Dynamic Problems of Thermoelasticity

Nowacki, Witold; Francis, Philip H.; Hetnarski, R. B.; Florence, A. L.

doi:10.1115/1.3424081

Cited by 135 publications

(201 citation statements)

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“…[2,3]. Here u is the displacement vector, θ the scalar field measuring the local absolute deviation from the ambient temperature T 0 , ω the angular frequency, ∇ the gradient operator, ρ the material density, κ the thermal conductivity and C the specific heat at constant strain.…”

Section: Governing Equationsmentioning

confidence: 99%

The Quasi-Adiabatic Approximation for Coupled Thermoelasticity

Pichugin¹

2010

AIP Conference Proceedings

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Abstract. The equations of coupled thermoelasticity are considered in the case of stationary vibrations. The dimensional and order-of-magnitude analysis of the parameters occurring within these equations prompts the introduction of the new non-dimensionalisation scheme, highlighting the nearly-adiabatic nature of the resulting motions. The departure from the purely adiabatic regime is characterised by a natural small parameter, proportional to the ratio of the mean free path of the thermal phonons to the vibration wavelength. When the governing equations are expanded in terms of the small parameter, one can formulate an equivalent "quasi-adiabatic" system of the equations of ordinary elasticity with frequency-dependent modulae, characterising the thermoelastic dissipation. Unfortunately, this model lacks the degrees of freedom necessary to satisfy boundary condition(s) for the temperature. Thus, we also derive a complementary boundary layer solution and show that to the leading order it is described by thermoelastic equations in the quasi-static approximation. Further simplifications are possible for purely dilatational motions; we illustrate this point by solving a model thermoelastic problem in 1D.

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Section: Governing Equationsmentioning

confidence: 99%

The Quasi-Adiabatic Approximation for Coupled Thermoelasticity

Pichugin¹

2010

AIP Conference Proceedings

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“…A comma followed by index j indicates partial differentiation with respect to the position x j of a material particle, and a repeated index implies summation over the range of the index. The constitutive equations of a linear thermopiezoelectric medium are [31] …”

Section: Formulation Of the Problemmentioning

confidence: 99%

Generalized Plane Strain Thermopiezoelectric Analysis of Multilayered Plates

Vel

Batra

2003

Journal of Thermal Stresses

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The generalized plane strain thermopiezoelectric deformations of laminated thick plates are analyzed using the Eshelby-Stroh formalism. The laminated plate consists of homogeneous laminae of arbitrary thicknesses. The three-dimensional equations of linear anisotropic thermopiezoelectricity simplified to the case of generalized plane strain deformations are exactly satisfied at every point in the body. The analytical solution is in terms of an infinite series. The continuity conditions at the interfaces and boundary conditions at the top and bottom surfaces and edges are used to determine coefficients in the series. The formulation admits different thermal, electrical, and mechanical boundary conditions at the edges of each lamina and is applicable to thick and thin laminated plates. Laminated plates containing piezoelectric laminae poled either in the thickness direction or in the axial direction are analyzed, and results are presented for plates with edges either rigidly clamped, simply supported, or traction-free.Smart structures, consisting of piezoelectric materials integrated with structural systems, have found widespread use in engineering applications. Piezoelectric materials are capable of altering the structure's response through sensing, actuation, and control. They exhibit two basic electromechanical phenomena that have led to their use as sensors and actuators in the control of structural systems. In sensor applications, an applied mechanical strain induces an electric potential in the material due to the direct piezoelectric effect; whereas in actuator applications, an applied electric field causes the material to deform. Of the 21 crystal classes that

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“…Thermal loads introduce stresses due to thermal expansion, which lead to changes in the modal properties. The basic problems of the thermoelastic vibrations can be found in the books of Boley and Weiner [10], Nowacki [11] and Thorton [12].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a reduced multimodal Timoshenko beam subjected to thermal and mechanical loadings

2014

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Large amplitude vibrations of a Timoshenko beam under an influence of temperature are analysed in this paper. In the considered model the temperature increases instantly and the heat is uniformly distributed along the beams length and crosssection. The mathematical model, represented by partial differential equations takes into account thermal and mechanical loadings. Next, the problem is reduced by means of the Galerkin method, considering the first three natural vibration modes of a simply supported beam in the both ends. The influence of the temperature on amplitudes and localisation of the resonance zones and stability of the solutions is studied numerically and analytically by the multiple time scale method. The bifurcation points, existence of unstable lobes and transition from regular to chaotic oscillations are shown.

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Dynamic Problems of Thermoelasticity

Cited by 135 publications

References 0 publications

The Quasi-Adiabatic Approximation for Coupled Thermoelasticity

The Quasi-Adiabatic Approximation for Coupled Thermoelasticity

Generalized Plane Strain Thermopiezoelectric Analysis of Multilayered Plates

Nonlinear dynamics of a reduced multimodal Timoshenko beam subjected to thermal and mechanical loadings

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