Nonlinear Temperature Change 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.

Aerodynamic stability and free vibration of FGP-Reinforced nano-fillers annular sector microplates exposed to supersonic flow

Metal foams have many different uses, but they also have some weaknesses. To address this issue, scientists are exploring the possibility of adding nano-fillers to make them stronger and more rigid. As a result, there has been increased interest in analyzing structures that are made from these materials among researchers. Here and now, the authors have conducted a new study that focuses on analyzing the aerodynamic stability and free vibrational characteristics of an annular sector microplate. This is the first time that such an analysis has been done for this type of microplate. The microplate is exposed to supersonic flow and nonlinear temperature changes. The actual properties of the microplate are determined via different introduced homogenization schemes; and four distinguished patterns for both pores and nano-fillers dispersion are considered. To evaluate the reinforcements impact, two most widely recognized nano-fillers, i.e., carbon nanotubes and graphene nanoplatelets are employed and their influence on the outcomes is observed. By utilizing Hamilton's principle and performing certain mathematical operations, the equations of motion were derived and solved numerically under different boundary conditions. A case study is conducted to examine how different parameters affect the natural frequencies, corresponding mode shapes, and critical aerodynamic pressures. Since no similar research has been found, the outcomes of this work may be accounted as reference points for upcoming investigations.

Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates

This paper investigates the thermal mechanical bending response of symmetric functionally graded material (FGM) plates. This article proposes a thermodynamic analysis model of both the FGM plate and FGM sandwich plate, and the model only involves four control equations and four unknown variables. The control equation is based on the refined shear deformation theory and the principle of minimum potential energy. The Navier method is used to solve the control equation. According to the method, numerical examples are provided for the thermo-mechanical bending of the symmetric FGM plate and FGM sandwich plate under a simply supported boundary condition, and the accuracy of the model is verified. Finally, parameter analysis is conducted to investigate the effects of the volume fraction index, side-to-thickness ratio, thermal load, and changes in core thickness on the thermal mechanical bending behavior of the symmetric FGM plate and FGM sandwich plate in detail. It was found that the deflection of the FGM plate is greater than that of the FGM sandwich plate, while the normal stress of the FGM plate is smaller than that of the FGM sandwich plate. Moreover, the FGM plate and FGM sandwich plate are sensitive to nonlinear temperature changes.

A study of electrothermomechanical converter for technological purposes with nonlinear changes in the loading and cooling medium

Heavy temperature processes with high-temperature loads require optimisation of technological processes, ensuring high reliability and combining rotating parts of electric machines with actuators to achieve greater efficiency of electromechanical converters. The research aims to provide a theoretical justification and experimental confirmation of the effect of higher harmonics in the air gap under nonlinear changes in the temperature of the medium. The research is based on the basic principles of electrodynamics, heat and mass transfer, mathematical modelling by the finite element method, and experimental verification of multi-physical parameters. Based on the analysis of the differential equation for determining the increase in the surface temperature of a ferromagnetic rotor under conditions of nonlinear temperature changes in the environment surrounding the electromechanical converter, the regularities of the formation of the free and forced components of the instantaneous temperature values of the massive rotor are established. Depending on the mode of interaction between the load-cooling medium and the electromechanical part of the screw units, kinematic diagrams of single-mass and two-mass systems with variable or constant moments of inertia and stiffness were formed. According to the size of the electromagnetic system of the experimental sample, a mathematical model for studying thermal and electromagnetic processes was built. The regularities of the spatial distribution of the temperature of the screw electromechanical unit are determined. The spectra of higher harmonics of voltage and current in the frequency range from 0 to 50 kHz have been experimentally determined, which confirms the presence of the effect of generating higher harmonics when the temperature of the medium surrounding the rotor screw changes. The detected harmonic spectrum affects both the formation of the dynamics of the rotating system and additional thermal power while increasing the overall efficiency of the screw electromechanical converter. The practical value of the obtained results lies in the possibility of predicting the optimal indicators of interrelated electromagnetic and heat exchange processes in screw electromechanical converters for technological purposes

A computationally efficient C0 continuous finite element model for thermo-mechanical analysis of cross-ply and angle-ply composite plates in non-polynomial axiomatic framework

In the present article, the thermo-mechanical bending response of multi-layered composite plates is investigated in the framework of inverse-hyperbolic shear deformation theory using a generalized finite element model. The mathematical development is carried out under the assumptions of linear structural kinematics for the materials following generalized Hooke’s law. Energy-based finite element formulation and the principle of minimum potential energy are employed to develop the finite element governing equations. A computationally efficient C0 continuous finite element formulation is developed to examine the response of laminated composites subjected to constant, linear, and non-linear temperature change. Numerical analyses are carried out for composite laminates considering various lamination sequences (cross-ply as well as angle-ply), boundary conditions, loading conditions, span-thickness ratio, etc. The present results are compared with the existing analytical and numerical results and their agreement is observed. The effect of fiber orientation angle on bending response is analyzed to enable the optimal design of laminated composite structures under thermo-mechanical loading.

Characteristics of Deep Groundwater Flow and Temperature in the Tertiary Pohang Area, South Korea

The geothermal characteristics of specific areas on Earth can be identified using geophysical and lithological logs based on deep boreholes, such as those more than 1000 m in depth. Based on the combined analyses of geophysical logs (temperature, caliper, electrical conductivity (EC), and natural gamma-ray logs) and lithological logs, as well as 1D steady-state heat transfer model, the deep groundwater flow and temperature were characterized in four deep boreholes (BH-1–BH-4) roughly 2000 m deep in the area of Heunghae-eup, Pohang, South Korea. The estimated thermal gradients from the temperature profiles are as follows: 22.37–30.77 °C/km for BH-1, 35.67–64.52 °C/km for BH-2, 40.85–46.44 °C/km for BH-3, and 33.33–35.71 °C/km for BH-4. According to the geophysical logs and lithology profiles, the groundwater mainly flows into and out of the boreholes through the basic dyke, rhyolite, and sandstone/mudstone. Evidently, the groundwater flows moving through the fractures and faults induce nonlinear temperature changes. The upward and downward groundwater flows passing through fractures and faults can be estimated using a 1D steady-state heat-transfer equation, by considering a fracture angle based on the lithological and geophysical profiles. To determine the direction (up/down) and rate of groundwater flow, the values for the parameter β were estimated as follows: −1.95 to 5.40 for BH-1, −13.48 to 4.87 for BH-2, −1.76 for BH-3, and −3.39 to 14.15 for BH-4.

Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

Pre-thermal buckling and frequency characteristics of imperfect graphene nanoplatelets reinforced composite curved open cylindrical micropanel under nonlinear thermal loading

This is the first research on the pre-thermal buckling and vibration analysis of imperfect graphene nanoplatelets reinforced composite (GPLRC) doubly curved open cylindrical micropanel in the framework of numerical based two dimensional-generalized differential quadrature method (2D-GDQM). Additionally, the small-scale effects are analyzed based on nonlocal strain gradient theory (NSGT). The stresses and strains are obtained using the high order shear deformable theory (HOSDT). Rule of mixture is employed to obtain varying mass density, thermal expansion, and Poisson’s ratio, while module of elasticity is computed by modified Halpin–Tsai model. In addition, nonlinear temperature changes along the GPLRC micro panel’s thickness direction. Governing equations and boundary conditions of the GPLRC doubly curved open cylindrical micropanel are obtained by implementing Hamilton’s principle. Besides, for the validation of the results, the results of current model are compared to the results acquired from analytical method. The results show that GPL weight function (), imperfection, the ratio of shell curvatures (R 1/R 2), NSG parameters, and geometric parameters have significant influence on the frequency and pre-thermal buckling characteristics of the GPLRC doubly curved open cylindrical micropanel.

Thermal Buckling Responses of a Graphene Reinforced Composite Micropanel Structure

This is the first research on the thermal buckling analysis of graphene nanoplatelets reinforced composite (GPLRC) doubly curved open cylindrical micropanel in the framework of numerical-based two-dimensional generalized differential quadrature method (2D-GDQM). Additionally, the small-scale effects are analyzed based on nonlocal strain gradient theory (NSGT). The stresses and strains are obtained using the high-order shear deformable theory (HOSDT). The rule of mixture is employed to obtain varying thermal expansion, and Poisson’s ratio, while module of elasticity is computed by modified Halpin–Tsai model. In addition, nonlinear temperature changes along the GPLRC micropanel’s thickness direction. Governing equations and boundary conditions of the GPLRC doubly curved open cylindrical micropanel are obtained by implementing the extended Hamilton’s principle. Besides, for the validation of the results, the results of current model are compared to the results acquired from analytical method. The results show that GPL weight function ([Formula: see text], the ratio of shell curvatures ([Formula: see text]/[Formula: see text], NSG parameters, and geometric parameters have a significant influence on the thermal buckling characteristics of the GPLRC doubly curved open cylindrical micropanel.

Thermal buckling analysis of moderately thick FGM plates based on the von Kármán nonlinearity and improved third order shear deformation theory

In this study, thermal buckling of moderately thick functionally graded rectangular plates with all edges simply supported is analyzed by means of an improved third order shear deformation theory (improved TSDT). The plate is assumed to be under two types of thermal loadings, namely; uniform temperature rise and nonlinear temperature change across the thickness. The equilibrium and stability equations are derived based on the von Kármán type of geometrical nonlinearity and the improved third-order theory. By solving the stability equations, the value of buckling temperature difference is obtained. To calculate the critical buckling temperature difference, this value is minimized with respect to the half-wave parameters. The results are compared with the known data in literatures. The results indicate that, the values of critical buckling temperature difference which are obtained based on the improved TSDT, are lower in comparison with those obtained based on TSDT. Also, the results show that incorporation of the von Kármán type of geometrical nonlinearity with the improved third-order theory, gives the lower values of the critical buckling temperature difference.

The drivers of nonlinear local temperature change under global warming

How the pattern of the Earth’s surface warming will change under global warming represents a fundamental question for our understanding of the climate system with implications for regional projections. Despite the importance of this problem there have been few analyses of nonlinear local temperature change as a function of global warming. Individual climate models project nonlinearities, but drivers of nonlinear local change are poorly understood. Here, I present a framework for the identification and quantification of local nonlinearities using a time-slice analysis of a multi-model ensemble. Accelerated local warming is more likely over land than ocean per unit global warming. By examining changes across the model ensemble, I show that models that exhibit summertime drying over mid-latitude land regions, such as in central Europe, tend to also project locally accelerated warming relative to global warming, and vice versa. A case study illustrating some uses of this framework for nonlinearity identification and analysis is presented for north-eastern Australia. In this region, model nonlinear warming in summertime is strongly connected to changes in precipitation, incoming shortwave radiation, and evaporative fraction. In north-eastern Australia, model nonlinearity is also connected to projections for El Niño. Uncertainty in nonlinear local warming patterns contributes to the spread in regional climate projections, so attempts to constrain projections are explored. This study provides a framework for the identification of local temperature nonlinearities as a function of global warming and analysis of associated drivers under prescribed global warming levels.

Thermo-electrical buckling response of actuated functionally graded piezoelectric nanoscale plates

Abstract In this work, the analytical investigation of thermo-electrical buckling of a functionally graded piezoelectric nanoscale plate is obtained via a refined hyperbolic higher-order shear deformation theory. Eringen’s nonlocal theory has been proposed to capture the small size influence. The nanoscale plate material properties vary continuously across the thickness based on a power law function. The softening nonlocal model is exposed to external electric voltage and three different thermal environments (uniform, linear, nonlinear temperature changes). The governing equations are derived using the total potential energy principle, and Navier’s procedure has been employed to determine the exact solution of the current problem. The critical buckling temperature of nanoscale plate exposed to various thermal environments loading and external electric voltages are obtained. The numerical results of thermo-electrical buckling are determined for several nonlocal parameters, thermal environments, geometric parameters, gradient indexes and external electrical voltages.

Influence of spring-mass systems on frequency behavior and critical voltage of a high-speed rotating cantilever cylindrical three-dimensional shell coupled with piezoelectric actuator

In this article, vibrational behavior and critical voltage of a spinning cylindrical thick shell covered with piezoelectric actuator (PIAC) carrying spring-mass systems are investigated. It should be noted that, the installed sensors on the proposed systems are considered as a tip mass. This structure rotates about axial direction and the formulations include the Coriolis and centrifugal effects. In addition, various cases of thermal (uniform, linear, and nonlinear) distributions are studied. The modeled cylindrical thick shell covered with PIAC, its equations of motion, and boundary conditions are derived by the principle of minimum total potential energy and based on a new three-dimensional refined higher-order theory (RHOST). For the first time in the present study, attached spring-mass systems have been considered in the rotating cylindrical thick shells covered with PIAC. The accuracy of the presented model is verified compared with previous studies. The novelty of the current study is consideration of the applied voltage, rotation, various temperature distributions and spring-mass systems implemented on the proposed model using the RHOST. The generalized differential quadrature method is presented to discretize the model and to approximate the governing equations. In this study the simply supported conditions have been applied to edges and cantilever (clamped-free) boundary conditions have been studied in x = 0, L, respectively. The results show that, applied voltage, angular velocity, temperature changes and spring-mass systems play an important role on the critical voltage, critical angular speed, critical temperature, and natural frequency of the structure. Another significant result is that, by increasing the lumped mass and coefficient of the spring in the first frequency of the cantilever cylindrical shell, increase or decrease of the natural frequency depends on the nonlinear temperature change parameter. The results of the current study are useful suggestions for designing electromechanical systems such as hydraulic pipes with the installation of the sensors to them.

Vibration Analysis of Non-Uniform Imperfect Functionally Graded Beams with Porosities in Thermal Environment

AbstractIn the present study, thermo-mechanical vibration behavior of non-uniform beams made of functionally graded (FG) porous material are investigated under different thermal loadings for the first time. It is observed that during the fabrication of functionally graded materials (FGMs) porosities and micro-voids can be occured inside the material, thus in this study vibration analysis of FG beams by considering the effect of these imperfections is performed. Material properties of the FG beam are assumed to be temperature-dependent and vary continuously through thickness direction according to a power-law scheme which is modified to approximate material properties for both even and uneven distributions of the porosities. Different thermal environmental conditions, including uniform, linear and non-linear temperature changes through the thickness direction are considered. The motion equations are derived based on the Euler-Bernoulli beam theory through Hamilton's principle and they are solved applying the differential transformation method (DTM). In order to show the accuracy of the present analysis, comparisons are made with previous researches and an excellent agreement is observed. The obtained results are presented for the thermo-mechanical vibration characteristics of the FG beams such as the influences of various temperature rises, gradient index, porosity volume fraction, taper ratio and the boundary conditions in detail.

Comparative Analysis of Various Control Strategies for a Nonlinear CSTR System

Abstract Continuous stirred tank reactor (CSTR) is a highly nonlinear process particularly when chemical reaction takes place. The heat energy will be either liberate or absorbed by the reactor due to the reaction. The control of temperature for this process is a real challenge due to nonlinear temperature changes during reaction. In this paper a mathematical model of CSTR with its transfer function is taken for controller design and analysis. The temperature inside the reactor is controlled by altering the coolant jacket temperature. This paper compares the performances of the proportional integral derivative controller (PID) controller, PID-based nonlinear autoregressive moving average (NARMA) controller and fuzzy-based PID controller. The proposed PID-based NARMA controller shows better control of temperature than the conventional PID controller. The fuzzy-based PID controller also shows a reasonable optimal performance.

Thermal Buckling Analysis of Size-Dependent FG Nanobeams Based on the Third-Order Shear Deformation Beam Theory

In this paper, the thermal effects on the buckling of functionally graded (FG) nanobeams subjected to various types of thermal loading including uniform, linear and non-linear temperature changes are investigated based on the nonlocal third-order shear deformation beam theory. The material properties of FG nanobeam are supposed to vary gradually along the thickness direction according to the power-law form. The governing equations are derived through Hamilton’s principle and solved analytically. Comparison examples are performed to verify the present results. Obtained results are presented for thermal buckling analysis of FG nanobeams such as the effects of the power-law index, nonlocal parameter, slenderness ratio and thermal loading in detail.

Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions

In this article, electro-thermo-mechanical vibrational behavior of functionally graded piezoelectric (FGP) plates with porosities is explored via a refined four-variable plate theory for the first time. Uniform, linear and nonlinear temperature changes are considered in this study. Electro-elastic material properties of porous FGP plate vary across the thickness based on modified power-law model. The governing equations derived from Hamilton’s principle are solved analytically. The exactness of solution is confirmed by comparing obtained results with those provided in the literature. Influences of applied voltage, porosity distribution, thermal loadings, material gradation, plate geometrical parameters and boundary conditions on the vibrational behavior of FGP plates are discussed. These results can be applied for accurate design of smart structures made of functionally graded piezoelectric materials by considering porosity distribution.

Analytical modeling for the thermoelastic buckling behavior of functionally graded rectangular plates using hyperbolic shear deformation theory under thermal loadings

Purpose– The purpose of this paper is to investigate an analytical modeling for the thermoelastic buckling behavior of functionally graded (FG) rectangular plates (FGM) under thermal loadings. The material properties of FGM are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Derivations of equations are based on novel refined theory using a new hyperbolic shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. In addition, numerical results for a variety of FG plates with simply supported edge are presented and compared with those available in the literature. Moreover, the effects of geometrical parameters of dimension the length to width aspect ratio (a/b), the plate width to thickness ratio (b/h), and material properties index (k) on the FGM buckling temperature difference are determined and discussed.Design/methodology/approach– In the current paper, the application of the refined theory proposed by Shimpi is based on the assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. It is extended to the analysis of buckling behavior of ceramic-metal FG plates subjected to the three types of thermal loadings, namely; uniform temperature rise, linear temperature change across the thickness, and nonlinear temperature change across the thickness. The material properties of the FG plates are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results, wherever possible. Additionally, the effects of geometrical parameters and material properties on the buckling temperature difference of FGM plates are determined and discussed.Findings– Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power-law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions.Originality/value– To the best of the authors’ knowledge, there are no research works for thermal buckling analysis of FG rectangular plates based on new four-variable refined plate theory (RPT). The novelty of this paper is extended the use of the above-mentioned RPT with the addition of a new function proposed by Shimpi for thermal buckling analysis of plates made of FG materials. Unlike any other theory, the number of unknown functions involved is only four, as against five in the case of other shear deformation theories. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. The plates subjected to the two types of thermal loadings, namely; uniform temperature rise and nonlinear temperature change across the thickness. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results.

Post-buckling analysis of rectangular plates comprising Functionally Graded Strips in thermal environments

Description is given of a semi-analytical finite strip method for analysing the post-buckling behaviour of functionally graded rectangular plates in thermal environments where plates are under uniform, tent-like or nonlinear temperature change across the thickness. The material properties are assumed to vary through the thickness according to the power law. The formulations are based on the classical plate theory and the concept of the principle of the minimum potential energy. The Newton–Raphson method is used to solve the equilibrium equations. A range of applications are described and the numerical results are compared to the available results, wherever possible.

Nonlinear temperature changes in the atmospheric mesopause region of the atmosphere against the background of global climate changes, 1960–2012

Nonlinear temperature changes in the atmospheric mesopause region of the atmosphere against the background of global climate changes, 1960–2012