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An approach for solving the plane nonaxisymmetric thermoelasticity problems in multilayer cylinders is suggested from the single-solid standpoint, which implies considering a multilayer structure as a single unity with a step-wise variation of material properties. The direct integration method was used to the advantage of our approach by applying toward the compatibility equation in terms of strains instead of the one in terms of stresses. As a result, the governing equation is derived without involving generalized derivatives by the radial coordinate and then reduced to an integral equation of the second kind. Using the resolvent-kernel for solving the latter equation, the thermal stresses are computed as the Fourier series whose constituents are explicitly determined by the corresponding constituents of the thermal loading. [ABSTRACT FROM AUTHOR]

This article enlightens the two-dimensional (2D) isotropic micro-polar thermoelastic problem of the three-phase-lag (3PHL) model and heat conduction equation is formulated in the context of memory-dependent derivative (MDD). The equations are converted into the domain of the Laplace transform vector matrix differential equation form and solved by using the eigenvalue technique. To obtain an analytical solution of displacement, temperature, and stress components Silicon material properties are used. Inversion of the Laplace transform with Fourier series expansion technique is used to obtain the numerical solution. For obtaining graphical results Mathematica software is used. For the purpose of exhibiting the beauty of MDD in the present model comparisons are made between the time delay parameters and kernel functions (constant, linear, and non-linear kernels), respectively, over the micro-polar panel. The results obtained have a valuable impact on structural analysis, especially in the design of rotating machinery structures using accurate material properties. [ABSTRACT FROM AUTHOR]

This manuscript aims to research the thermal buckling of saturated thick (Timoshenko) nanobeams under different boundary conditions using Fourier sine and cosine series for the first time. The equation of motion and related boundary conditions are derived by using the kinematic relations of shear deformation (Timoshenko beam) theory to contain the shear effect. Consequently, the rotary inertia and transverse shear strain are considered through the mathematical analysis. Fourier sine and cosine series are used to compute the critical buckling temperature of the thick saturated nanobeam with deformable boundaries. To check the validity of the presented method, the developed Fourier series method with Stokes' transformation is applied to validate the thermal buckling of rigidly supported thick nanobeam by giving the proper values to spring parameters. In particular, the presented analytical procedure can also be degenerated to the thin Euler-Bernoulli nanobeam by assigning proper value to shear correction factor. Influence of the deformable boundary conditions, small scale parameter and the saturated parameter (porosity coefficient) on the thermal buckling temperature are discussed in detail. The theoretical models and eigen-value formulation presented herein should also be served to solve the thermal stability response of different micro sized-structures with various temperature effects and supporting conditions. [ABSTRACT FROM AUTHOR]

Thermoelastic damping (TED) has been confirmed as an intrinsic energy loss and determines the upper limit of the quality factor of micro/nanoelectromechanical system (M/NEMS) resonators. A framework for determining the TED in the full clamped (C-C-C-C), clamped-free-clamped-free (C-F-C-F), and cantilever (C-F-F-F) rectangular microplate resonators operating in the fundamental mode by considering three-dimensional heat conduction in conjunction with modified couple stress theory (MCST) is proposed in this article. Then by using Rayleigh's method, three analytical models expressed by Fourier series for TED are derived, respectively. The difference between the present TED model and the previous one-dimensional (1-D) MCST model and 3-D classical model are comprehensively investigated. The comparison results indicate that the size effect on TED decreases to be ignorable as the thickness increases to h/l ≥ 50. In the case of h/l ≤ 50, the size effect cannot be ignored. The corresponding critical thicknesses for TED peaks are independent of the size effect. TED behaviors vary significantly under different structural support types. [ABSTRACT FROM AUTHOR]

Closed-form expressions for temperatures and elastic thermal stresses in an infinite hollow two-material compound cylinder subject to steady-periodic sinusoidal ambient temperatures are presented, taking finite heat transfer coefficients into account. The fluctuating temperatures and stresses in the cylinder are expressed in terms of complex-valued modified Bessel functions under the assumption of temperature-independent material properties. Transient thermal loads composed of linear temperature ramps are expressed as Fourier series, and studied by the presented method. In order to verify the analytic results, examples involving sinusoidal and linear loads are examined by finite element calculations. [ABSTRACT FROM AUTHOR]

In this article, a three dimensional multilayered annular disk with internal heat generation under unsteady temperature distribution is considered. Finite integral transform method is used to eliminate the partial derivatives with respect to r, while Fourier series and Fourier transform are used to deal with the variables θ and z, respectively. Exact solution for the temperature distribution is obtained. The thermal bending moments, thermal deflection and the resulting thermal stresses are obtained and analyzed. The results obtained in series form are numerically evaluated and analyzed by using graphical illustrations. [ABSTRACT FROM AUTHOR]

Based on theory of piezoelectricity and using generalized coupled thermoelasticity, transient response of a simply supported functionally graded material rectangular plate embedded in sensor and actuator piezoelectric layers under applied electric field and thermal shock is studied. Thermoelastic properties of the plate vary continuously along the thickness direction according to exponential functions and Poisson ratio is assumed to be constant. Applying Fourier series state space technique to the basic coupled thermoelastic differential equations results in the ordinary differential equations which are solved analytically by using Laplace transform. Validation of the present approach is assessed by comparing the numerical results with the available results in literature. In parametric study, effect of the relaxation time, applied voltage and temperature and time history of the thermoelastic response of FGM plate attached to piezoelectric layers are investigated. [ABSTRACT FROM AUTHOR]

The model of equations of thermo-viscoelasticity with fractional order heat transfer is constructed. Some fundamental theorems on the linear coupled and generalized theories of thermo-viscoelasticity can be easily obtained as special cases. The medium is assumed initially quiescent. Laplace and Fourier integral transforms are utilized. The method of the matrix exponential which constitutes the basis of the state–space approach of modern control theory is applied to the system of two-dimensional equations. The resulting formulation is applied to a thermal shock half-space problem. The inversion process for Fourier and Laplace transforms is carried out using numerical method based on Fourier series expansions. Numerical results are given and illustrated graphically for the problem considered. Comparisons are made with the results predicted by the coupled theory and generalized theory. The effect of the fractional order parameter on all the considered fields is examined. [ABSTRACT FROM AUTHOR]

Mechanical behavior of a viscoelastic cylindrical panel with various edge boundary conditions, made up of functionally graded material (FGM) and subjected to thermal or mechanical load is investigated. For cases of simply supported boundary conditions, analytical solution is presented through Fourier series expansion along the axial and circumferential coordinates as well as state space method along the radial coordinate. For nonsimply supported conditions, semi-analytical solution is performed using differential quadrature method instead of Fourier series solution. Governing differential equations are transformed to Laplace transform domain and using inverse Laplace transform, obtained solutions are converted to time domain. In the present work, relaxation modulus of FGM is supposed to be according to the Prony series with power law variations along the radial direction. Numerical comparison was made with the available published results to assess the validity of present technique. Effect of relaxation time constant, thickness to mid-radius ratio, edges boundary condition and outer surface temperature on stress and displacement fields are discussed. Besides, time history of stresses for different relaxation time constant and for various boundary conditions is presented. [ABSTRACT FROM AUTHOR]

Thermoelastic analysis of a functionally graded cylinder under nonsymmetric thermal and mechanical loadings subjected to uniform magnetic field is presented in this article. All material properties are assumed to be variable along the thickness direction based on the power law. Due to nonsymmetric thermal and mechanical loadings and boundary conditions, a two-dimensional displacement field along the radial and circumferential directions is assumed for our analysis. The complex form of Fourier series is used as the method of solution. The nonsymmetric analysis of this problem for Lorentz force leads to radial and circumferential force components. The obtained results of this analysis indicate that the different parameters of material and loading have a considerable effect on the nonsymmetric behavior of cylinder. [ABSTRACT FROM PUBLISHER]

The general solution of steady-state asymmetric mechanical and thermal stresses of a hollow thick cylinder made of fluid-saturated functionally graded porous piezoelectric materials based on two-dimensional equations of thermoelasticity is considered. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and the nonhomogeneous system of partial differential Navier equations, using the complex Fourier series and the power law functions method. The material properties are assumed to depend on the radial and circumferential variables and are expressed as power law functions along the radial and circumferential direction. [ABSTRACT FROM PUBLISHER]

The aim of this article is to study the gravitational response in an infinite, homogeneous, transversely isotropic thick plate. The upper surface of the plate is free from traction, and the surface temperature distribution is imposed on it. The lower surface of the plate is kept on a rigid base and is thermally insulated. The heat conduction equations in the presence of heat source are of hyperbolic types among them (i) without energy dissipation (GN-II model) and (ii) with energy dissipation (GN-III model). The Laplace–Fourier double-transform technique has been developed to solve the nondimensional coupled field equations. The physical quantities are obtained in the space–time domain using a numerical inversion method. Numerical calculations are performed for a thick plate made of magnesium (Mg) metal and have been depicted graphically to estimate the effect of gravity. The results for the isotropic material (Cu) and that of the transversely isotropic material (Mg) have been compared for both the models. [ABSTRACT FROM PUBLISHER]

The static behavior of a rotating cylindrical shell with surface bounded sensor and actuator in an axisymmetric hygrothermal condition is analyzed. The shell is simply supported and could be rested on an elastic foundation. The material properties of the shell and piezoelectric sensor and actuator are assumed to be functionally graded in the radial direction. Using the Fourier series expansion method through the longitudinal direction and the differential quadrature method (DQM) across the radial direction, and governing differential equations are solved. The validity of the present work was verified by comparisons with other published works. Numerical results are presented to illuminate the effects of key parameters on the responses of the hybrid shell. [ABSTRACT FROM AUTHOR]

In this article, the effect of two temperatures on an axially moving microbeam subjected to ramp-type heating is studied. The generalized thermoelasticity theory with one relaxation time model is used. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique, the inversion of Laplace transform is done numerically. Some comparisons have been shown in figures to present the effect of the temperature discrepancy and the transport speed on all the studied field quantities. Additional results across the thickness of the microbeam are presented graphically. [ABSTRACT FROM PUBLISHER]

In this study, we consider an infinitely long solid circular cylinder, whose lateral surface is traction free and subject to a known surrounding temperature. The problem is in the context of the fractional order thermoelasticity theory. The medium is assumed to be initially quiescent. The solution is obtained by a direct approach without the customary use of potential functions. Laplace transform technique is used to obtain the general solution for any set of boundary conditions. The inversion process is carried out using a numerical method based on Fourier series expansions. Numerical results are given and represented graphically. [ABSTRACT FROM AUTHOR]

Three general solutions of the three-dimensional steady-state governing equations of isotropic thermoelastic materials are derived in this article. For this object, two displacement functions are first introduced to simplify the govering equation. Then, using the differential operator theory, three general solutions can be expressed in terms of two functions, one satisfies a harmonic equation and the other satisfies a six-order partial differential equation. By virtue of Almansi's theorem, three general solutions can be further transferred to two general solutions, which are expressed in terms of three harmonic functions. At last, one more relatively completed general solution expressed in four harmonic functions is obtained by superposing the two general solutions. The proposed general solutions are simple in form and hence they may bring more convenience to certain boundary problems. As two examples, the fundamental solutions for both a point heat source in the interior of infinite thermoelastic body and a point heat source on the surface of semi-infinite thermoelastic body are presented by virtue of the obtained general solutions. [ABSTRACT FROM PUBLISHER]

In this article, the induced displacement, temperature and stress fields in an infinite non-homogeneous elastic medium with a spherical cavity are obtained in the context dual-phase-lag model. The surface of the cavity is stress free and is subjected to a thermal shock. The material is assumed to be elastic and has an inhomogeneity in the radial direction. The type of non-homogeneity is such that the elastic constants, thermal conductivity and density are proportional to the n th power of the radial distance. The solutions are obtained analytically employing the Laplace transforms technique. The numerical inversion of the transforms is carried out using Fourier series expansions. The stresses components, temperature and displacement are computed numerically and presented graphically. A comparison of the results is made for different theories. If the magnetic field is neglected, the results obtained are deduced as a special case from this study. [ABSTRACT FROM AUTHOR]

The present work is concerned with the solution of a problem on fractional order theory of thermoelasticity for an elastic medium. We investigate the thermoelastic interactions inside the medium by employing the fractional order theory of thermoelasticity, recently advocated by Sherief et al. (Int. J. Solids Struct., 47, 269-275, 2010). State space approach together with the Laplace transform technique is used to obtain the general solution of the problem. The general solution is then applied to three specific problems on an elastic half space, whose boundary is subjected to (i) a thermal shock (i.e., a step input in temperature and zero stress), (ii) a normal load (i.e., a step input in stress and zero temperature change) and (iii) a ramp type increase in temperature and zero stress. To observe the variations of displacement, temperature and stress inside the half-space we compute the numerical values of the field variables for a particular material by utilizing a numerical method of Laplace inversion. The effects of fractional order parameter on the variations of different fields inside the medium are analyzed graphically. [ABSTRACT FROM AUTHOR]

Based on theory of piezoelasticity, a functionally graded material (FGM) host plate under applied electric field and thermal or mechanical load is studied. The thermo-elastic constants of the plate vary continuously throughout the thickness direction in the form of an exponential function and the Poisson ratio is held constant. Analytical solutions for the temperature, stress and displacement fields for the plate with simply supported edges are derived by using the Fourier series expansions and state-space method. The theory is assessed by comparison with the previously published results. The effects of surface boundary conditions, gradient index, applied voltage, aspect ratio and length-to-thickness ratio on the behavior of the FGM plate are examined. [ABSTRACT FROM AUTHOR]

A hybrid numerical method of the Laplace transformation and the finite difference is applied to solve the transient heat transfer problem of a gun barrel, in which the interlayer thermal contact resistance between the steel cylinder and the chrome coating is taken into account in the boundary conditions. The general solutions of the governing equations are first solved in the transform domain. Then the inversion to the real domain is completed by the method of Fourier series technique. The transient distributions of temperature and thermal stresses for the gun barrel in the real domain are calculated numerically. [ABSTRACT FROM AUTHOR]

Analytical solutions for nonaxisymmetric, thermomechanical response of functionally graded hollow cylinders are obtained in this article. The hollow cylinders are assumed to be subjected to nonaxisymmetric mechanical and transient thermal loads. Properties of functionally graded material are considered as temperature-independent and continuously varying in radial direction. Employing complex Fourier series and Laplace transform techniques, analytical solutions of time-dependent temperature and thermomechanical stresses are obtained. Numerical values of temperature and stresses of a FGM hollow cylinder under assumed thermomechanical loads are presented in graphical form. [ABSTRACT FROM AUTHOR]

Distribution of Joule heating and the corresponding electromagnetic field in the vicinity of the crack in a thermo- and electro-conductive thin-walled shell carrying a non-stationary electrical current is investigated. Specifically, a circular cylindrical shell with one finitely long crack that is perpendicular to the current direction is considered. The crack is free of mechanical loads. The underlying boundary-value problem is addressed via the use of Fourier series expansion and the solution reduces to that of a singular integral equation with Hilbert-type singular kernel. The influence of the presence of crack, and the effect of non-stationarity of the current on the distribution of current and Joule heating in the shell are investigated and pertinent conclusions are drawn. The results are instrumental toward crack detection and active arrest of crack propagation in structures made of electro-conductive materials or aged structure components in aerospace industry. [ABSTRACT FROM AUTHOR]

The constitutive laws are obtained for the linear micropolar thermopiezoelectric/ piezomagnetic continuum with one relaxation time. The Maxwell–Cattaneo equation is expressed, as a constitutive law, in a form similar to the classical Fourier law. A new model is introduced, whereas the constitutive equations, not only the heat equation, are modified by the relaxation time. For this model a uniqueness theorem is proved. The constitutive laws, the equations of motion and the boundary conditions are obtained from a Hamilton's type variational principle and the Hamilton's principle is derived. [ABSTRACT FROM AUTHOR]

The analysis of axisymmetric mechanical and thermal stresses for a long hollow cylinder made of functionally graded material, as functions of radial and longitudinal directions, is developed. The material properties are graded along the radial direction according to power functions of radial direction. The temperature and Navier equations are solved analytically, using the generalized Bessel function and complex form of Fourier integral. A direct method of solution of Navier equations is presented, rather than potential functions method. [ABSTRACT FROM AUTHOR]

A geometrically nonlinear theory of magnetothermoelasticity of electroconductive anisotropic plates in a magnetic field is developed. In this context, the Kirchhoff hypothesis is adopted for the plate modeling and the geometrical nonlinearities are considered in the von Kármán sense. In addition, the assumptions related to the distribution of electric and magnetic field disturbances through the plate thickness as proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e., the ones by Faraday, Ampère, Ohm, Maxwell, and Lorentz), on the modified Fourier law of heat conduction, and elastokinetic field equations, the three-dimensional coupled problem is reduced to an equivalent two-dimensional one appropriate to the theory of plates. The theory developed herein enables one to investigate the interacting effects among the magnetic, thermal, and elastic fields in orthotropic thin plates. As a special case, the problem of the free vibration of simply supported plate strips immersed in a transversal magnetic field is considered. Effects of the directionality property of the constituent material, magnetic and temperature fields, and electric conductivity, as well as thermal expansion coefficients, on the characteristics of vibrational behavior of the plate strips are investigated. [ABSTRACT FROM AUTHOR]

Of concern is the steady-state thermoelastodynamics of a helix, whose material is governed by a coupled thermoelastic model. Heat transfer follows either a parabolic (Fourier) or a hyperbolic (Maxwell-Cattaneo) rule. As a result, in the one-dimensional setting, there are three coupled differential equations that lead to a fast (primarily axial) and a slow (primarily torsional) wave. Particularly for harmonic motions, we find that the thermal diffusivity and the relaxation time (of the Maxwell-Cattaneo model) have minor effects, whereas the thermoelastic coupling constant is dominant--it speeds up these waves--and overall there is damping. Additionally, we review and note differences from solutions of equations governing plane harmonic waves in a non-centrosymmetric, thermoelastic micropolar continuum in three dimensions. [ABSTRACT FROM AUTHOR]

This article examines the coupled thermoelasticity of an infinitely long, triple-layer annular cylinder subjected to a constant or time-dependent change in boundary temperatures. The governing equations, taking into account the thermomechanical coupling term, are expressed in terms of temperature increment and displacement. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The transient distributions of temperature increments and stresses in the real domain are presented numerically. Using a Fourier series technique, the inversion to the real domain is obtained, and no thermoelastic potentials are presented in the solution process. The results indicate that the coupling parameter can lead to a lagging effect in both the temperature and the stress distributions. The present method is also suitable for cases with different boundary conditions, such as time-dependent changes in surrounding temperature. [ABSTRACT FROM AUTHOR]