Different Types Of Thermal Loads Research Articles

Coupled influences of magnetic field and several thermal loads on vibration of thermoelastic nano-ceramic (Si3N4) beam

Our study investigates the vibration of a thermoelastic nano-ceramic (Si3N4) beam exposed to a magnetic field under the effect of a moving heat source and different types of thermal loads. These nanobeams are modeled as non-Fourier heat conduction. In our formulation, the equation of motion and the principle of energy conservation from two coupled partial differential equations have been driven. A direct approach has been used to find the solutions to the governing equations using the Laplace transform definition. Numerical Laplace transform inversion was calculated using Hoing's approximation approach. Solutions have been applied to silicon nitride (Si3N4) nanobeam ceramics. Figures show the distribution of temperature increment, lateral deflection, and stress with different values of magnetic field and several thermal load parameters. In all the studied nanobeam functions, the magnetic field and several thermal loads’s parameters have significant effects. They could be used as tuners to control the vibration and temperature increment. In the present study, a moving heat source, and different thermal loads have been applied to a non-Fourier nanobeam exposed to a magnetic field. The results have been compared with those obtained in the thermoelastic cases.

Nonlinear large-amplitude vibration analysis of annular sector plates made of FGMs subjected to cooling shock

A numerical approach is developed in the present article to study the geometrically nonlinear vibrations of annular sector plates made of functionally graded materials (FGMs) due to being exposed to cooling shock. The first-order shear deformation plate theory (FSDT) is used in the modeling of plate, and the governing equations of motion are derived based on Hamilton's principle considering von Kármán nonlinear kinematic relations. It is also considered that the properties of FGMs are dependent on temperature and distribution of materials. According to the uncoupled thermoelasticity theory, the temperature distribution is obtained via 1D Fourier-type transient heat conduction equation. To numerically solve the problem, the generalized differential quadrature (GDQ) method and Newmark-beta integration scheme are utilized. Considering two different types of thermal loading as cooling shock, the effects of various parameters including thermal load rapidity time, geometry, magnitude of thermal load and material properties on the large-amplitude vibrations of annular sector plates are investigated.

Nonlinear large amplitude vibrations of higher-order functionally graded beams under cooling shock

In this paper, thermally induced vibrations of beams made of functionally graded materials (FGMs) subjected to cooling shocks are investigated. It is considered that the beam has been made of a mixture of stainless steel (SUS 304) and low-carbon steel (AISI 1020). To model the displacement field, the third-order beam theory, known as the Reddy beam theory (RBT), is used. Material properties depend on temperature and distribution of materials, and this dependence is modeled through the temperature and the location of materials along the thickness direction. Considering the uncoupled thermoelasticity theory, the temperature distribution is obtained using a one-dimensional Fourier-type transient heat conduction equation, and the equations of motion governing the higher-order beam are derived utilizing Hamilton's principle. Solving the equations is done numerically; the generalized differential quadrature method (GDQM) is employed to approximate the spatial derivatives, and the Newton-Raphson scheme is applied to linearize the equations. In addition, for approximation of the time derivatives, the Newmark method is utilized. Subsequently, the effects of various parameters on the non-dimensional lateral deflection of the higher-order beam considering two different types of thermal loading are investigated. A comprehensive parametric study is conducted to study the effects of important parameters including beam thickness, thermal load rapidity time, the amount of applied load, and the FG parameter.

Three-dimensional convection regimes in a two-layer system with evaporation for different types of thermal loads on a substrate

Three-dimensional convection regimes in a two-layer system with evaporation for different types of thermal loads on a substrate

Effect of Porosity on the Thermal Buckling Analysis of Power and Sigmoid Law Functionally Graded Material Sandwich Plates Based on Sinusoidal Shear Deformation Theory

This work examines the effect of porosity distributions on thermal buckling analysis of functionally graded material (FGM) sandwich plates. To consider the porosity effect, five different types of distribution models, even, uneven, logarithmic uneven, linear uneven, and sinusoidal uneven are considered. It is assumed that the FGM faces of the sandwich plate are porous while the ceramic core is nonporous. To investigate the thermal buckling behavior of porous FGM sandwich plates, four different types of thermal loads, such as uniform, linear, nonlinear, and sinusoidal temperature rise along the thickness direction are considered. Effective material properties and thermal expansion coefficients of FGM sandwich plates are evaluated based on Voigt’s micromechanical model considering power law FGM (P-FGM) and sigmoid function FGM (S-FGM). The analytical solution is carried out using Hamilton’s variational principle considering the von Karman nonlinearity. The equilibrium and stability equations are derived based on sinusoidal shear deformation theory (SSDT). Numerical results are obtained to observe the influence of different porosity distributions, porosity coefficients, thermal loadings, and geometrical parameters over critical thermal buckling temperature.

Thermo-vibrational analyses of skin tissue subjected to laser heating source in thermal therapy

Laser-induced thermal therapy, due to its applications in various clinical treatments, has become an efficient alternative, especially for skin ablation. In this work, the two-dimensional thermomechanical response of skin tissue subjected to different types of thermal loading is investigated. Considering the thermoelastic coupling term, the two-dimensional differential equation of heat conduction in the skin tissue based on the Cattaneo–Vernotte heat conduction law is presented. The two-dimensional differential equation of the tissue displacement coupled with the two-dimensional hyperbolic heat conduction equation in the tissue is solved simultaneously to analyze the thermal and mechanical response of the skin tissue. The existence of mixed complicated boundary conditions makes the problem so complex and intricate. The Galerkin-based reduced-order model has been utilized to solve the two-sided coupled differential equations of vibration and heat transfer in the tissue with accompanying complicated boundary conditions. The effect of various types of heating sources such as thermal shock, single and repetitive pulses, repeating sequence stairs, ramp-type, and harmonic-type heating, on the thermomechanical response of the tissue is investigated. The temperature distribution in the tissue along depth and radial direction is also presented. The transient temperature and displacement response of tissue considering different relaxation times are studied, and the results are discussed in detail.

Nonlinear thermal buckling and postbuckling analysis of bidirectional functionally graded tapered microbeams based on Reddy beam theory

In the present study, the nonlinear thermal buckling, postbuckling, and snap-through phenomenon of higher-order shear deformable tapered bidirectional functionally graded (BDFG) microbeams are comprehensively investigated under different types of thermal loading, for the first time. The thermomechanical properties of the BDFG microbeam are assumed to be functions of temperature, axial, and thickness directions. Reddy’s parabolic shear deformation beam theory with the von Karman nonlinearity is employed to derive the variable coefficient governing nonlinear differential equations on the basis the physical neutral surface concept. Size-dependent effect is captured in the formulation employing the modified couple stress theory. The generalized differential quadrature method (GDQM) is used to discretize the motion equations considering different boundary conditions. The resulting system of nonlinear algebraic equations is solved iteratively using Newton’s method. Theoretical analysis and numerical results indicate that, depending on the shear deformation beam theory, boundary conditions, and the type of thermal load, the response of the BDFG microbeam may be of the bifurcation or snap-through buckling type of instability. Numerical parametric studies are conducted to explore the influences of thermal load type, material property gradient indexes, boundary conditions, material temperature dependency, taperness ratio, and microstructural length scale on critical thermal buckling load, thermal postbuckling, and equilibrium paths of the BDFG microbeam.

Fractional thermo-viscoelastic response of biological tissue with variable thermal material properties

In this study, the fractional model of thermo-viscoelasticity theory with variable thermal conductivity and rheological properties of the volume is considered to investigate bio-thermo-mechanics behavior in living tissue. The model is applied to a problem of cancerous layer with arbitrary thickness and its outer surface traction free. The bounding plane of the cancerous tissue is subjected to two different types of thermal loading; a non-Gaussian laser beam and harmonic heating. The problem is solved analytically by Kirchhoff and Laplace transformation. The exact solution in Laplace’s transform domain is obtained. Numerical results for the temperature, displacement, and stress distributions are given and illustrated graphically. The effects of time-fractional parameter and materials properties on the behavior of various fields are examined.

Nonlinear dynamical responses of forced carbon nanotube-based mass sensors under the influence of thermal loadings

This study presents an analytical solution for the nonlinear forced vibration response of bridged carbon nanotube (CNT)-based mass sensors subjected to different types of thermal loading and external harmonic excitations. The structure undergoes a temperature change through its thickness when considering three different distribution patterns of the temperature, namely uniform, linear, and nonlinear. The CNT is modeled as a nonlocal doubly clamped beam that complies with Euler–Bernoulli beam theory and Eringen’s nonlocal elasticity theory. The von Karman geometric nonlinearity is adopted to account for the mid-plane stretching of end-constrained beams. The extended Hamilton’s principle is used to derive the nonlinear governing equations of motion, boundary conditions, and continuity conditions accounting for the location of the deposited particle. The method of multiple scales (MMS) is employed to perform the nonlinear dynamical analysis of the nanobeam. Analytical expressions of the nonlinear dynamic response of the system exposed to thermal loadings in the case of primary resonance are presented. An important contribution of this work is the provision for closed-form expressions of the resonance frequency and the critical amplitude of the considered system. Simultaneously, validation of the results by MMS is achieved by Galerkin’s procedure and Runge–Kutta method. Then, the effects of the thermal loads and some key parameters on the nonlinear resonance frequency and amplitude shifts are discussed, and some meaningful conclusions are drawn.

Modeling of One-Dimensional Thermoelastic Dual-Phase-Lag Skin Tissue Subjected to Different Types of Thermal Loading

This work introduces a mathematical model of thermoelastic skin tissue in the context of the dual-phase-lag heat conduction law. One-dimensional skin tissue has been considered with a small thickness and its outer surface traction free. The bounding plane of the skin tissue is subjected to three different types of thermal loading; thermal shock, ramp type heating, and harmonic heating. The inner surface has no temperature increment and traction free. Laplace transform techniques have been used, and its inversions have been calculated by using the Tzuo method. The numerical results have been represented in figures. The thermal shock time parameter, the ramp-type heat parameter, and the angular thermal parameter have significant effects on the temperature increment, the strain, the displacement, and the stress distributions, and they play vital roles in the speed propagation of the thermomechanical waves through the skin tissue.

Thermal buckling and postbuckling responses of geometrically imperfect FG porous beams based on physical neutral plane

Considering the third-order shear deformation and physical neutral plane theories, thermal postbuckling analysis for functionally graded (FG) porous beam are performed in this research. The cases of shear deformable functionally graded materials (FGM) beams with initial deflection and uniformly distributed porosity are considered. Geometrically imperfect FG porous beams with two different types of immovable boundary conditions as clamped–rolling and clamped–clamped are analyzed. Thermomechanical nonhomogeneous material properties of the FG porous beam are assumed to be temperature and position dependent. FG porous beams are subjected to different types of thermal loads as heat conduction and uniform temperature rise. Heat conduction equation is solved analytically using the polynomial series solution for the one-dimensional condition. The governing equilibrium equations are obtained by applying the virtual displacement principle. Assuming von Kármán type of geometrical nonlinearity, equilibrium equations are nonlinear and are solved using an analytical method. A two-step perturbation technique is used to obtain the thermal buckling and postbuckling responses of FG porous beams. The numerical results are compared with the case of perfect FGM Timoshenko beams without porosity distribution based on the midplane formulation. Parametric studies of the perfect/imperfect FG porous beams for two types of thermal loading and boundary conditions are provided.

Thermal vibration analysis of embedded graphene oxide powder-reinforced nanocomposite plates

In this research, thermal vibration analysis of a graphene oxide powder-reinforced (GOPR) nanocomposite embedded plate is carried out once the plate is exposed to different types of thermal loading. The plate is reinforced with various functionally graded (FG) distributions through the thickness, namely uniform, X, V, and O in a comparative way to find out the most efficient model of GOPs’ distribution for the purpose of improving vibrational behaviors of the structure. Also, the Halpin–Tsai micromechanical model is employed to describe the material properties of an FG nanocomposite plate. The shear deformation effects are taken into account using a refined higher order shear deformation plate theory. Moreover, the governing equations of the structure have been derived using Hamilton’s principle and then solved analytically for a simply supported GOPR nanocomposite plate. Besides, detailed parametric studies are procured to show the influences of different variants on the natural frequency of the nanocomposite plates. Presented results reveal that the frequency responses of the nanocomposite plates in a thermal environment dramatically depend on the distribution pattern of the GOPs.

Thermal buckling and post-buckling analysis of geometrically imperfect FGM clamped tubes on nonlinear elastic foundation

• Closed form expressions are used to estimate the deflection of curved FGM tubes under thermal load . • Different types of thermal loading are considered and temperature dependency is considered. • The solution method is based on the two step perturbation technique . • Interaction of the tube with hardening/softening nonlinear elastic foundation and initial imperfection are taken into account. • The developed formulation is based on a higher order tube theory which satisfies the traction free boundary conditions. Present research deals with the thermal buckling and post-buckling analysis of the geometrically imperfect functionally graded tubes on nonlinear elastic foundation. Imperfect FGM tube with immovable clamped–clamped end conditions is subjected to thermal environments. Tube under different types of thermal loads, such as heat conduction, linear temperature change, and uniform temperature rise is analyzed. Material properties of the FGM tube are assumed to be temperature dependent and are distributed through the radial direction. Displacement field satisfies the tangential traction free boundary conditions on the inner and outer surfaces of the FGM tube. The nonlinear governing equations of the FGM tube are obtained by means of the virtual displacement principle. The equilibrium equations are based on the nonlinear von Kármán assumption and higher order shear deformation circular tube theory. These coupled differential equations are solved using the two-step perturbation method. Approximate solutions are provided to estimate the thermal post-buckling response of the perfect/imperfect FGM tube as explicit functions of the various thermal loads. Numerical results are provided to explore the effects of different geometrical parameters of the FGM tube subjected to different types of thermal loads. The effects of power law index, springs stiffness of elastic foundation, and geometrical imperfection parameter of tube are also included.

Thermal Buckling Analysis of a Mindlin Rectangular FGM Microplate Based on the Strain Gradient Theory

This article is aimed at developing a nonclassical Mindlin rectangular functionally graded material (FGM) microplate based on the strain gradient theory (SGT) to study the thermal buckling behavior of microplates with different boundary conditions. This theory comprises material length scale parameters to interpret size effects. The developed model encompasses classical and modified couple stress Mindlin microplate models, if all the material length scale parameters or two of them are taken to be zero, respectively. The Mindlin rectangular FGM microplate is considered to be made of a mixture of metal and ceramic of which the volume fraction is described through a power low function. According to Hamilton's principle and the generalized differential quadrature (GDQ) method, the stability equations and associated boundary conditions are obtained and discretized, respectively. Current formulations provide a possibility to have all types of boundary conditions which herein, FGM microplates with three commonly used boundary conditions are considered. Three different types of thermal loads including uniform, linear and nonlinear temperature rises along the thickness of FGM microplates are considered. The dimensionless critical buckling temperature difference (DCBTD) predicted by SGT is compared with that of modified couple stress theory (CST) and classical theory (CT) which it is found that CST and CT underestimate the DCBTD. Also, effects of the boundary conditions, length scale parameter and material gradient index of FGM microplates on the DCBTD are judiciously investigated.

Vibration of Gold Nanobeam Induced by Different Types of Thermal Loading—A State-Space Approach

There are two significant effects in the nanoscale beam. One is the non-Fourier effect in heat conduction and the other is the coupling effect between temperature and strain rate. In the present study, a generalized solution for the generalized thermoelastic vibration of a gold nanobeam resonator induced by ramp-type heat and harmonically varying heat is developed. The solution takes into account the above two effects. State-space and Laplace transform methods are used to determine the lateral vibration, temperature, displacement, stress, and strain energy of the gold nanobeam. The effects of relaxation time, ramping time, and angular frequency parameters were studied and are represented graphically with some comparisons.

Thermoelastic buckling behavior of thick functionally graded rectangular plates

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.

Two-Temperature Generalized Thermopiezoelasticity of Finite Rod Subjected to Different Types of Thermal Loading

In this work the theory of two-temperature generalized thermoelasticity, based on the theory of Youssef is used to solve boundary value problems of one-dimensional finite piezoelectric rod with loading on its boundary with different types of heating. The governing equations are solved in the Laplace transform domain by using a direct approach. The general solution obtained is applied to specific problems of a finite piezoelectric rod subjected to two types of heating: a thermal shock type, and a ramp type. The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. The conductive temperature, the dynamical temperature, the stress, the strain and the displacement distributions are shown graphically.

State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

In this work, we will consider an infinite elastic body with a spherical cavity and constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in J Appl Math Mech 26(4):470–475 2005a, IMA J Appl Math, pp 1–8, 2005). The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem when the bounding plane of the cavity is subjected to thermal loading (thermal shock and ramp-type heating). The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature and the ramping parameters.