Showing papers on "Thermoelastic damping published in 2011"

Von Karman Evolution Equations: Well-posedness and Long Time Dynamics

Abstract: Well-Posedness.- Preliminaries.- Evolutionary Equations.- Von Karman Models with Rotational Forces.- Von Karman Equations Without Rotational Inertia.- Thermoelastic Plates.- Structural Acoustic Problems and Plates in a Potential Flow of Gas.- Long-Time Dynamics.- Attractors for Evolutionary Equations.- Long-Time Behavior of Second-Order Abstract Equations.- Plates with Internal Damping.- Plates with Boundary Damping.- Thermoelasticity.- Composite Wave-Plate Systems.- Inertial Manifolds for von Karman Plate Equations.

A model for seasonal changes in GPS positions and seismic wave speeds due to thermoelastic and hydrologic variations

Abstract: It is known that GPS time series contain a seasonal variation that is not due to tectonic motions, and it has recently been shown that crustal seismic velocities may also vary seasonally. In order to explain these changes, a number of hypotheses have been given, among which thermoelastic and hydrology-induced stresses and strains are leading candidates. Unfortunately, though, since a general framework does not exist for understanding such seasonal variations, it is currently not possible to quickly evaluate the plausibility of these hypotheses. To fill this gap in the literature, I generalize a two-dimensional thermoelastic strain model to provide an analytic solution for the displacements and wave speed changes due to either thermoelastic stresses or hydrologic loading, which consists of poroelastic stresses and purely elastic stresses. The thermoelastic model assumes a periodic surface temperature, and the hydrologic models similarly assume a periodic near-surface water load. Since all three models are two-dimensional and periodic, they are expected to only approximate any realistic scenario; but the models nonetheless provide a quantitative framework for estimating the effects of thermoelastic and hydrologic variations. Quantitative comparison between the models and observations is further complicated by the large uncertainty in some of the relevant parameters. Despite this uncertainty, though, I find that maximum realistic thermoelastic effects are unlikely to explain a large fraction of the observed annual variation in a typical GPS displacement time series or of the observed annual variations in seismic wave speeds in southern California. Hydrologic loading, on the other hand, may be able to explain a larger fraction of both the annual variations in displacements and seismic wave speeds. Neither model is likely to explain all of the seismic wave speed variations inferred from observations. However, more definitive conclusions cannot be made until the model parameters are better constrained.

Formulation of thermoelastic dissipative material behavior using GENERIC

Abstract: We show that the coupled balance equations for a large class of dissipative materials can be cast in the form of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling). In dissipative solids (generalized standard materials), the state of a material point is described by dissipative internal variables in addition to the elastic deformation and the temperature. The framework GENERIC allows for an efficient derivation of thermodynamically consistent coupled field equations, while revealing additional underlying physical structures, like the role of the free energy as the driving potential for reversible effects and the role of the free entropy (Massieu potential) as the driving potential for dissipative effects. Applications to large and small-strain thermoplasticity are given. Moreover, for the quasistatic case, where the deformation can be statically eliminated, we derive a generalized gradient structure for the internal variable and the temperature with a reduced entropy as driving functional.

Fractional order theory of a perfect conducting thermoelastic medium

Abstract: In this work, a new mathematical model of magneto-thermoelasticity theory is constructed in the context of a new consideration of heat conduction law with time-fractional order. This model is appli...

Clipped viscous damping with negative stiffness for semi-active cable damping

Abstract: This paper investigates numerically and experimentally clipped viscous damping with negative stiffness for semi-active cable damping. From simulations it is concluded that unclipped and clipped viscous damping with negative stiffness is equivalent to unclipped and clipped LQR. It is shown that optimized unclipped viscous damping with negative stiffness generates critical cable damping by an anti-node at the actuator position. The resulting curvature at the actuator position is larger than the curvature close to the anchors due to the disturbance forces which may lead to premature cable fatigue at the actuator position. Optimized clipped viscous damping with negative stiffness does not show this drawback, can be implemented using a semi-active damper and produces twice as much cable damping as optimal viscous damping. Close to the optimal tuning, it leads to approximately the same control force as optimal semi-active friction damping with negative stiffness, which explains the superior cable damping. The superior damping results from the negative stiffness that increases the damper motion. Clipped viscous damping with negative stiffness is validated on a strand cable with a magneto-rheological damper. The measured cable damping is twice that achieved by emulated viscous damping, which confirms the numerical results. A tuning rule for clipped viscous damping with negative stiffness of real cables with flexural rigidity is given.

Fractional Order Theory of Thermoelastic Diffusion

Abstract: In this work, a new theory of thermodiffusion in elastic solids is derived using the methodology of fractional calculus. The theories of coupled thermoelastic diffusion and of generalized thermoelastic diffusion problem with one relaxation time follow as limit cases. A variational theorem is then obtained for the governing equations. Finally, a uniqueness and reciprocity theorems for these equations are derived.

Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment

Abstract: Free vibration analysis of functionally graded (FG) thin-to-moderately thick annular plates subjected to thermal environment and supported on two-parameter elastic foundation is investigated. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The equations of motion and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the Hamilton’s principle based on the first order shear deformation theory (FSDT). The initial thermal stresses are obtained by solving the thermoelastic equilibrium equations. Differential quadrature method (DQM) as an efficient and accurate numerical tool is adopted to solve the thermoelastic equilibrium equations and the equations of motion. The formulations are validated by comparing the results in the limit cases with the available solutions in the literature for isotropic and FG circular and annular plates. The effects of the temperature rise, elastic foundation coefficients, the material graded index and different geometrical parameters on the frequency parameters of the FG annular plates are investigated. The new results can be used as benchmark solutions for future researches.

Theory of Two-Temperature Thermoelasticity without Energy Dissipation

Abstract: This paper deals with thermoelastic behavior without energy dissipation; it deals with linear theory of thermoelasticity. In particular, in this work, a new theory of generalized thermoelasticity has been constructed by taking into account two-temperature generalized thermoelasticity theory for a homogeneous and isotropic body without energy dissipation. The new theorem has been derived in the context of Green and Naghdi model of type II of linear thermoelasticity. Also, a general uniqueness theorem is proved for two-temperature generalized thermoelasticity without energy dissipation.

Two-Variable Refined Plate Theory for Thermoelastic Bending Analysis of Functionally Graded Sandwich Plates

Abstract: The thermoelastic bending analysis of functionally graded sandwich plates using the two-variable refined plate theory is presented in this paper Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions 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

Thermomechanics of shells undergoing phase transition

Abstract: The resultant, two-dimensional thermomechanics of shells undergoing diffusionless, displacive phase transitions of martensitic type of the shell material is developed. In particular, we extend the resultant surface entropy inequality by introducing two temperature fields on the shell base surface: the referential mean temperature and its deviation, with corresponding dual fields: the referential entropy and its deviation. Additionally, several extra surface fields related to the deviation fields are introduced to assure that the resultant surface entropy inequality be direct implication of the entropy inequality of continuum thermomechanics. The corresponding constitutive equations for thermoelastic and thermoviscoelastic shells of differential type are worked out. Within this formulation of shell thermomechanics, we also derive the thermodynamic continuity condition along the curvilinear phase interface and propose the kinetic equation allowing one to determine position and quasistatic motion of the interface relative to the base surface. The theoretical model is illustrated by two axisymmetric numerical examples of stretching and bending of the circular plate undergoing phase transition within the range of small deformations.

Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid

Abstract: The flexural vibration of viscoelastic carbon nanotubes (CNTs) conveying fluid and embedded in viscous fluid is investigated by the nonlocal Timoshenko beam model. The governing equations are developed by Hamilton's principle, including the effects of structural damping of the CNT, internal moving fluid, external viscous fluid, temperature change and nonlocal parameter. Applying Galerkin’s approach, the resulting equations are transformed into a set of eigenvalue equations. The validity of the present analysis is confirmed by comparing the results with those obtained in literature. The effects of the main parameters on the vibration characteristics of the CNT are also elucidated. Most results presented in the present investigation have been absent from the literature for the vibration and instability of the CNT conveying fluid.

Damping of materials and members in structures

Abstract: The state of a structure subject to oscillatory deformation can be described by the combination of kinetic and potential energy. In the case of real structures there is also an energy dissipative element as some of the energy is lost per deformation cycle. The energy dissipation is caused by material damping which basically depends on three factors: amplitude of stress, number of cycles and geometry. In the case of non-homogeneous stress distribution the geometry of the structure influences the vibration damping. In this paper the influence of the geometry will be investigated with special regard to the cross-section. The examinations can be executed experimentally, theoretically and by the help of computer programs using FEM. In most cases the main goal is to increase the damping of the structure.

Effects of axial and residual stresses on thermoelastic damping in capacitive micro-beam resonators

Abstract: This paper deals with effects of residual and axial stresses on thermoelastic damping (TED) in micro-beam resonators. Equations of coupled thermoelastic case for a capacitive micro-beam resonator have been governed using two dimensional non-Fourier heat conduction model based on continuum theory frame. A Galerkin based finite element formulation has been used to analyze TED for the first mode of vibration of the micro-beam resonator with both ends clamped and isothermal. Effect of axial stresses owing to stretching of the micro-beam on the TED ratio has been investigated. As results illustrate, this effect gets importance only when the resonator is vibrating about a large static deflection due to a bias DC voltage close to the pull-in voltage of the resonator, otherwise it can be neglected in calculations. Effect of compressive and tensile residual stresses has been also studied. The results show that compressive (tensile) residual stresses increase (decrease) the TED ratio considerably. The residual stresses effect has been also studied for various values of the micro-beam thicknesses. The results illustrate that the effect of residual stress on the TED ratio decreases by increasing the thickness of the micro-beam. The results show that, applying DC voltages near the pull-in voltage increases energy dissipation due to the TED considerably, therefore, there is a limitation for applied DC voltage for resonators, since residual stresses change the pull-in voltage of the resonator, hence, existing residual stresses can change the interval of the applied voltage limitation.

On the Two-Temperature Green–Naghdi Thermoelasticity Theories

Abstract: The constitutive laws for two-temperature Green–Naghdi theories are given. It is proved that the two-temperature thermoelasticity theory admits dissipation of energy and the theory of elasticity without energy dissipation is valid only when the two-temperatures coincide. The uniqueness and reciprocal theorems are proved for a linear anisotropic and inhomogeneous thermoelastic centro-symmetric solid in the frame of two-temperature Green–Naghdi theories. The convolutional variational principle is established for the two-temperature Green–Naghdi theory of type III. A continuous dependence result is given for an isotropic solid.

Effect of rotation on plane waves at the free surface of a fibre-reinforced thermoelastic half-space using the finite element method

Abstract: The propagation of plane waves in fibre-reinforced, rotating thermoelastic half-space proposed by Lord-Shulman is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the coupled theory and the theory of generalized thermoelasticity with one relaxation time in the presence and absence of rotation and reinforcement. It is found that the rotation has a significant effect and the reinforcement has great effect on the distribution of field quantities when the rotation is considered.

Generalized Magneto-thermoelasticity in a Fiber-Reinforced Anisotropic Half-Space

Abstract: The propagation of plane waves in a fiber-reinforced, anisotropic thermoelastic half-space proposed by Lord–Shulman under the effect of a magnetic field is discussed. The problem has been solved numerically using a finite element method. Numerical results for the temperature distribution, the displacement components, and the thermal stress are given and illustrated graphically. Comparisons are made with the results predicted by the theory of generalized thermoelasticity with one relaxation time for different values of time. It is found that the reinforcement has a great effect on the distribution of field quantities.

Nonlinear Reduced-Order Models for Thermoelastodynamic Response of Isotropic and Functionally Graded Panels

Abstract: The focus of this investigation is on the development and validation of thermoelastic reduced-order models for the geometrically nonlinear response and temperature of heated structures. The reduced-order modeling approach is based on a modal-type expansion of both displacements and temperatures in the undeformed, unheated configuration. A set of coupled nonlinear differential equations governing the time-varying generalized coordinates of the response and temperature expansion are derived from finite thermoelasticity using a Galerkin approach. Furthermore, the selection of the basis functions to be used in these reduced-order models is discussed, and the numerical evaluation of the model coefficients is addressed. This approach is first validated on an isotropic beam subjected to both thermal effects and external loads. The thermal effects are large enough to induce a significant buckling of the panel, while the time-varying loads lead to snap-throughs ranging in frequency from infrequent to continuous. Validation to a functionally graded material panel in similar conditions is then performed. In both cases, the reduced-order modeling predicted temperatures and responses are found to very closely match their full finite element counterparts.

On Generalized Magneto-thermoelastic Rayleigh Waves in a Granular Medium Under the Influence of a Gravity Field and Initial Stress

Abstract: In this paper, the influence of magnetic field, gravity field and initial stress on Rayleigh waves propagation in a granular medium under incremental thermal stresses and relaxation times is studied. The frequency equation of Rayleigh waves is obtained in the form of a determinant containing a term involving the coefficient of friction of a granular medium. Some special cases are obtained from this study. Analytically, from the results obtained, one may illustrate that the effect of relaxation times, gravity field, initial stress and magnetic field on Rayleigh wave velocity are very pronounced. It is found that the frequency equation of Rayleigh waves changes with respect to this friction. When the medium is an orthotropic and the magnetic field and friction coefficient vanish, the derived frequency equation reduces to that obtained by Abd-Alla and Ahmed. Relevant results from previous investigations are deduced as special cases of this study.

Thermoelastic Damping and Frequency Shift in Micro/Nanoscale Anisotropic Beams

Abstract: The governing equations of flexural vibrations in a transversely isotropic thermoelastic beam are derived in closed form based on Euler–Bernoulli theory. The out-of- plane vibrations have been studied under different beam dimensions and boundary conditions. The analytical expressions for thermoelastic damping and frequency shift of vibrations are obtained. The damping and frequency shift of beam vibrations significantly depend on thermal relaxation time and surface conditions at resonance. The expressions for displacement and temperature fields in the beam resonator are obtained. Some numerical results with help of MATLAB software have been computed and presented graphically for silicon material beams.

On decay and blow-up of the solution for a viscoelastic wave equation with boundary damping and source terms

Abstract: In this paper we consider the decay and blow-up properties of a viscoelastic wave equation with boundary damping and source terms. We first extend the decay result (for the case of linear damping) obtained by Lu et al. (On a viscoelastic equation with nonlinear boundary damping and source terms: Global existence and decay of the solution, Nonlinear Analysis: Real World Applications 12 (1) (2011), 295–303) to the nonlinear damping case under weaker assumption on the relaxation function g ( t ) . Then, we give an exponential decay result without the relation between g ′ ( t ) and g ( t ) for the linear damping case, provided that ‖ g ‖ L 1 ( 0 , ∞ ) is small enough. Finally, we establish two blow-up results: one is for certain solutions with nonpositive initial energy as well as positive initial energy for both the linear and nonlinear damping cases, the other is for certain solutions with arbitrarily positive initial energy for the linear damping case.

Thermoelastic buckling behavior of thick functionally graded rectangular plates

Abstract: Thermoelastic buckling behavior of thick rectangular plate made of functionally graded materials is investigated in this article. The material properties of the plate are assumed to vary continuously through the thickness of the plate according to a power-law distribution. Three types of thermal loading as uniform temperature raise, nonlinear and linear temperature distribution through the thickness of plate are considered. The coupled governing stability equations are derived based on the Reddy’s higher-order shear deformation plate theory using the energy method. The resulted stability equations are decoupled and solved analytically for the functionally graded rectangular plates with two opposite edges simply supported subjected to different types of thermal loading. A comparison of the present results with those available in the literature is carried out to establish the accuracy of the presented analytical method. The influences of power of functionally graded material, plate thickness, aspect ratio, thermal loading conditions and boundary conditions on the critical buckling temperature of aluminum/alumina functionally graded rectangular plates are investigated and discussed in detail. The critical buckling temperatures of thick functionally graded rectangular plates with various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.

A two-dimensional problem for a fibre-reinforced anisotropic thermoelastic half-space with energy dissipation

Abstract: The theory of thermoelasticity with energy dissipation is employed to study plane waves in a fibre-reinforced anisotropic thermoelastic half-space. We apply a thermal shock on the surface of the half-space which is taken to be traction free. The problem is solved numerically using a finite element method. Moreover, the numerical solutions of the non-dimensional governing partial differential equations of the problem are shown graphically. Comparisons are made with the results predicted by Green–Naghdi theory of the two types (GNII without energy dissipation) and (GNIII with energy dissipation). We found that the reinforcement has great effect on the distribution of field quantities. Results carried out in this paper can be used to design various fibre-reinforced anisotropic thermoelastic elements under thermal load to meet special engineering requirements.