Nonlinear Temperature Rise Research Articles

A semi-analytical methodology for predicting the vibroacoustic response of functionally graded nanoplates under thermal loads

In this investigation, the analysis of the nonlinear vibroacoustic and sound transmission loss behaviors of nanoplates made of functionally graded materials considering the nonlocal strain gradient theory is presented. It is presumed that the properties of the functionally graded nanoplate are in the form of the simple power law scheme and continuous along the thickness, under nonlinear temperature rise and incident oblique acoustic wave as well as the first-order shear deformation theory. For this purpose, applying Hamilton’s principle, the nonlinear partial differential equations of motion are derived by the displacement field function approach and by considering the von Kármán nonlinear strain-displacement relations. To solve the equations, using the Galerkin method, the nonlinear partial differential equations of motion lead to the Duffing equation. Then, applying the homotopy analysis method, the equation of the transverse movement of the nanoplate is solved semi-analytically to obtain the nonlinear frequencies. Lastly, the nonlinear vibration and acoustic response of functionally graded nanoplate are investigated by considering the variation of the significant factors such as material gradient indices, nonlocal parameters, length scale parameters, aspect ratio, dimensionless amplitude, nonlinear temperature changes, and sound characteristics of the functionally graded nanoplate.

Effect of free vibration on mechanical characteristics of Bi-directional functionally graded beams under hygrothermal effect

ABSTRACT The effect of free vibration on mechanical characteristics of bi-directional functionally graded material (BDFGM) beams under the influence of hygrothermal effects involves the application of the harmonic differential quadrature method (HDQM). The material parameters are supposed to vary in both axial and thickness directions. The temperature distribution is employed along the length direction of the BDFGM beams while maintaining a constant moisture concentration. An exponential law with axial thermal variation under moisture effect is investigated to analyse vibration behaviour in the BDFGM beams using the HDQM. Hamilton’s principle is used to obtain governing equations. Three kinds of temperature distribution profile were considered i.e. uniform (UTR), linear (LTR) and nonlinear temperature rise (NLTR). Free vibration analysis is performed using the HDQM. The precision of the HDQM is validated by comparing it with prior studies. Various configurations of boundary conditions, including supported, clamped, and free, are considered. Parametric results are investigated to explore the effect of the exponent parameters, temperature profile and constant humidity content. Results indicate that temperature, constant moisture content, material properties, and different end conditions significantly influence natural frequency. The outcomes can be applied to designing two or more directional FGM structures for different environmental conditions.

Correction to: A harmonic balance-based method to predict nonlinear forced response and temperature rise of dry friction systems including frictional heat transfer

Correction to: A harmonic balance-based method to predict nonlinear forced response and temperature rise of dry friction systems including frictional heat transfer

A harmonic balance-based method to predict nonlinear forced response and temperature rise of dry friction systems including frictional heat transfer

A harmonic balance-based method to predict nonlinear forced response and temperature rise of dry friction systems including frictional heat transfer

Heat transfer constraints and performance mapping of a closed liquid sorption heat storage process

Sorption storage is a potential game changer for heat storage in buildings, providing high volumetric energy storage density and no loss over storage time. Application specific temperatures and material specific thermodynamic properties are recognized as key for potential performance evaluation. Nevertheless, in system operation, finite heat and mass transfer kinetics detract from the theoretical maximum performance. In this study, it is found that a nonlinear relationship between temperature gain and heat release of the sorbent, afflicts an unavoidable restriction to the performance potential. Heat transport increases as temperature gain decreases, bringing about a temperature induced heat transfer stagnation to a heat transport fluid with linear temperature to heat gain correlation.In this paper, we present the background for performance analysis with emphasis on this nonlinear relationship. We propose a method for performance mapping, including the sorbent equilibrium line (the state where the sorbent is in temperature, concentration and vapor pressure equilibrium) and the unavoidable deviation from this line due to the afore stated non-linearity. As an example of this proposed mapping, we visualize results from an absorption process with liquid aqueous sodium hydroxide and water.Due to the nonlinear temperature rise in heat release, we conclude that it is important to operate a sorption heat storage system in a way that only the minimum required temperature rise is achieved. By doing so, the heat transport fluid capacity is increased in respect to the sorbent capacity, augmenting heat transfer and improving the energy density.

An extension of Carrera unified formulation in polar coordinates for mechanical and thermal buckling analysis of axisymmetric FG circular plate using FEM

The main goal of this article is to extend the Carrera unified formulation (CUF) in polar coordinates to analyze the mechanical and thermal buckling of functionally graded (FG) circular plates with axisymmetry. The governing equations are derived using CUF in polar coordinates for FEM. The fundamental nuclei, and accordingly, the elemental matrices for a 3-node line axisymmetric element are proposed. Mechanical and thermal buckling under uniform, nonlinear temperature rise with and without the effect of convection has been investigated. The results have been verified with several plate theories and the finite element method using the second-order axisymmetric 2D elements.

Solution of the Thermoelastic Problem for a Two-Dimensional Curved Beam with Bimodular Effects

In classical thermoelasticity, the bimodular effect of materials is rarely considered. However, all materials will present, in essence, different properties in tension and compression, more or less. The bimodular effect is generally ignored only for simple analysis. In this study, we theoretically analyze a two-dimensional curved beam with a bimodular effect and under mechanical and thermal loads. We first establish a simplified model on a subarea in tension and compression. On the basis of this model, we adopt the Duhamel similarity theorem to change the initial thermoelastic problem as an elasticity problem without the thermal effect. The superposition of the special solution and supplement solution of the Lamé displacement equation enables us to satisfy the boundary conditions and stress continuity conditions of the bimodular curved beam, thus obtaining a two-dimensional thermoelastic solution. The results indicate that the solution obtained can reduce to bimodular curved beam problems without thermal loads and to the classical Golovin solution. In addition, the bimodular effect on thermal stresses is discussed under linear and non-linear temperature rise modes. Specially, when the compressive modulus is far greater than the tensile modulus, a large compressive stress will occur at the inner edge of the curved beam, which should be paid with more attention in the design of the curved beams in a thermal environment.

Coupled thermal stability analysis of piezomagnetic nano-sensors and nano-actuators considering the flexomagnetic effect

The current investigation deals with an analytical formulation and solution procedure for the thermal stability characteristics of piezomagnetic nano-sensors and nano-actuators considering the flexomagnetic effects and geometrical imperfection. Piezo-flexomagnetic nano-plate strips with the mid-plane initial rise are subjected to external uniform, linear, and nonlinear temperature rise loading across the thickness. The nonlinear size-dependent governing equations are derived within the framework of the first-order shear deformation plate theory, nonlocal strain gradient theory and considering the nonlinear von- Kármán strains. The proposed closed-form solutions and the obtained results are validated with the available data in the literature. The calculated buckling and post-buckling temperatures of piezo-flexomagnetic nano-plate strips are shown to be dependent on several factors including the scaling parameters, plate slenderness ratio, mid-plane initial rise, different temperature distributions, and scalar magnetic potential. The presented closed-form solutions and numerical results can serve as benchmarks for future analyses of piezo-flexomagnetic nano-sensors and nano-actuators.

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.

Thermal buckling behavior of power and sigmoid functionally graded material sandwich plates using nonpolynomial shear deformation theories

PurposeThe purpose of this article is to carry out the thermal buckling analysis of power and sigmoid functionally graded material Sandwich plate (P-FGM and S-FGM) under uniform, linear, nonlinear and sinusoidal temperature rise.Design/methodology/approachThermal buckling of FGM Sandwich plates namely, FGM face with ceramic core (Type-A) and homogeneous face layers with FGM core (Type-B), incorporated with nonpolynomial shear deformation theories are considered for an analytical solution in this investigation. Effective material properties and thermal expansion coefficients of FGM Sandwich plates are evaluated based on Voigt's micromechanical model considering power and sigmoid law. The governing equilibrium and stability equations for the thermal buckling analysis are derived based on sinusoidal shear deformation theory (SSDT) and inverse trigonometric shear deformation theory (ITSDT) along with Von Karman nonlinearity. Analytical solutions for thermal buckling are carried out using the principle of minimum potential energy and Navier's solution technique.FindingsCritical buckling temperature of P-FGM and S-FGM Sandwich plates Type-A and B under uniform, linear, non-linear, and sinusoidal temperature rise are obtained and analyzed based on SSDT and ITSDT. Influence of power law, sigmoid law, span to thickness ratio, aspect ratio, volume fraction index, different types of thermal loadings and Sandwich plate types over critical buckling temperature are investigated. An analytical method of solution for thermal buckling of power and sigmoid FGM Sandwich plates with efficient shear deformation theories has been successfully analyzed and validated.Originality/valueThe temperature distribution across FGM plate under a high thermal environment may be uniform, linear, nonlinear, etc. In practice, temperature variation is an unpredictable phenomenon; therefore, it is essential to have a temperature distribution model which can address a sinusoidal temperature variation too. In the present work, a new sinusoidal temperature rise is proposed to describe the effect of sinusoidal temperature variation over critical buckling temperature for P-FGM and S-FGM Sandwich plates. For the first time, the FGM Sandwich plate is modeled using the sigmoid function to investigate the thermal buckling behavior under the uniform, linear, nonlinear and sinusoidal temperature rise. Nonpolynomial shear deformation theories are utilized to obtain the equilibrium and stability equations for thermal buckling analysis of P-FGM and S-FGM Sandwich plates.

Thermal behavior estimation of the power switches with an empirical formulation optimized by Artificial Bee Colony algorithm

Temperature rise and thermal management in power electronic circuits is a very important issue both electrically and in terms of more compact circuit design. Considering the non-linear temperature rise in the power switches, it is necessary to accurately estimate the temperature rise before the circuit can be experimentally executed. In this study, the temperature rise values in the switching elements for the different current, switching frequency, and duty ratio values of a DC-DC boost converter circuit are analyzed parametrically with ANSYS-Twin Builder software and a total of 715 data are obtained. Based on these data obtained, the temperature rise that occurs during the operation of the power switches in different parameters can be predicted and can be predicted accurately and quickly with a mathematical expression in order to effectively provide the cooling system and thermal management of the power electronics circuit. The proposed expression has eight parameters that need to be optimized. In optimization of these parameters, the Artificial Bee Colony algorithm is used. The Mean Absolute Error is used as the performance indicator. The temperature rise values are calculated via the optimized expression with 0.7446 °C error. Thus, the accuracy of expression is about 95.17%.

Vibration analysis of an axially functionally graded material non-prismatic beam under axial thermal variation in humid environment

The vibration analysis of an axially functionally graded material non-prismatic Timoshenko beam under axial thermal variation in humid environment is carried out using the harmonic differential quadrature method. In this modeling, the length and width of the beam remains constant whereas thickness of the beam is linearly varied along the axis of the beam. The material properties are temperature dependent and are assumed to be varied continuously along the axial direction according to power law distribution. Three types of temperature variations are considered in this study, that is, uniform temperature rise, linear temperature rise, and non-linear temperature rise. The temperature of the beam remains constant under uniform temperature rise condition and it is varied linearly and nonlinearly along the length of beam for rest of the conditions. The beam is subjected to uniform moisture concentration to impose humidity. Hamiltonian’s approach is used to derive the governing equations of motion. The resultant governing equations are then solved using the harmonic differential quadrature method to obtain the natural frequencies of the axially functionally graded material non-prismatic beam. The results obtained using the harmonic differential quadrature method are compared with results obtained for special cases. The effects of thermal variation, humidity, non-homogeneity parameter, and end conditions on natural frequencies of the non-prismatic beam are reported.

Vibration response of a geometrically discontinuous bi-directional functionally graded plate resting on elastic foundations in thermal environment with initial imperfections

The present study includes the free vibration analysis of geometrically imperfect and discontinuous porous functionally graded bi-directional plate (B-FGP) resting on an elastic foundation in a thermal environment. The geometric discontinuity is present in the form of a circular cutout at the center of the plate whereas initial imperfections have been incorporated in terms of geometric as well as porosity inclusions. The kinematic formulation is based on the refined non-polynomial trigonometric higher-order shear deformation theory (HSDT). A new porosity model has been developed to incorporate the influence of the microstructure defect on the effective material properties of the B-FGP. The gradation of properties is done along the thickness (z-direction) as well as the length (x-direction) of the plate using the power-law distribution. A new expression has been given to obtain the solution of the non-linear temperature rise along the thickness of the B-FGP. A continuous Lagrangian four-noded quadrilateral element has been used to perform the finite element formulation with eight degrees of freedom per node. The equations of motion have been derived using a variational approach. The validation and comparative study have been done to authenticate the present formulation. The influence of the cutout radius, elastic foundation parameters, porosity, thermal environment, geometric imperfection, and volume fraction indexes has been discussed in detail.

Size-Dependent Higher Order Thermo-Mechanical Vibration Analysis of Two Directional Functionally Graded Material Nanobeam

This paper represented a numerical technique for discovering the vibrational behavior of a two-directional FGM (2-FGM) nanobeam exposed to thermal load for the first time. Mechanical attributes of two-directional FGM (2-FGM) nanobeam are changed along the thickness and length directions of nanobeam. The nonlocal Eringen parameter is taken into the nonlocal elasticity theory (NET). Uniform temperature rise (UTR), linear temperature rise (LTR), non-linear temperature rise (NLTR) and sinusoidal temperature rise (STR) during the thickness and length directions of nanobeam is analyzed. Third-order shear deformation theory (TSDT) is used to derive the governing equations of motion and associated boundary conditions of the two-directional FGM (2-FGM) nanobeam via Hamilton’s principle. The differential quadrature method (DQM) is employed to achieve the natural frequency of two-directional FGM (2-FGM) nanobeam. A parametric study is led to assess the efficacy of coefficients of two-directional FGM (2-FGM), Nonlocal parameter, FG power index, temperature changes, thermal rises loading and temperature rises on the non-dimensional natural frequencies of two-directional FGM (2-FGM) nanobeam.

Effect of Thermal Environment and Peripheral Loading on Axisymmetric Vibrations of Non-uniform FG Circular Plates via Generalized Differential Quadrature Method

In this article, axisymmetric vibrations of a non-uniform functionally graded circular plate subjected to uniform in-plane peripheral loading and non-linear temperature rise across the thickness have been analyzed on the basis of classical theory of plates. The thickness of the plate is assumed to vary exponentially along the radial direction. The plate material is graded in thickness direction using a power-law model and its mechanical properties are temperature-dependent. Keeping the uniform thermal environment over the top and bottom surfaces, the equations for thermoelastic equilibrium and axisymmetric motion for such a plate model have been derived by Hamilton’s energy principle. Employing generalized differential quadrature method, the frequency equations for clamped and simply supported plates have been obtained and solved numerically using MATLAB. The lowest three roots have been retained as the frequencies for the first three modes of vibration. The influence of various parameters, such as power-law index, in-plane force parameter and temperature difference with varying values of thickness parameter, has been analyzed on the vibration characteristics of the plate. By allowing the frequency to approach zero, the critical buckling loads with varying values of other parameters have been computed. The benchmark results for linear as well as uniform temperature rise have also been computed. The validity of the present technique is verified by comparing the results with the published work.

Thermal free vibration analysis of functionally graded plates and panels with an improved finite shell element

This article deals with thermal free vibration analysis of functionally graded material (FGM) plates and panels using an improved first-order shear deformable (I-FSDT) shell model. The Effective material properties of the FGMs are estimated according to a power law distribution with temperature dependency. The FGM structure can be subjected to uniform or nonlinear temperature rise. The results obtained from the proposed formulation are validated with those available in the literature. Natural frequencies of FGM plates and cylindrical panels are computed for different power law indexes, thermal loadings, boundary conditions and aspect ratios. The present (I-FSDT) finite shell element model is much like the standard (FSDT) model but does not need shear correction factors and is of high accuracy. This work is the first application of the formulation to free vibration analysis of FG plate and shell structures including thermal effects.

Nonlinear Thermal Stability of Rotating Pre-twisted Temperature-Dependent FG Microblades

The main objective of this study is to investigate the post-buckling thermal load–deflection path of rotating pre-twisted microblades/beams made of temperature-dependent functionally graded materials (FGMs) via nonlinear non-classical first-order shear deformation theory (FSDT). To this end, modified strain gradient theory (MSGT) as well as the von Karman geometric nonlinearity is used to develop the size-dependent nonlinear beam theory. Thermal loading is exerted by providing nonlinear (non-uniform) temperature rise across the microbeam thickness at steady-state condition. By using the principle of virtual work and Ritz method, the discretized form of nonlinear equations governing the post-buckling behavior of rotating pre-twisted functionally graded (FG) microbeams is achieved. To solve the obtained nonlinear equations numerically, Broyden’s method is employed. The effects of twist angle along the beam axis, angular velocity, index of the material gradient, length-scale parameter and thickness-to-length ratio on the post-buckling path of FG microbeams are carefully investigated. Findings show that making a correct assumption about the temperature dependence of material is an important factor to increase accuracy of results.

Fundamental frequency analysis of functionally graded plates with temperature-dependent properties based on improved exponential-trigonometric two-dimensional higher shear deformation theory

The objective of this paper is to provide a computational method to analyze free vibrations of advanced composite plates in thermal environments according to a recently developed higher-order shear deformation theory. This method is based upon the assumptions that displacements field include just four unknowns and considers a combination of trigonometric and exponential shear shape functions which satisfy shear stress free boundary conditions on the plate surfaces. The FG plates are simply supported and subjected to uniform, linear, nonlinear and sinusoidal temperature rise. The temperature field considered is assumed to vary in the thickness direction and constant in the axial directions of plates. It is supposed that the constituent materials possess temperature-dependent properties changing across the thickness with a simple power law function. The equations of motion are obtained by employing Hamilton’s principle and solved based on Navier’s method to determine natural frequencies of the FG plate. A parametric study for FGM plates with different values of power law index and under different sets of thermal environmental conditions has been carried out. The obtained results are compared for temperature-dependent and temperature-independent FG Plates and validated with available results in the literature.

A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.

Thermal Buckling Analysis of Functionally Graded Euler-Bernoulli Beams with Temperature-dependent Properties

Thermal buckling behavior of functionally graded Euler-Bernoulli beams in thermal conditions is investigated analytically. The beam with material and thermal properties dependent on the temperature and position is considered. Based on the transformed-section method, the functionally graded beam is considered as an equivalent homogeneous Euler-Bernoulli beam with an effective bending rigidity under an eccentric thermal load. Then, the thermal elastic buckling equation associated with the bending deflection about the neutral axis is established. The easily usable closed-form solutions for the critical thermal buckling temperature of functionally graded beams under uniform and non-linear temperature rise are obtained and used to calculate the thermal buckling temperature. Some results are evaluated and compared with those by other investigators to validate the accuracy of the presented method. The effects of material compositions, temperature-dependent material properties, slenderness ratios and restraint conditions on thermal buckling behaviors are discussed. It is believed that the proposed model provides engineers and designers an easy and useful method to investigate the effects of various parameters affecting the thermal buckling characteristics of functionally graded beams.