Nonlinear Temperature Distribution Research Articles

Thermoelastic free vibration of rotating pretwisted porous p-FGM, e-FGM, and s-FGM conical shells in nonlinear temperature distribution

The free vibration response of rotating pretwisted functionally graded (FG) conical shells in nonlinear thermal conditions is investigated using a finite element approach with the purpose of application in turbomachinery blades. With the aid of power, exponential, and sigmoid laws, the pretwisted conical shell is functionally graded in its transverse direction. The distribution of both even and uneven porosity is considered. The one-dimensional Fourier heat conduction equation is used to assess the nonlinear temperature distribution across the thickness of the FG conical shell. Lagrange’s equation is used to obtain the dynamic equation of motion of the rotating pretwisted FG conical shell. The proposed finite element model employs an eight-noded isoparametric shell element with five degrees of freedom per node. The effect of several factors, including porosity, temperature, twist angle, and rotational speed on the free vibration response of the FG porous conical shell has been investigated. The findings reveal that the porosity volume fraction has a significant influence on the natural frequency. The nonlinear temperature difference and pretwist angle both cause stiffness reduction to the FG conical shell upon increasing, whereas the presence of rotational speed inducts geometrical stiffness resulting in centrifugal stiffening.

Interfacial failure behavior of longitudinally coupled slab tracks restored by interface adhesives

Longitudinally coupled slab tracks (LCSTs), one of the most popular slab track types, have experienced severe damage like interfacial debonding and gapping over the past few years. Although adhesives have been used to restore the separated interfaces of LCSTs, the high-temperature environment still poses a great challenge to the repaired tracks. Therefore, this paper presents a numerical investigation on the interfacial failure behavior of LCSTs restored by interface adhesives under high-temperature load. Firstly, the constitutive relationships and the damage behavior of the original and the restored interfaces between the track slabs and mortar layers was modelled based on the cohesive zone theory. Secondly, a finite element model of the LCST was established in which the nonlinear mechanical properties of the interfaces and the materials, as well as the nonlinear distribution of track temperature were considered. Last but not least, damage evolution law of interfaces restored by adhesives, the effects of adhesive-use area, and the performance of adhesives on interfacial debonding and gapping under high-temperature loads were studied. The following conclusions are drawn: (1) After adopting the adhesive, the maximum vertical displacement of track slabs can be reduced by 35.2%. (2) An adhesive-use depth above 500 mm on both sides of the lateral path is recommended to lower the height of interfacial gaps to below 1 mm. (3) In addition to using adhesives, keeping the T-shaped joints in a good condition also plays a crucial role in mitigating interfacial gapping. (4) The distribution of the interfacial damage index D on the lateral path of the track shows a significant asymmetry when adhesives are only used on one side of the lateral path.

Free vibration analysis of FGM spherical and elliptical shells under nonlinear thermal environments

The thermo-mechanical effects of the free vibration of functionally graded (FG) spherical and elliptical shells under nonlinear temperature distributions (NTD) are investigated. The geometries of the FG spherical and elliptical shells are expressed in terms of the surface fundamental form, and the displacement function is derived based on higher-order shear deformation theory (HSDT). Temperature-dependent (TD) material and heat conduction are investigated based on Voigt's micromechanical model. The equation of motion of the thermo-elastic FG shells is formulated using the classical Hamilton's principle. Numerical results are obtained using the finite element method with quadrilateral Lagrangian isoparametric elements. A comparison of the results for the free vibration of FG shells based on the FSDT and HSDT approaches is presented. The first fundamental mode is the axisymmetric mode for the circular plate and oblate shell, but the results are otherwise for spherical and prolate shells. The torsional mode occurs in the seventh mode within the first ten vibrational modes for the prolate shell. In addition, the frequency parameter in the torsional mode is independent of the different support conditions. Parametric studies show that the non-dimensional frequency parameters of the FG shells decrease quickly, then slowly, as the volume fraction index increases. Finally, the frequency parameters decrease when the temperature at the top of the FG shell surface increases.

Analysis of temperature-dependent thermal conductivity and fin efficiency: Direct Akbari-Ganji method

The vast majority of engineering issues, particularly heat transport equations, have a non-linear form. The analytical solution of temperature distribution, fin effectiveness, and fin efficiency of straight convective fins that transport heat with temperature-dependent thermal conductivity convection is derived in this work using the Direct Akbari-Ganji method (DAGM). DAGM is an effective methodology that is very simple and takes less time to solve non-linear temperature distribution fin problems. In the present investigation, Direct Akbari-Ganji technique offers desirable solutions to heat transfer problems. The round-off error is smaller compared to other methods. For the purpose of calibrating the error accuracy of the suggested direct technique, this result is compared with the numerical and earlier solution. The outcomes show that the DAGM for heat transfer equations in engineering situations has excellent validity and considerable promise. Finally, it is clear that when the thermo-geometric fin parameter increases, so does the fin efficiency. The homogeneity of the fin is due to the variable thermal conductivity. Four convection conditions with constant coefficients, growing and decaying convection coefficient with fin temperature are discussed.

Thermoelastic free vibration analysis of functionally graded conical shell based on trigonometric higher-order shear deformation theory

The fundamental frequency of a rotating cantilevered porous functionally graded (FG) twisted conical shell with varying thickness along the longitudinal direction is calculated using a trigonometric higher-order shear deformation theory under thermal loading. Finite element method is employed for this purpose. The shell is discretized using eight-noded isoparametric shell elements with seven degrees of freedom per node. Using a simple power law across the transverse direction, the temperature-dependent material properties of the FG shell are determined. The nonlinear temperature distribution across the thickness direction is calculated using the one-dimensional Fourier heat conduction equation. The dynamic equation of motion is derived using Lagrange's equation. Finally, a parametric investigation of the effects of taper ratio, porosity, pretwist angle, temperature, and rotational speed on the fundamental frequency of the porous FG rotating conical shell is performed. It is also discussed how such characteristics affect mode shapes.

Free vibration response of rotating pretwisted porous exponential and sigmoid functionally graded conical shells in thermal environment

A finite element method is used to analyze the free vibration of rotating functionally graded (FG) porous conical shell in thermal environment. Exponential and sigmoid laws are used for grading the FG conical shell in the presence of even and uneven porosity distributions. The one-dimensional Fourier heat conduction equation is used to calculate the nonlinear temperature distribution across the thickness of the shell. The parametric studies reveal that the porosity volume fraction has a significant impact on natural frequency. Centrifugal stiffening, which manifests as a geometrical stiffness matrix, causes rotational speed to enhance the natural frequency of the FG shell.

Thermoelastic free vibration of rotating tapered porous functionally graded conical shell based on non-polynomial higher-order shear deformation theory

This study uses a non-polynomial higher-order shear deformation theory to calculate the fundamental frequency of a rotating cantilevered porous functionally graded (FG) conical shell with variable thickness. Eight noded isoparametric shell elements having seven degrees of freedom per node are used to discretize the shell. Utilizing a simple power law, the temperature-dependent material characteristics of the FG conical shell are determined. The one-dimensional Fourier heat conduction equation is used to obtain the nonlinear temperature distribution. Lagrange’s equation is used to derive the dynamic equation of motion. Finally, a parametric study is presented.

Marangoni instability of an evaporating binary mixture droplet

Evaporation of a binary mixture droplet (BMD) is a common natural phenomenon and widely applied in many industrial fields. For the case of a sessile BMD being the only contact-line pinning throughout an entire evaporation, a theoretical model describing the evaporating dynamics is established when considering the comprehensive effect of evaporative cooling, the thermal Marangoni effect, the solutal Marangoni effect, the convection effect, and the Stefan flow. The dynamics of a binary ethanol–water droplet on a heated substrate is simulated using a cylindrical coordinate system. The reasons for Marangoni instability-driven flow (MIF) are discussed, and the influence of initial ethanol concentration and substrate heating temperature are examined. An evaporating BMD first forms a MIF at the contact line and quickly affects the whole droplet. Under the influence of the Marangoni instability, the BMD presents a complex internal flow structure with multiple-vortex and nonlinear temperature and ethanol concentration distributions. The positive feedback induced by vortices and the nonlinear distribution of concentration and temperature promotes the development of a MIF. At low initial ethanol concentrations, the MIF loses its driving force and turns into a stable counterclockwise single-vortex flow as ethanol evaporates completely. However, at high initial ethanol concentrations, the MIF exists in the entire evaporation. Increasing ethanol concentration and substrate heating temperature can delay the appearance of the MIF; ethanol concentration affects the MIF duration time, and heating temperature alters the MIF intensity. To enhance flow intensity and mass transfer of BMDs, the temperature difference should first be increased, followed by increased ethanol concentration.

Study of Seebeck coefficient in organic materials under nonlinear temperature distributions

Environmental issues and energy crisis are huge challenges in today’s world. As one of green energy sources, thermoelectric (TE) materials have attracted tremendous attraction for they can convert free heat energy to electricity. In our work, through the master equation (ME) method, we studied the characteristics of charge transport in the organic material under nonlinear temperature distributions. Under each temperature distribution, Seebeck coefficient is analyzed with different factors such as the temperature, the reorganization energy and the energetic disorder strength. Especially, Seebeck coefficient of different temperature distributions showed different performances when the reorganization energy changes. Our studies will be helpful to look further into TE properties of organic materials and improve the application of TE devices.

Nonlinear thermal stress analysis of functionally graded spherical pressure vessels

In this study, nonlinear analysis of functionally graded spherical pressure vessels composed of metal/ceramic mixture for both high strength and high thermal resistance is discussed. The originality of this study is to think that all material properties change with temperature as well as thickness by using a realistic and physically meaningful graded material model with the Halpin–Tsai homogenization scheme. These conditions results in nonlinear differential equation that may not be solved with conventional methods. The nonlinear temperature and stress distributions of the functionally graded sphere under the thermo-mechanical loads are determined by using the pseudospectral Chebyshev method. Some stress results based on the assumptions of temperature-dependencies and temperature-independencies of the material properties are derived and effects of various parameters on the thermoelasticity are studied. Besides, elastic limits based on the von Mises’ yield criterion are also discussed according to whether the material properties are dependent on temperature or not. Benchmark linear examples are used to check the accuracy of the method. The nonlinear solutions are verified with the finite element method using the ANSYS package program.

Steady-state and transient vibration analysis of a thermally loaded power law-based functionally graded rotor system with induced porosities

The dynamic analysis of a power law-based functionally graded (FG) rotor-bearing system with induced porosities for non-uniform porosity distributions has been performed using the finite element method. A novel porous rotor element considering the effects of transverse shear deformation, gyroscopic moments, translational and rotational inertial has been developed for non-uniform porosity distributions based on the Timoshenko beam theory. Material properties are graded based on the power law along the radial direction of the FG shaft. The nonlinear temperature distribution law has been considered in conjunction with the power law to vary the temperature across the cross-section of the FG shaft. Material is graded in such a way that the stainless steel is comprised at the core of the FG shaft and the outer periphery of the FG shaft is made of Zirconia. The steady-state and transient time and frequency responses of a thermally loaded porous FG rotor-bearing system have been computed for both types of uneven porosity distribution using the Houbolt time marching technique and Fast Fourier Transform, respectively. The free vibration analysis has also been performed on the porous FG rotor-bearing system for various parameters such as power law index, the volume fraction of porosity and porosity distribution under different thermal gradients. The reduction of critical speed with increased amplitude is observed from the steady-state and transient frequency responses with an increase in volume fraction of porosity and temperature gradients

Thermomechanical vibration and buckling response of nonlocal strain gradient porous FG nanobeams subjected to magnetic and thermal fields

This study investigates the free vibration and thermal buckling behavior of functionally graded porous nanobeams in magnetic and thermal fields using high-order trigonometric shear stress and nonlocal strain gradient elasticity theories. The results demonstrated the effects of nonlocal differential and strain gradient elasticities on softening and stiffness enhancements, respectively. Additionally, the Lorentz force induced by the magnetic field makes nanobeam’s vibratory motion difficult, causing the natural frequencies to increase. This situation can contribute to the dynamic stability of nanobeams exposed to the nonlinear temperature distribution. This study’s results will assist in designing and implementing micro/nanoelectromechanical systems.

Extrapolation method for reliable measurement of Seebeck coefficient of organic thin films

Measurement of the Seebeck coefficient of an organic thermoelectric (TE) thin film necessitates the accurate measurement of the temperature difference across the film. However, direct measurement of temperature difference is difficult for a small-gap organic TE device, which is favored for the high-resistance organic materials. Here, the effect of a nonlinear temperature distribution on the Seebeck coefficient measurement of organic TE films was systematically investigated to enable clear identification of the Seebeck coefficient for an organic TE film. The nonlinear temperature distribution across an organic TE device was analyzed by a finite-element analysis simulation and IR thermal imaging. The nonlinear temperature distribution resulted in a difference between the measured temperature difference and the actual temperature difference across the organic TE film. The conventional interpolation method significantly overestimated the Seebeck coefficient when the temperature distribution was nonlinear. To reduce the measurement error, the ideal Seebeck voltage was extrapolated from a series of Seebeck voltages measured at different position in the edge-contacted device configuration. The ideal Seebeck coefficients of various organic TE films with a wide range of electrical conductivities were determined successfully, and the Seebeck coefficient measured by extrapolation method was not affected by the geometry of the organic TE film. • Nonlinear temperature distribution during Seebeck coefficient measurement is systematically investigated. • An extrapolation method is used for evaluating an ideal Seebeck voltage that directly corresponded to the temperature difference across organic films. • Our method enables accurate measurement of the Seebeck coefficient of an organic thin film with a short-channel architecture and a high-resistance.

Thermal Analysis and Prediction Methods for Temperature Distribution of Slab Track Using Meteorological Data

The structural temperature distribution, especially temperature difference caused by solar radiation, has a great impact on the deformation and curvature of the concrete slab tracks of high-speed railways. Previous studies mainly focused on the temperature prediction of slab tracks, while how the temperature distribution is affected by environmental conditions has been rarely investigated. Based on the integral transformation method, this work presents an analytical method to determine and decompose the temperature distribution of the concrete slab track. A field temperature test of a half-scaled specimen of concrete slab track was conducted to validate the developed methodology. In the proposed method, we decompose the temperature distribution of the slab track into an initial temperature component and a boundary temperature component. Then, the boundary temperature components caused by solar radiation and atmospheric temperature are investigated, respectively. The results show that the solar radiation plays a significant role in the nonlinear temperature distribution, while the atmospheric temperature has little effect. By contrast, the temperature change in the slab surface resulting from the atmospheric temperature accounts on average for only 5% in the hot weather condition. The proposed method establishes a relation between the structural temperature and meteorological parameters (i.e., the solar radiation and atmospheric temperature). Consequently, the temperature distribution of the concrete slab track is predicted via the meteorological parameters.

Dynamic Stiffness Matrix Approach to Free Vibration Analysis of Functionally Graded Rotor Bearing System Subjected to Thermal Gradients.

The dynamic stiffness matrix (DSM) method, an analytical method that provides exact solutions, has been used for the first time for the free vibration analysis of a functionally graded (FG) rotor bearing system subjected to temperature gradients and to investigate its application to FG rotors. The material gradation occurs based on the power law between the inner metal core and the outer ceramic rich layer of the FG rotor. The temperature gradation follows the Fourier law of heat conduction which leads to non-linear temperature distribution (NLTD) in the radial direction of the FG rotor. The development of the DSM formulations for Timoshenko FG rotor elements using the governing equations derived from translational and rotational equilibrium conditions is the novelty of the present work. The DSM of the FG rotor elements, rigid disk and linear isotropic bearings are assembled to obtain the global dynamic stiffness matrix of the FG rotor bearing system. The natural whirl frequencies are computed from the global DSM using the Wittrick–William algorithm as a root searching technique. The natural and whirl frequencies are validated with the results available in the literature and the exactness of the DSM method has been exemplified.

Study on the effects of solar reflective coatings on the interfacial damage of the CRTS II slab track

In this work, the effects of novel solar reflective coatings on interfacial damage of the China Railway Track System (CRTS) II slab track were studied. Firstly, the effects of two different types of solar reflective coatings on the non-linear temperature distribution of the track slabs were investigated. Then, the influence of the solar reflective coatings on the damage of the interface between the concrete slabs and the cement asphalt mortar layer was studied based on a finite element model of the CRTS II slab track incorporating a bi-linear cohesive zone model of the interface. Finally, the effects of interface bonding properties on the interfacial damage of the coated tracks were analyzed by the finite element model. Results show: The interfacial damage can be underrated if linear rather than non-linear temperature distribution of the track slabs is applied. Both types of coatings can mitigate interfacial damage and reduce slab vertical displacement significantly compared with the uncoated tracks, while the organic solar reflective coating shows better performance than the inorganic solar reflective coating. To avoid interface debonding, the interface bond strength of the coated tracks should be larger than 0.02 MPa.

An investigation of aero-thermo-elastic flutter and divergence of functionally graded porous skew plates

Aero-thermo-elastic flutter and divergence analyses of functionally graded (FG) porous skew plates subjected to supersonic airflow are investigated in this study. The material properties of skew plates vary across the thickness based on the modified power-law model. Three types of thermal loading as constant, linear and nonlinear temperature distributions in the thickness direction of the plate are considered. Applying the Hamilton’s principle, the coupled partial differential equations of motion and the associated boundary conditions based on the first-order shear deformation theory and linear piston theory are derived in the Cartesian coordinates. Also, the principle of minimum total potential energy and adjacent equilibrium criterion are used to obtain the stability equations. Using a mapping, the partial differential equations of motion and stability equations are converted from Cartesian coordinate system to a skew coordinate. The partial differential equations in the skew coordinate are discretized by generalized differential quadrature method (GDQM) and solved using the state space method. Consequently, the effects of geometrical, mechanical and thermal parameters such as thermal loading types, angle of skew, power-law index, porosity, and boundary conditions on the flutter and divergence boundaries of skew plate are studied in detail.

Application of Hermite Wavelet Method and Differential Transformation Method for Nonlinear Temperature Distribution in a Rectangular Moving Porous Fin

Application of Hermite Wavelet Method and Differential Transformation Method for Nonlinear Temperature Distribution in a Rectangular Moving Porous Fin

Vertical Nonlinear Temperature Gradient and Temperature Load Mode of Ballastless Track in China

In the process of heat exchange with the external environment, the internal temperature of ballastless track structure presents a nonlinear distribution. The vertical temperature gradient will cause repeated warping and deformation of track slab, resulting in mortar layer separation, which will affect driving comfort and track durability. The traditional temperature field analysis method of concrete structure based on thermodynamics has the disadvantages of too many assumptions, difficult parameter selection and too much calculation of energy consumption. In this paper, based on the finite element software ANSYS, the heat exchange was transformed into the boundary condition of heat flux, which was applied to the thermodynamic analysis model to study the nonlinear temperature distribution law of ballastless track. The accuracy of the analysis method was verified by the measured data. On this basis, the regional distribution law of temperature gradient of ballastless track under different geographical coordinates and climatic conditions was studied. By adding a regional adjustment coefficient, the vertical temperature load model of ballastless track suitable for typical areas in China was proposed. The proposed temperature load model makes up for the lack of refinement of climate division and temperature load model in relevant specifications, and has strong engineering application and popularization value.

Reconsidering the strength of concrete pavements

ABSTRACT Concrete pavements develop cracks with the accumulation of fatigue damage caused by the combined effect of vehicular and environmental loadings. In Mechanistic-Empirical (ME) design, the ratio of stresses to some measure of strength is used to evaluate incremental damage, which is then related to cracking. Typically, this measure is the Modulus of Rupture (MOR) of a beam made of the same material. The flexural strength is also known to vary with the thickness of the beam. However, the variation of flexural strength due the presence of eigenstresses from temperature or moisture distributions has not received sufficient attention. A non-linear fracture mechanics model demonstrated that the thickness-adjusted flexural strength can also be used for characterising the maximum elastic stress under a linear temperature distribution. However, under a non-linear temperature distribution, the material may sustain a higher or lower maximum elastic stress than the flexural strength. To model this, a practical analytical expression for the apparent flexural strength was derived and showed excellent agreement with numerical simulations as well as with a model based on equivalent elastic deformation energy. The model was used to show that the fatigue capacity under a typical axle load varies with various non-linear temperature distributions.