viscous damping forces that are extremely high, but that are not easy to detect. Such artificial damping forces may lead to completely invalid analysis. The paper ends with recommendations for performing analysis where the artificial damping is eliminated, or at least controlled.

The extended finite element method in thermoelastic fracture mechanics

Abstract: The extended finite element method (XFEM) is applied to the simulation of thermally stressed, cracked solids. Both thermal and mechanical fields are enriched in the XFEM way in order to represent discontinuous temperature, heat flux, displacement, and traction across the crack surface, as well as singular heat flux and stress at the crack front. Consequently, the cracked thermomechanical problem may be solved on a mesh that is independent of the crack. Either adiabatic or isothermal condition is considered on the crack surface. In the second case, the temperature field is enriched such that it is continuous across the crack but with a discontinuous derivative and the temperature is enforced to the prescribed value by a penalty method. The stress intensity factors are extracted from the XFEM solution by an interaction integral in domain form with no crack face integration. The method is illustrated on several numerical examples (including a curvilinear crack, a propagating crack, and a three-dimensional crack) and is compared with existing solutions. Copyright © 2007 John Wiley & Sons, Ltd.

Theory of Thermoelastic Damping in Micromechanical Resonators With Two-Dimensional Heat Conduction

Abstract: Analysis of thermoelastic damping (TED) is an important component of the design of low-loss vacuum-operated micro- and nanomechanical resonators used in microelectro- mechanical systems (MEMS). The quasi-1-D theories developed by Zener in 1937, and subsequently improved by Lifshitz and Roukes in 2000, are now widely used in MEMS design. This paper presents an exact theory for TED with 2-D heat conduction that enables a detailed evaluation of the accuracy of the quasi-1-D theories. A Green's function method is used to solve the 2-D heat- conduction equation, and an expression for TED is derived in the form of an infinite series. The effects of beam geometry, length-to- thickness aspect ratio, natural frequency, flexural mode shapes, and structural boundary conditions on TED are investigated for the representative case of single-crystal silicon microbeam resonators. The errors in the exact quasi-1-D theory range from 2% to 80% depending upon the aspect ratio and the mode shape. Implications for the use of the quasi-1-D and 2-D theories in MEMS design are discussed. [2007-0199].

Thermoelastic contact mechanics for a flat punch sliding over a graded coating/substrate system with frictional heat generation

Abstract: The problem of thermoelastic contact mechanics for the coating/substrate system with functionally graded properties is investigated, where the rigid flat punch is assumed to slide over the surface of the coating involving frictional heat generation. With the coefficient of friction being constant, the inertia effects are neglected and the solution is obtained within the framework of steady-state plane thermoelasticity. The graded material exists as a nonhomogeneous interlayer between dissimilar, homogeneous phases of the coating/substrate system or as a nonhomogeneous coating deposited on the substrate. The material nonhomogeneity is represented by spatially varying thermoelastic moduli expressed in terms of exponential functions. The Fourier integral transform method is employed and the formulation of the current thermoelastic contact problem is reduced to a Cauchy-type singular integral equation of the second kind for the unknown contact pressure. Numerical results include the distributions of the contact pressure and the in-plane component of the surface stress under the prescribed thermoelastic environment for various combinations of geometric, loading, and material parameters of the coated medium. Moreover, in order to quantify and characterize the singular behavior of contact pressure distributions at the edges of the flat punch, the stress intensity factors are defined and evaluated in terms of the solution to the governing integral equation.

Generalized Theory of Thermoelastic Diffusion for Anisotropic Media

Abstract: The equations of generalized thermoelastic diffusion, based on the theory of Lord and Shulman with one relaxation time, are given in anisotropic media. A variational principle for the governing equations is obtained. Then we show that the variational principle can be used to obtain a uniqueness theorem under suitable conditions. A reciprocity theorem for these equations is given. The obtained results are valid for some special cases that can be deduced from our generalized model.

Damping analysis of orthotropic composite materials and laminates

Abstract: The paper presents an analysis of the damping of unidirectional fibre composites, orthotropic composites and laminates. Damping parameters are investigated using beam test specimens and an impulse technique. Damping modelling is developed using a finite element analysis which evaluated the different energies dissipated in the material directions of the layers. The results obtained show that this analysis describes fairly well the experimental results. The finite element analysis can be applied to complex shape structures.

Problems with Rayleigh Damping in Base-Isolated Buildings

Abstract: In dynamic analysis, the energy dissipation in a base-isolated building is typically accounted for by allocating damping properties independently to the superstructure and to the isolation system. Rayleigh damping applied to the superstructure component alone is often used to represent the superstructure energy dissipation. At least one study has indicated that when used improperly, superstructure Rayleigh damping leads to excessive damping of the response of a base-isolated structure. As shown here, even when used as recommended for combining subsystems with disparate damping properties, Rayleigh damping results in undesirable suppression of the first mode response. To correct this behavior, stiffness-proportional damping can be used in lieu of Rayleigh damping. Stiffness-proportional damping is demonstrated to negligibly affect the first mode response, yet provide the expected energy dissipation in higher modes.

Thermoelastic bending analysis of functionally graded sandwich plates

Abstract: The thermoelastic bending analysis of functionally graded ceramic–metal sandwich plates is studied. The governing equations of equilibrium are solved for a functionally graded sandwich plates under the effect of thermal loads. The sandwich plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson’s ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. Several kinds of sandwich plates are used taking into account the symmetry of the plate and the thickness of each layer. Field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory are derived. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. The influences played by the transverse normal strain, shear deformation, thermal load, plate aspect ratio, side-to-thickness ratio, and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded metal–ceramic plates are investigated.

Damping mechanisms of single-clamped and prestressed double-clamped resonant polymer microbeams

Abstract: In this article, an investigation of the damping mechanisms of resonant single- and double-clamped polymer microbeams for a frequency range from 10 kHz to 5 MHz is presented. The suspended structures are made of SU-8, an epoxy-type photoresist, by means of a sacrificial layer technique. The vibration was measured with a laser-Doppler vibrometer in high vacuum at different temperatures and at atmospheric pressure. The influence of air damping in rarefied air was investigated and the intrinsic damping mechanisms were determined in high vacuum (p<0.05 Pa). After excluding a variety of possible damping factors, the dominant intrinsic dissipation mechanism of the single-clamped microbeams was understood to be the material damping with maximum quality factors (Q) of around 70 at 20 °C. Quality factors of up to 720 at 20 °C were measured for stringlike double-clamped microbeams, which suggest a different intrinsic damping mechanism than material loss. It is shown that internal damping mechanisms due to flexure a...

Thermomechanical Analysis of Elastoplastic Bodies in a Sliding Spherical Contact and the Effects of Sliding Speed, Heat Partition, and Thermal Softening

Abstract: A thermomechanical analysis of elasto-plastic bodies is a necessary step toward the understanding of tribological behaviors of machine components subjected to both mechanical loading and frictional heating. A three-dimensional thermoelastoplastic contact model for counterformal bodies has been developed, which takes into account steady state heat flux, temperature-dependent strain hardening behavior, and interaction of mechanical and thermal loads. The fast Fourier transform and conjugate gradient. method are the underlying numerical algorithms used in this model. Sliding of a half-space over a stationary sphere is simulated with this model. The friction-induced heat is partitioned into two bodies based on surface temperature distributions. In the simulation, the sphere is considered to be fully thermoelastoplastic, while the half-space is treated to be thermoelastic. Simulation results include surface pressure, temperature rise, and subsurface stress and plastic strain fields. The paper also studies the influences of sliding speed and thermal softening on contact behaviors for sliding speed ranging three orders of magnitude.

High mechanical Q-factor measurements on silicon bulk samples

Abstract: Future gravitational wave detectors will be limited by different kinds of noise. Thermal noise from the coatings and the substrate material will be a serious noise contribution within the detection band of these detectors. Cooling and the use of a high mechanical Q-factor material as a substrate material will reduce the thermal noise contribution from the substrates. Silicon is one of the most interesting materials for a third generation cryogenic detector. Due to the fact that the coefficient of thermal expansion vanishes at 18 and 125 K the thermoelastic contribution to the thermal noise will disappear. We present a systematic analysis of the mechanical Q-factor at low temperatures between 5 and 300 K on bulk silicon (100) samples which are boron doped. The thickness of the cylindrical samples is varied between 6, 12, 24, and 75mm with a constant diameter of 3 inches. For the 75mm substrate a comparison between the (100) and the (111) orientation is presented. In order to obtain the mechanical Q-factor a ring-down measurement is performed. Thus, the substrate is excited to resonant vibrations by means of an electrostatic driving plate and the subsequent ring-down is recorded using a Michelson-like interferometer. The substrate itself is suspended as a pendulum by means of a tungsten wire loop. All measurements are carried out in a special cryostat which provides a temperature stability of better than 0.1K between 5 and 300K during the experiment. The influence of the suspension on the measurements is experimentally investigated and discussed. At 5.8K a highest Q-factor of 4.5 ? 108 was achieved for the 14.9 kHz mode of a silicon (100) substrate with a diameter of 3 inches and a thickness of 12 mm.

Thermoelastic Stress Analysis

Abstract: In this chapter an outline of the theoretical foundations for the experimental technique of thermoelastic stress analysis is presented, followed by a description of the equipment, test materials, and methods required to perform an analysis. Thermoelastic stress analysis is a technique by which maps of a linear combination of the in-plane surface stresses of a component are obtained by measuring the surface temperature changes induced by time-varying stress/strain distributions using a sensitive infrared detector. Experimental considerations relating to issues such as shielding from background radiation, edge effects, motion compensation, detector setup, calibration, and data interpretation are discussed. The potential of the technique is illustrated using a number of examples that involve isotropic as well as orthotropic materials, fracture mechanics, separation of component stresses, and vibration analysis. Applications of the method to situations involving residual stresses, elevated temperatures, and variable amplitude loading are also considered.

Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors

Abstract: Preliminary.- A One-dimensional Nonlinear Viscous and Heat-conductive Real Gas.- A One-dimensional Polytropic Viscous and Heat-conductive Gas.- A Polytropic Ideal Gas in Bounded Annular Domains in .- A Polytropic Viscous Gas with Cylinder Symmetry in .- One-dimensional Nonlinear Thermoviscoelasticity.- A Nonlinear One-dimensional Thermoelastic System with a Thermal Memory.- One-dimensional Thermoelastic Equations of Hyperbolic Type.- Blow-up for the Cauchy Problem in Nonlinear One-dimensional Thermoelasticity.- Large-Time Behavior of Energy in Multi-Dimensional Elasticity.

Infrared Image Processing for the Calorimetric Analysis of Fatigue Phenomena

Abstract: This paper presents an infrared image processing procedure that was developed to study calorific effects accompanying material fatigue. This method enables us to separately estimate patterns of thermoelastic and dissipative sources. Heat sources were estimated on the basis of partial derivative operators present in a local form of the heat equation by using a set of approximation functions that locally fits the temperature field and takes the spectral properties of the sought sources into account. Numerical examples were used to check the validity of the method and to highlight its capabilities along with its limits. The paper concludes with examples of thermal image processing extracted from fatigue tests performed on a dual-phase steel. The coupling sources were compared to the theoretical predictions induced by a basic thermoelastic model, while the heterogeneous character of the fatigue development was highlighted in terms of dissipation sources.

An accelerated FFT algorithm for thermoelastic and non-linear composites

Abstract: A fast numerical algorithm to compute the local and overall responses of non-linear composite materials is developed. This alternative formulation allows us to improve the convergence of the existing method of Moulinec and Suquet (e.g. Comput. Meth. Appl. Mech. Eng. 1998; 157(1–2):69–94). In the present method, a non-linear elastic (or conducting) material is replaced by infinitely many locally linear thermoelastic materials with moduli that depend on the values of the local fields. This makes it possible to use the advantages of an algorithm developed by Eyre and Milton (Eur. Phys. J. Appl. Phys. 1999; 6(1):41–47), which has faster convergence. The method is applied to compute the local fields as well as the effective response of non-linear conducting and elastic periodic composites. Copyright © 2008 John Wiley & Sons, Ltd.

Local energy analysis of high-cycle fatigue using digital image correlation and infrared thermography

Abstract: This paper presents the first results provided by an experimental set-up developed to estimate locally the terms of the energy balance associated with the high-cycle fatigue (HCF) of DP 600 steel. The experimental approach involves two quantitative imaging techniques: digital image correlation and infrared thermography. First, a variational method is used to derive stress fields from the displacement fields. Patterns of deformation energy per cycle can then be determined on the basis of stress and strain data. Second, a local form of the heat equation is used to derive separately the thermoelastic and dissipative sources accompanying HCF. Energy balances show that around 50 per cent of the deformation energy associated with the mechanical hysteresis loop is dissipated while the rest corresponds to stored energy variations.

A Uniform Optimum Material Based Model for Concurrent Optimization of Thermoelastic Structures and Materials

Abstract: This paper presents an optimization technique for structures composed of uniform cellular materials in macro scale. The optimization aims at to obtain optimal configurations of macro scale structures and microstructures of material under certain mechanical and thermal loads with specific base material volume. A concurrent topology optimization me- thod is proposed for structures and materials to minimize compliance of thermoelastic structures. In this method macro and micro densities are introduced as the design variables for structure and material microstructure independently. Penalization approaches are adopted at both scales to ensure clear topologies, i.e. SIMP (Solid Isotropic Material Penalization) in micro- scale and PAMP (Porous Anisotropic Material Penalization) in macro-scale. Optimizations in two scales are integrated into one system with homogenization theory and the distribution of base material between two scales can be decided automati- cally by the optimization model. Microstructure of materials is assumed to be uniform at macro scale to reduce manufactur- ing cost. The proposed method and computational model are validated by the numerical experiments. The effects of tem- perature differential, volume of base material, numerical parameters on the optimum results are also discussed. At last, for cases in which both mechanical and thermal loads apply, the configuration of porous material can help to reduce the system compliance.