Thermally Induced Fields in Electroelastic Composite Materials: Average Fields and Effective Behavior

1994 ◽  
Vol 116 (2) ◽  
pp. 200-207 ◽  
Author(s):  
M. L. Dunn
Keyword(s):  
Thermal Expansion ◽  
Composite Materials ◽  
Mean Field Theory ◽  
Mean Field ◽  
Matrix Formulation ◽  
Two Phase ◽  
Thermally Induced ◽  
Electroelastic Fields ◽  
Wide Range ◽  
Effective Thermal Expansion

The average thermally induced electroelastic fields and the effective thermal expansion and pyroelectric coefficients of two-phase composite materials are obtained by applying the Mori-Tanaka mean-field theory to the coupled response of electroelastic composites through a field superposition scheme. Results are obtained for composites reinforced by ellipsoidal piezoelectric and pyroelectric inhomogeneities and thus are applicable to a wide range of microstructural geometry including lamina, spherical particle, and continuous fiber reinforcement. The results are shown to obey the recently derived Levin-type equations relating the effective thermal expansion and pyroelectric coefficients of a two-phase composite to those of the constituents and the electroelastic moduli of the constituents and the composite. The analysis is developed in a matrix formulation convenient for numerical computation in which the electroelastic (elastic, piezoelectric, and dielectric) moduli are represented by a 9×9 matrix and the thermal expansion and pyroelectric coefficients by a 9×1 column vector. A limited parametric study is performed to illustrate the interesting behavior exhibited by some typical composite microstructures. Finally, analytical predictions are examined in light of existing experimental observations.

Reduced Order Finite Element Modeling of Thermally Induced Bearing Loads in Machine Tool Spindles

1999 ◽  
Author(s):  
Alex O. Gibson ◽  
Jeffrey L. Stein
Keyword(s):  
Finite Element ◽  
Thermal Expansion ◽  
Machine Tool ◽  
Mechanical Load ◽  
Machining Process ◽  
Thermally Induced ◽  
Reduced Order ◽  
Wide Range ◽  
Bearing Load ◽  
Bearing Loads

Abstract Machine tool spindle bearings are subjected to a large range of axial and radial loads due to the machining process. Further the rotating spindle must be extremely stiff to minimize the cutting tool’s deflection. The high spindle stiffness is achieved by applying a mechanical load to the bearings, the preload. In fixed preload spindles the bearing loads tend to increase with increasing spindle speed due to thermal expansion and it is well established that these thermally induced loads can lead to premature bearing failure. A model of thermally induced bearing load in angular contact bearing spindles is developed that includes an axis-symmetric reduced order finite element model of the heat transfer and thermal expansion within the spindle’s housing and shaft and the bearing and shaft dynamics. Nodal reduction is used in the reduced order model to minimize the number of temperature states and the computational load. The reduced order model’s calculated temperature and bearing load values are shown to closely match experimentally measured values over a wide range of spindle speeds. The paper ends with a parameter variation study which predicts a dramatic decrease in the thermally induced bearing load when silicon nitride balls are substituted for steel balls.

scholarly journals Impact of the Nuclear Equation of State on the Stability of Hybrid Neutron Stars

Universe ◽  
2019 ◽  
Vol 5 (8) ◽  
pp. 186 ◽  
Author(s):  
Mateusz Cierniak ◽  
Tobias Fischer ◽  
Niels-Uwe Bastian ◽  
Thomas Klähn ◽  
Marc Salinas
Keyword(s):  
Equations Of State ◽  
Mean Field Theory ◽  
Mean Field ◽  
Type Model ◽  
Two Phase ◽  
Relativistic Mean Field ◽  
Nuclear Equation Of State ◽  
Hot Matter ◽  
The Stability ◽  
Quark Phase

We construct a set of equations of state (EoS) of dense and hot matter with a 1st order phase transition from a hadronic system to a deconfined quark matter state. In this two-phase approach, hadrons are described using the relativistic mean field theory with different parametrisations and the deconfined quark phase is modeled using vBag, a bag–type model extended to include vector interactions as well as a simultaneous onset of chiral symmetry restoration and deconfinement. This feature results in a non–trivial connection between the hadron and quark EoS, modifying the quark phase beyond its onset density. We find that this unique property has an impact on the predicted hybrid (quark core) neutron star mass–radius relations.

Re-Examination of A1 → L10 Ordering: Generalized Bragg-Williams Model with Elastic Relaxation

2011 ◽  
Vol 172-174 ◽  
pp. 608-617 ◽  
Author(s):  
William A. Soffa ◽  
David E. Laughlin ◽  
Nitin Singh
Keyword(s):  
Nearest Neighbor ◽  
Binary Solution ◽  
Mean Field ◽  
Lattice Relaxation ◽  
Two Phase ◽  
First Order ◽  
Tetragonal Lattice ◽  
Wide Range ◽  
Third Law Of Thermodynamics ◽  
The Mean

The tetragonal lattice relaxation has been included in the thermodynamics of the fcc→L10ordering to produce a first-order character of the transition within the mean field description of the binary solution energetics. In view of growing interest in such systems e.g. Fe-Pd and Co-Pt alloys, which display a wide range of applications relevant to current and futuristic technologies, the fcc→L10two-phase field is re-examined utilizing a generalized Bragg-Williams approach including first and second nearest neighbor interactions. The thermodynamic behavior is examined in the limit of T→0K and discussed in terms of the implications of the Third Law of Thermodynamics.

scholarly journals Sensitivity Analysis for the Spring-in of Composite Shells

2011 ◽  
Vol 20 (5) ◽  
pp. 096369351102000
Author(s):  
Chensong Dong
Keyword(s):  
Sensitivity Analysis ◽  
Thermal Expansion ◽  
Composite Materials ◽  
Design Of Experiments ◽  
Composite Shells ◽  
Dimensional Control ◽  
Surface Method ◽  
Wide Range ◽  
The Matrix ◽  
Dimensional Variation

Composite materials are a class of engineering materials widely used in a wide range of industries. Spring-in is a common dimensional variation of composite shells. It is well known that spring-in is dependent on many factors e.g. the constituent properties and coefficients of thermal expansion (CTE). A sensitivity analysis on the spring-in is presented in this paper. The sensitivities of the spring-in to the constituent properties and CTE are studied by the Design of Experiments (DOE) and the Response Surface Method (RSM). It is shown that the spring-in is predominantly sensitive to the Poisson's ratio of the matrix and the transverse CTE of the fibres. The results can be used to estimate the uncertainty of the spring-in from the uncertainties of the constituent properties and CTE, which is potentially useful for the design of composite products with improved dimensional control.

scholarly journals QUASI-HAMILTONIAN METHOD FOR COMPUTATION OF DECOHERENCE RATES

2011 ◽  
Vol 25 (16) ◽  
pp. 2115-2134 ◽  
Author(s):  
ROBERT JOYNT ◽  
DONG ZHOU ◽  
QIANG-HUA WANG
Keyword(s):  
Field Theory ◽  
Stochastic Process ◽  
Mean Field Theory ◽  
Mean Field ◽  
Hamiltonian Method ◽  
Single Qubit ◽  
Pure Dephasing ◽  
Wide Range ◽  
Two Level Systems ◽  
Arbitrary Quantum

We present a general formalism for the dissipative dynamics of an arbitrary quantum system in the presence of a classical stochastic process. It is applicable to a wide range of physical situations, and in particular it can be used for qubit arrays in the presence of classical two-level systems (TLS). In this formalism, all decoherence rates appear as eigenvalues of an evolution matrix. Thus the method is linear, and the close analogy to Hamiltonian systems opens up a toolbox of well-developed methods such as perturbation theory and mean-field theory. We apply the method to the problem of a single qubit in the presence of TLS that give rise to pure dephasing 1/f noise and solve this problem exactly.

Exact relations between the thermoelectroelastic moduli of heterogeneous materials

1993 ◽  
Vol 441 (1913) ◽  
pp. 549-557 ◽  
Keyword(s):  
Thermal Expansion ◽  
Heterogeneous Media ◽  
Composite Media ◽  
Two Phase ◽  
Elastic Fields ◽  
Piezoelectric Coupling ◽  
Effective Thermal Expansion ◽  
The Individual ◽  
Exact Relations ◽  
Pyroelectric Response

Exact relations are obtained between the effective thermoelectroelastic moduli of two-phase heterogeneous media and their corresponding isothermal effective electroelastic moduli. The relations are obtained by generalizing the results of V. M. Levin, and B. W. Rosen and Z. Hashin to the inherently anisotropic coupling between the electric and elastic fields in thermoelectroelastic composites. The explicit expressions that are obtained can be used to obtain the effective thermal expansion and pyroelectric coefficients of the composite when the effective electroelastic (elastic, piezoelectric and dielectric) moduli are known, either by theory or experiment. The results also provide a means to assess the internal consistency of any micromechanics model that is proposed to estimate the thermoelectroelastic and electroelastic moduli of the composite. It is verified that when piezoelectric coupling is absent, the expressions reduce to those of B. W. Rosen and Z. Hashin for thermoelastic composite media. Finally, the resulting exact relations are exploited to prove the interesting phenomena that two-phase heterogeneous media can exhibit a net pyroelectric response even though neither of the individual phases exhibits pyroelectricity.

Sign in / Sign up

Export Citation Format

Share Document