Thermoelastic Coupling Research Articles

A thermal flexible rotor dynamic modelling for rapid prediction of thermo-elastic coupling vibration characteristics in non-uniform temperature fields

The flexible rotors within aero-engines operate in complex thermal environments, where temperature influences both the vibration frequency and amplitude. This study establishes a simple thermal flexible rotor dynamics model to rapidly and precisely predict thermo-elastic coupling vibration characteristics within a non-uniform temperature field. The thermal potential energy of the thermal rotor element is derived for any temperature field, and the motion equation is obtained using the Euler-Lagrange equation. Specifically, the generalized vector of an arbitrary point and cross-sectional non-uniform thermal stress of the thermal rotor element are considered in the thermal potential energy. The model's frequency error is less than 1% under identical boundary conditions. Numerical findings indicate that thermal stress, temperature-dependent material properties, and the coupling effect collectively reduce the natural frequency (NF), with thermal stress having a more pronounced impact under axial constraint. Additionally, thermal stress and material decrease the amplitude across a broad range of rotation speeds, contrasting with thermal bending. This model will play a key role in the iterative calculation of thermo-elastic coupling vibration control due to its accuracy and simplicity.

Thermoelastic damping in asymmetric vibrations of nonlocal circular plate resonators with Moore-Gibson-Thompson heat conduction

Precise estimation of the amount of thermoelastic damping (TED) in small-sized resonators is one of the crucial issues in their optimal design. According to several experimental, numerical and theoretical findings, the behavior of structures with such small dimensions in structural and thermal domains does not follow classical elasticity theory and the Fourier law of heat conduction. The objective of this work is to develop a nonclassical formulation for computing TED in asymmetric vibrations of circular nanoplates according to nonlocal theory (NT) and Moore-Gibson-Thompson (MGT) heat transfer model. To do so, first, the coupled equations of motion and heat are derived in the purview of NT and MGT model. Then, the real and imaginary parts of the system frequency are extracted from the frequency equation affected by thermoelastic coupling. Finally, by means of the existing definition for TED, a mathematical expression including nonlocal parameter of NT and nonclassical constants of MGT model is obtained to make an estimate of TED value. In the numerical examples section, to ensure the credibility of the provided formulation, the results obtained through this model are compared with those reported in the literature in the context of simpler models. Then, by presenting various graphical data, the type and extent of the role of different factors in TED changes are appraised. The obtained results indicate that employing NT and MGT model can substantially impact the amount of TED compared to the estimations of the classical formulation. Furthermore, the comparison of results reveals that the magnitude of TED in asymmetric vibration modes surpasses that in symmetric ones, and consequently incorporating asymmetric vibration modes is crucial for thorough analysis of TED in circular nanoplates. Thus, the formulation presented in this article can aid in achieving an optimal design for such plates, particularly in terms of minimizing energy loss.

Topology optimization framework for thermoelastic multiphase materials under vibration and stress constraints using extended solid isotropic material penalization

This paper proposes a multiphase material topology optimization (MMTO) method for thermal–mechanical structures that takes into account the effect of the temperature field under stress and frequency constraints. Thermoelastic coupling occurs when an engineering structure is concurrently subjected to thermal and mechanical loads. This work focuses on the following: (1) the derivation of three interpolation schemes that use stress, dynamic, and thermal loads based on the extended solid isotropic material penalization (SIMP) method; (2) the incorporation of stress and dynamic constraints of multi-material thermal-elastic structural designs; and (3) the effective control of the impact of thermal loads on structures based on stress and frequency levels. Numerical experiments show that a clear distinction exists in the final topologies for mechanical and thermal loads among materials. Coupled and uncoupled mechanical and thermal behaviors can be predicted using finite element models based on materials’ coefficients of thermal expansion. We see this method is capable of optimizing a structure’s strength and stability while solving the issue of a thermal environment. In addition, it allows for the precise management of stress and vibration levels when structures are not exposed to a thermal environment.

A deep learning method for solving thermoelastic coupling problem

Abstract The study of thermoelasticity problems holds significant importance in the field of engineering. When analyzing non-Fourier thermoelastic problems, it was found that as the thermal relaxation time increases, the finite element solution will face convergence difficulties. Therefore, it is necessary to use alternative methods to solve. This paper proposes a physics-informed neural network (PINN) based on the DeepXDE deep learning library to analyze thermoelastic problems, including classical thermoelastic problems, thermoelastic coupling problems, and generalized thermoelastic problems. The loss function is constructed based on equations, initial conditions, and boundary conditions. Unlike traditional data-driven methods, this approach does not rely on known solutions. By comparing with analytical and finite element solutions, the applicability and accuracy of the deep learning method have been validated, providing new insights for the study of thermoelastic problems.

Representation of Thermomechanical Damage in Fiber-Reinforced Ceramic Composites at High Thermal Gradients

Ceramic matrix composites (CMCs) are the core strategic materials for the thermal structure of new-generation hypersonic aircraft. The unclear understanding of the cross-scale thermomechanical behavior and failure mechanism of materials and structures in high-temperature transient environments is a key scientific issue that restricts the reliable design and safe operation of hypersonic aircraft. In this study, a high-temperature test module in a supersonic wind tunnel with integrated various test systems was independently designed to systematically investigate the thermal mechanical damage evolution of CMCs used in astronautics applications under high-temperature transient conditions. Furthermore, a numerical method for fluid-heat-solid coupling based on an iterative solution strategy was developed and compared with an algorithm based on a wall modification strategy in terms of computational efficiency and accuracy. Besides, a comparative analysis was conducted with the temperature field distribution of the sample obtained in the hypersonic wind tunnel integration test to verify the correctness of the developed thermal-fluid-solid coupling calculation method. Finally, through thermoelastic coupling computational models, the high-thermal-gradient-induced thermomechanical damage mechanism of the CMCs was revealed, providing support for further optimizing the material system and thermal structure design of the CMCs.

Generalized thermoelastic wave response in a hollow cylinder with temperature-dependent properties based on the memory-dependent derivative of the heat conduction model

High-temperature pipelines are susceptible to defects due to the long-term service in high-temperature environments. The guided wave technology is promising for online non-destructive testing. Before implementing it in engineering, it is essential to better understand guided wave characteristics, especially attenuation, which significantly decreases the test distance and the resolution. However, describing the large attenuation is challenging due to the strong thermoelastic coupling, resulting in limitations of available models. To address these limitations, this paper aims to introduce a memory-dependent generalized thermoelastic model for investigating guided waves propagating in a hollow cylinder with temperature-dependent material properties. The analytical solutions are obtained using the Legendre polynomial method. The influence of the memory-dependent effect, temperature variation, and boundary conditions are studied. Some interesting findings are revealed: (1) The time delay factor is more dominant when adjusting κ and n to accurately describe guided wave propagation at high temperatures. (2): The mode conversion is accompanied by the attenuation and group velocity jump when the adjacent flexural torsional and longitudinal modes intersect, which is advisable to avoid when choosing the excitation frequency. (3) The relationship between phase velocity and attenuation versus temperature for quasi-elastic modes is nonlinear, while that for thermal modes is approximately linear.

Generalized frequency shift and attenuation in simply-supported micro/nano-beam resonators with thermoelastic dissipation

The low frequency shift, weak frequency attenuation, and large quality factor (Q) are strongly required for micro/nano-resonators with excellent operation performance. Therefore, the accurate predictions of frequency shift, frequency attenuation, and Q based on thermoelastic dissipation (QTED ) are significant when optimally designing micro/nano-resonators. In this work, employing the modified-couple-stress (MCS) and nonlocal-single-phase-lag (NSPL) models, the generalized analytical expressions of the frequency-shift ratio, frequency-attenuation ratio, and QTED are first proposed for the simply-supported micro/nano-beam resonator with two-dimensional (2D) heat conduction. In the modeling procedure, utilizing the Galerkin approach, the function of 2D fluctuation temperature is solved from the governing equation of NSPL thermoelasticity. For simplicity, the function of one-dimensional (1D) fluctuation temperature is presented directly. Various expressions of complex natural frequency are obtained from the governing equation of MCS vibration with thermoelastic coupling, and then the models of the frequency-shift ratio, frequency-attenuation ratio, and QTED are developed based on the relevant expressions of complex natural frequency. It is confirmed that the present developed models with generality can effectively degenerate into the classical models. In the simulation cases, silicon (Si) that is a representative semiconductor material is selected. Results reveal that the MCS size-dependence effect can affect the frequency shift more markedly than the NSPL and heat-conduction-dimension (HCD) effects. Moreover, for the beam with a small thickness and operated in a high-order mode, the NSPL and HCD effects will significantly determine behaviors of the frequency shift, frequency attenuation, and QTED .

Infrared imaging surface roughness criticality assessment of Wire Arc Additive Manufactured specimens

Infrared imaging surface roughness criticality assessment of Wire Arc Additive Manufactured specimens

Investigation of Time-Varying Backlash of Spur Gears in Thermoelastic Coupling Conditions

Investigation of Time-Varying Backlash of Spur Gears in Thermoelastic Coupling Conditions

Legendre wavelet collocation method for investigating thermo-mechanical responses on biological tissue during laser irradiation

Objective of the present work is to propose a numerical approach based on the Legendre wavelet to address a problem of biological tissue in the presence of superficial cancer and analyze the thermo-mechanical behavior during laser irradiation. The model of thermoelasticity with variable thermal conductivity is considered to investigate transient thermoelastic coupling response in the framework of Moore–Gibson–Thompson (MGT) bioheat transfer. The Kirchhoff mapping is first performed to linearize the nonlinear governing equations due to variable thermal properties, then finite difference discretization is applied for the time domain and subsequently space domain is approximated using Legendre wavelets. The collocation points are taken to transform the system of partial differential equations into a set of algebraic equations, from which the solution can be determined. A thorough parametric analysis is carried out to examine the effects of some material and geometrical parameters on the behavior of various fields such as the displacement, temperature, stress and the tumor-normal tissue interface. The outcomes of the present work are graphically shown and compared to the predictions of other existing models. The advantages of the current numerical procedure include its simplicity, effectiveness and low computational cost even with the few collocation points.

Dynamic behavior of nanoplate on viscoelastic foundation based on spatial-temporal fractional order viscoelasticity and thermoelasticity

The nanodevices often work in a thermal environment and lead to the viscoelastic and thermoelastic coupling which becomes more complicated when further coupled with the size effects. A spatial-temporal fractional order model is proposed to study the dynamic behavior of thermoelastic nanoplate in the present work. The integer order differential is extended to the fractional order differential with the integer order differential as a special case. This extension makes the modeling of small-scale effects of mechanical behavior and generalized heat conduction more flexible. Non-local strain gradient elasticity and non-local heat conduction are used to describe the spatial non-local effects while the fractional order differential to describe the complicated history-dependent effects or the temporal nonlocal effects. The standard solid viscoelastic model and generalized heat conduction model with the fractional order differentials lead to the fractional-order differential governing equations. The fractional order differential equation is solved by the Laplace transform method, and the analytical solution of the response is expressed in terms of the Mittag-Leffler function. In order to verify the reliability of the analytical solution, the numerical solution is also provided for comparison. Based on the numerical results of dynamic response under the step load, the effects of thermoelastic fractional order parameters, viscoelastic fractional order parameters, and small-scale parameters are discussed. The new spatial-temporal fractional order model is a natural extension of the traditional integer order model which can be recovered from the present model.

Elasto-thermoelectronic diffusion waves with changing thermal conductivity and thermal heating of microtemperature semiconductor

This paper presents a theoretical investigation of linear thermal conductivity temperature-dependent coupled elasto-thermoelectronic diffusion (ETD) waves in a micro-temperature semiconductor, specifically focusing on the effects of photo-excited processes. The governing equations are formulated for a semi-infinite silicon wafer, which serves as a semiconductor material. The explicit study of the strong coupling between the equations governing elastic wave transport, carrier (plasma) transport, and thermal wave transport is conducted in the presence of microtemperature influence. The electron–hole interaction is obtained within the framework of the ETD theory. Laplace transform is used to resolve the governing equations in a non-dimensional framework for thermoelastic and electronic deformation in one-dimensional (1D) scenarios. The present study employs the proposed model to analyze the impact of ramp-type heating on a stationary plane of unbounded semiconductor material. Thermoelastic electronic coupling is found to be affected by the presence of variable thermal conductivity and microtemperature parameters.

Time-varying thermoelastic coupling analysis of heat source of ball screw feed drive system

Time-varying thermoelastic coupling analysis of heat source of ball screw feed drive system

A Fast Reduced-Order Model for Radial Integration Boundary Element Method Based on Proper Orthogonal Decomposition in the Non-Uniform Coupled Thermoelastic Problems

To efficiently address the challenge of thermoelastic coupling in functionally graded materials, we propose an approach that combines the radial integral boundary element method (RIBEM) with proper orthogonal decomposition (POD). This integration establishes a swift reduced-order model to transform the high-dimensional system of equations into a more manageable, low-dimensional counterpart. The implementation of this reduced-order model offers the potential for rapid numerical simulations of functionally graded materials (FGMs) under thermal shock loading. Initially, the RIBEM is utilized to resolve the thermal coupling issue within the FGMs. From these solutions, a snapshot matrix is constructed, capturing the solved temperature and displacement fields. Subsequently, the POD modes are established and a POD reduced-order model is constructed for the boundary element format of the thermally coupled problem. Finally, a system of low-order discrete differential equations is solved. Numerical experiments demonstrate that the results obtained from the reduced-order model closely align with those of the full-order model, even when considering variations in structural parameters or impact loads. Thus, the introduction of the reduced-order model not only guarantees solution accuracy but also significantly enhances computational efficiency.

On multiphysics concurrent multiscale topology optimization for designing porous heat-activated compliant mechanism under convection for additive manufacture

In this research, we investigated the use of concurrent multiscale topology optimization to design additively manufacturable lightweight porous compliant mechanisms that enable harnessing heat energy as the energy source to perform mechanical actions. By establishing two independent dimensionless representations of the design problem, i.e., macro and microscale domains, a concurrent multiscale topology optimization framework is implemented, and the effective properties of the microscale (i.e., elastic and heat conductivity tensors, as well as the thermal expansion coefficient) are calculated and used as the thermo-elastic modeling effective properties of the macroscale. For heat transfer physics, heat transport in solids, as well as heat convection, are simultaneously considered in this study. Sensitivity analysis on the suggested concurrent optimization scheme was derived to address the macro and microstructure coupling as well as the thermo-elastic physics coupling. Several numerical cases are studied with single and multiple microstructure systems. To investigate the macrostructure dependency on the microstructure systems, a study was performed for multiple microstructure subsystems. Incorporating several microstructures into a single macro design domain increased design freedom and improved the performance-to-weight ratio. Furthermore, and for achieving good additive manufacturability we investigated the connectivity of the multi-microstructure optimization and implement boundary competitivity technique to attain fully connected design for attaining good additive manufacturability.

Event-Triggered Control for a Second Order ODE-Heat System Coupling at Intermediate Point

Motivated by the thermoelastic coupling effect arising in microelectromechanical systems (MEMS), event-triggered control of second-order ODE-heat systems coupled at intermediate point is investigated. The event-triggered control includes two parts, one is the feedback control signal, and the other is the event-triggered mechanism that decides when to update the control input. First, we design an event-triggered controller by using Zero-Order Hold to a continuous-time controller. Then, a dynamic triggering condition is established. Next, we derive that the existence of a minimal dwell-time, which avoids the occurrence of Zeno behavior. By utilizing Lyapunov-Krasovskii functional method, the global exponential stability of the closed-loop system is demonstrated. Finally, the simulation data based on the thermoelastic coupling system is displayed to demonstrate the availability of the theoretical results.

Analytical, numerical, and experimental methods to study thermo-elastic coupling inherent and vibration characteristics of a flexible rotor system

The thermal deformation of a flexible rotor system in a high-temperature environment causes changes in the inherent and vibration characteristics. A theoretical model of the flexible rotor was established based on the theory of thermal deformation, the assumed mode method, and the Lagrangian principle. The mode natural frequencies and shapes were explored in detail when the temperature of different nickel-based alloy rotor blades increased gradually (from 0 to 1200°C). The changes in the unstable speed points as the temperature gradually increased were studied based on the rotation speed–frequency diagram. In addition, experimental methods were performed. Mode and steady-state speed tests in a supported state were conducted. Mode experiments were completed on a five-blade rotor test rig with a thermal insulation device, and the acceleration frequency-domain signal showed that the natural frequency decreased with increasing temperature. Through steady-state speed experiments, it was found that the position of the unstable speed points moved forward, and the displacement amplitude increased after local heating.

Band gaps of thermoelastic waves in 1D phononic crystal with fractional order generalized thermoelasticity and dipolar gradient elasticity

A coupled thermoelastic model with fractional order derivative which incorporates the microstructural effects and thermoelastic coupling effects simultaneously at small scale is provided and is used to study wave dispersion and bandgap features of Bloch waves in one-dimensional phononic crystals. Dipolar gradient elasticity is used to account for the effects of microstructure while the non-Fourier heat conduction with fractional order derivatives is used to model thermal conduction at small scale. The interaction of thermo-elastic coupled waves with a periodic structure leads to Bloch waves, and the transfer matrix method is used to obtain the dispersion equation of the Bloch waves based on the Bloch theorem. A parameter study is performed in the numerical example to investigate the influence of the strain gradient parameter, the micro-inertial parameter, the relaxation time and the fractional order on the dispersion and bandgap of Bloch waves.

Thermomechanical Peridynamic Modeling for Ductile Fracture.

In this paper, we propose a modeling method based on peridynamics for ductile fracture at high temperatures. We use a thermoelastic coupling model combining peridynamics and classical continuum mechanics to limit peridynamics calculations to the failure region of a given structure, thereby reducing computational costs. Additionally, we develop a plastic constitutive model of peridynamic bonds to capture the process of ductile fracture in the structure. Furthermore, we introduce an iterative algorithm for ductile-fracture calculations. We present several numerical examples illustrating the performance of our approach. More specifically, we simulated the fracture processes of a superalloy structure in 800 ℃ and 900 ℃ environments and compared the results with experimental data. Our comparisons show that the crack modes captured by the proposed model are similar to the experimental observations, verfying the validity of the proposed model.

Simulation of thermoelastic coupling in silicon single crystal growth based on alternate two-stage physics-informed neural network

This paper proposes a alternate physics-informed neural network (PINN) with a two-stage training strategy to solve the thermoelastic coupling in the growth of Czochralski silicon single crystal. Particularly, neural networks with a two-stage training strategy are established for solving partial differential equations in the thermoelastic coupling model. At present, PINN still faces challenges in solving coupling models. Especially for the imbalance between and within equations in the coupling model. To solve this problem, this paper splits the model into two independent systems with their coupling term exchanged in the alternating iteration. Then, the imbalance inside a single solution of the coupling model is solved by the proposed two-stage training strategy, and the imbalance between solutions is avoided by alternative iterations. Experimental results show that the proposed alternate two-stage PINN (ATPINN) can accurately simulate the temperature and displacement in the thermoelastic coupling model. Compared with the finite element results, the error of temperature prediction and displacement prediction is acceptable. The numerical results demonstrate the feasibility and performance of the ATPINN. Furthermore, ATPINN can be extended to any type of coupling model, especially for coupling models with large differences in the magnitudes of the loss functions. The codes developed in this manuscript are publicy available at https://github.com/callmedrcom/ATPINN.