Applied Mathematical Modelling最新文献

{"title":"Semi-analytical modeling columnar-to-equiaxed transition during metal powder bed fusion","authors":"Zhi-Jian Li ,&nbsp;Hong-Liang Dai ,&nbsp;Yuan Yao ,&nbsp;Wei-Feng Luo ,&nbsp;Peng Xiao","doi":"10.1016/j.apm.2024.115900","DOIUrl":"10.1016/j.apm.2024.115900","url":null,"abstract":"<div><div>Columnar-to-equiaxed transition (CET) is crucial to the microstructure design and mechanical performance optimization of metallic parts via powder bed fusion (PBF). It is essential to effectively understand the CET behavior under various process conditions. However, the straightforward relation between process parameters, porosity, and CET of PBF-built alloys remains unclear. To address this, this paper develops an integrated semi-analytical modeling framework to efficiently characterize the CET behavior of multicomponent alloys under various process settings. The thermal behavior of multicomponent alloys during PBF is first predicted based on the differential quadrature method combined with the rule of the mixture. Subsequently, the thermal-induced porosity, element diffusion, rapid solidification, undercooling, and nucleation distributions are comprehensively formulated to analytically capture the CET in PBF-built multicomponent alloys. The predicted model is validated by the comparisons with the reported CET behaviors of five typical multicomponent alloys during PBF. Additionally, the crucial process parameters on the thermal-induced CET during metal PBF are demonstrated, including the energy density, preheating temperature, heat source dimension, part dimension, and compositional content. The results show that the ratio of process-related thermal gradient and solidification velocity plays a dominant role in the CET during metal PBF. When higher energy density or lower preheating temperature is used, the growth of equiaxed grains is significantly suppressed during solidification. In contrast, due to the reduction in thermal gradient, the growth of equiaxed grains is promoted with the increasing length-to-thickness ratio of as-built parts and heat source dimensions. In addition, the addition of ceramic particles can promote CET in the consolidation process of metal PBF. The findings can serve as a guideline for the design and printing of multicomponent alloys with desired mechanical properties.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"140 ","pages":"Article 115900"},"PeriodicalIF":4.4,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Seismic response analysis of a seawater–stratified seabed–bedrock system based on a fractional derivative viscoelastic model","authors":"Sen Zheng ,&nbsp;Weihua Li ,&nbsp;Yexin Wan ,&nbsp;Zhe Yang ,&nbsp;Sainan Zhu","doi":"10.1016/j.apm.2024.115901","DOIUrl":"10.1016/j.apm.2024.115901","url":null,"abstract":"<div><div>In this study, considering the flow-independent viscosity of the soil skeleton, a seawater–stratified seabed–bedrock system modelled considering fluid–porous viscoelastic–solid media dynamic interactions is developed to evaluate the seismic response of marine sites under obliquely incident earthquakes. A fractional Zener (FZ) model is introduced to describe the flow-independent viscosity of the seabed soil skeleton, and a fractional derivative viscoelastic wave equation for a saturated porous medium is proposed based on the Biot theory framework. A transfer matrix is derived by applying continuity conditions between the adjacent seabed layers. Subsequently, based on the boundary and continuity conditions between different media, an analytical solution for the wave propagation problem in an entire seawater–stratified seabed–bedrock system is proposed. The correctness and reliability of the proposed method are verified by comparison with existing analytical and numerical methods. Finally, a series of investigations are conducted to study the influences of seawater (free surface waves and depth) and seabed properties (viscoelastic parameters, fractional order, and thickness of the overlying soft soil layer) on seabed displacement at the water–soil interface.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"140 ","pages":"Article 115901"},"PeriodicalIF":4.4,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143139648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive physics-informed neural networks for dynamic coupled thermo-mechanical problems in large-size-ratio functionally graded materials","authors":"Lin Qiu ,&nbsp;Yanjie Wang ,&nbsp;Yan Gu ,&nbsp;Qing-Hua Qin ,&nbsp;Fajie Wang","doi":"10.1016/j.apm.2024.115906","DOIUrl":"10.1016/j.apm.2024.115906","url":null,"abstract":"<div><div>In this paper, we present the adaptive physics-informed neural networks for resolving three-dimensional dynamic coupled thermo-mechanical problems in large-size-ratio functionally graded materials. The physical laws described by coupled governing equations and the constraints imposed by the initial and boundary conditions are leveraged to form the loss function of networks by means of the automatic differentiation algorithm, and an adaptive loss balancing scheme is introduced to improve the performance of networks. The adaptive networks are meshfree and trained on batches of randomly sampled collocation and training points, which is the key feature and superiority of the approach, since mesh-based methods will encounter difficulties in solving problems with complex large-size-ratio structures. The developed methodology is tested for several coupled thermo-mechanical problems in large-size-ratio materials, and the numerical results demonstrate that the adaptive networks are effective and reliable for dealing with coupled problems defined in coating structures with large size ratios up to 10⁹, as well as complex large-size-ratio geometries such as the electrostatic comb and the flange.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"140 ","pages":"Article 115906"},"PeriodicalIF":4.4,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143139650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A generalized mathematical model predicting the mechanical response of tunnel yielding supports in extremely large deformation environments","authors":"Kui Wu,&nbsp;Menglin Yang,&nbsp;Zhushan Shao,&nbsp;Nannan Zhao","doi":"10.1016/j.apm.2024.115909","DOIUrl":"10.1016/j.apm.2024.115909","url":null,"abstract":"<div><div>“Radial–circumferential” combined yielding supports can tolerate extremely large deformations of the surrounding rock without being damaged. However, to date, the coordinated deformation mechanism of combined yielding supports remains unclear, and a well-established design model is still unavailable. This study analyzed the mechanical responses of tunnels with combined yielding supports using a mathematical analytical method. First, the mechanical characteristics of the compressible layer and primary lining with highly deformable elements were introduced, and their deformation processes were divided into three stages in the analytical model. Second, the deformation modes of the combined yielding supports were proposed, and their mechanical responses were classified into three cases. A mechanical model of the interaction between the surrounding rock and combined yielding supports was established. In the proposed analytical model, the rock geomaterial exhibited viscoelastic behaviour, and the effects of tunnel face advancement and support installation delay were considered. An analytical solution corresponding to each deformation mode of the combined yielding supports was provided to predict the rock displacement and interface contact stresses. Furthermore, numerical modelling was conducted for comparison with the analytically predicted results, indicating the reliability and feasibility of the proposed analytical model. Finally, a quick and convenient parametric investigation was performed to determine the sensitivity of the model output results to three design parameters: the yielding lengths of both the compressible layer and primary lining, and the yielding stress of the compressible layer. The analysis revealed that within a certain range, the tunnel displacement and interface contact stresses were highly sensitive to these three parameters. Below or beyond this range, changes in these parameters did not significantly affect the output results of the model. Based on the results of the parametric analysis, several design insights into the combined yielding supports were obtained.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"141 ","pages":"Article 115909"},"PeriodicalIF":4.4,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Research on impact vibration of cantilever fluid-conveying pipe with foundation excitation and gap constraint","authors":"Tianlin Wang ,&nbsp;Feng Xu ,&nbsp;Changqing Guo ,&nbsp;Chenzhou Fan","doi":"10.1016/j.apm.2024.115889","DOIUrl":"10.1016/j.apm.2024.115889","url":null,"abstract":"<div><div>In practical engineering, the unilateral gap constraint impact vibration in fluid-conveying pipes is a critical concern, often arising from constraint loosening or the presence of barriers around the pipe. These factors can significantly affect the service life and safety reliability of the pipes. A tension and compression anisotropy spring with rapidly increasing restoring force in compression but almost zero restoring force in tension is proposed to simulate the unilateral gap constraint, model a fluid-conveying pipe with a Pfluger column. Its reliability is also verified based on the bifurcation phase diagram comparison between the small and large stiffness conditions. Subsequently, we establish a vibration mechanics analysis model for the cantilever fluid-conveying pipe under foundation excitation to assess the effects of basic excitation frequency, fluid velocity, distributed follower force, position coordinate of unilateral gap constraint, and the viscoelastic coefficient on the impact vibration stability of the fluid-conveying pipe. Our findings reveal that when the period-doubling bifurcation sequence is interrupted by Bare-grazing bifurcation, the system directly transitions into chaotic vibration or induces a new period-doubling bifurcation sequence, followed by re-entry into chaotic vibration. These results provide valuable insights into the intricate dynamics of fluid-conveying pipes under foundation excitation, offering a deeper understanding of the impact of various parameters on the pipe's vibration.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"140 ","pages":"Article 115889"},"PeriodicalIF":4.4,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coupled nonlinear modeling of a novel high-sensitivity MEMS capacitive accelerometer enhanced by tilted pillars","authors":"Omar Akram Saleh Alwazzan ,&nbsp;Mohammad Fathalilou ,&nbsp;Ghader Rezazadeh","doi":"10.1016/j.apm.2024.115897","DOIUrl":"10.1016/j.apm.2024.115897","url":null,"abstract":"<div><div>The investigation of novel models, methodologies and materials with the objective of enhancing the sensitivity of capacitive micro-accelerometers represents a topic of enduring interest to researchers. This paper presents a novel model enhanced by a microstructured gap comprising tilted polydimethylsiloxane pillars. A complex mathematical model has been developed to describe the system's behavior, comprising a set of coupled nonlinear equations. The results reveal the accelerometer's response to both sinusoidal and shock inputs. It has been demonstrated that the novel model can enhance sensitivity by more than fourfold. A crucial aspect of the investigation is a comparative evaluation of scenarios with and without micro-pillars, as well as variations in micro-pillars' number and tilt angles. These findings yield valuable insights into the effects of these design parameters on the sensor's performance, laying the groundwork for optimizing the design to achieve heightened sensitivity and reduced actuation voltage.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"140 ","pages":"Article 115897"},"PeriodicalIF":4.4,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Design of double-coupled HR-FN neural network with memristors and its application in image encryption","authors":"Yanfeng Wang ,&nbsp;Pengke Su ,&nbsp;Zicheng Wang ,&nbsp;Junwei Sun","doi":"10.1016/j.apm.2024.115898","DOIUrl":"10.1016/j.apm.2024.115898","url":null,"abstract":"<div><div>In this paper, a double-coupled neural network based on hyperbolic memristors between HR neuron and FN neuron is proposed. Complex dynamic behaviors of the neural network are investigated by stability analysis and dynamic analysis. The maximum Lyapunov exponent cube of three-parameter is proposed, which is used in the dynamics analysis. The Lyapunov exponent cube allows a more intuitive observation of the dynamic characteristics of neural network. The accuracy of numerical analysis is validated through the circuit implementation of neural network. Furthermore, a medical image encryption algorithm based on double-coupled neural network is proposed. The image encryption algorithm combines Latin square permutation and Bit cross-coded diffusion, which effectively improves the randomness of the pixel replacement process. A series of random tests are used to detect the algorithm. Simulation results and numerical analysis show that the algorithm has high security and anti-cracking ability.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"140 ","pages":"Article 115898"},"PeriodicalIF":4.4,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A spatial train-track-tunnel coupled dynamics model for assessing influences of curved railway line on circular tunnel vibrations","authors":"Jianjin Yang ,&nbsp;Shengyang Zhu ,&nbsp;Qiuyi Li ,&nbsp;Chengbiao Cai ,&nbsp;Wanming Zhai","doi":"10.1016/j.apm.2024.115892","DOIUrl":"10.1016/j.apm.2024.115892","url":null,"abstract":"<div><div>A spatial train-track-tunnel coupled dynamics model is established in this paper, which exhibits high computational efficiency and can effectively capture the influences of curved railway lines and the spatial dynamic interactions between the subsystems. In the model, the circular tunnel and grouting area are simplified as a dual-layer cylindrical shell with finite length and then are modelled using semi-analytical method for high computational efficiency. The effects of surrounding soil are simulated using unified viscous-spring artificial boundaries. After being verified by the field measurements, the proposed model is employed to assess influences of curved railway line on the train-induced vibrations of circular tunnel. The results indicate that there are significant differences in tunnel vibrations induced by trains moving on curved railways compared to straight railways, and tunnel vibrations are not monotonously reduced by decreasing the train running speed. The model enables more realistic assessments of the train-induced vibrations of circular tunnels, particularly in the cases involving curved railways.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"140 ","pages":"Article 115892"},"PeriodicalIF":4.4,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vibration PID control design by receptance-based partial eigenstructure assignment","authors":"Huping Mao,&nbsp;Yulong Du","doi":"10.1016/j.apm.2024.115902","DOIUrl":"10.1016/j.apm.2024.115902","url":null,"abstract":"<div><div>In recent decades, the partial eigenstructure assignment problem has attracted considerable attention due to its practicality and significant benefits in vibration control. For linear vibration systems, enhancing system response can be achieved by strategically assigning zeros and poles. To meet the dynamic requirements of vibration systems, this paper presents a receptance-based approach for partial eigenstructure assignment using a novel PID controller. A comprehensive description and validation of the proposed method are provided. The PID controller is applied to the free vibration equation of a multi-degree-of-freedom linear system. Through the use of the Laplace transform and the Sherman-Morrison formula, the flexibility matrix of the closed-loop system is obtained. Under certain assumptions and constraints, the theoretical gain vector for PID control is determined using the Moore-Penrose generalized inverse. Furthermore, a practical strategy for optimizing sensor placement is proposed. The introduction of integral control inevitably results in the generation of new zero-pole pairs. A comprehensive explanation and analysis of these newly introduced zeros and poles, as well as the modified system, are provided. Two numerical examples validate the effectiveness of the proposed methodology.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"140 ","pages":"Article 115902"},"PeriodicalIF":4.4,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143139649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Research on parameter identification of transmission line galloping model under different degrees of freedom","authors":"Xiaohui Liu ,&nbsp;Libing Chen ,&nbsp;Chuan Wu ,&nbsp;Zhongfei Ye ,&nbsp;Bo Zhang ,&nbsp;Yaguang Tao","doi":"10.1016/j.apm.2024.115899","DOIUrl":"10.1016/j.apm.2024.115899","url":null,"abstract":"<div><div>The phenomenon of galloping in transmission lines has long been a topic of significant interest, and establishing an accurate galloping model is highly challenging. Consequently, the sparse identification of nonlinear dynamics (SINDy), Integral SINDy (ISINDy), and Weak SINDy (WSINDy) algorithms are employed to directly identify galloping models from data. A theoretical mechanical model is established for different degrees of freedom (DOFs), using the galloping of iced quad bundle conductors as an illustrative example. Simulated data obtained from the theoretical model are utilized to perform parameter identification of the galloping model using the three algorithms. For the 1-DOF and 2-DOF galloping models, the data is preprocessed using the Hodrick-Prescott (H-P) filter method, and then the parameter identification effects of the three algorithms are compared under different noise levels. The parameter identification effects of the three algorithms for the 3-DOF galloping model are analyzed using noise-free data, while also comparing their robustness across different data lengths. The research findings demonstrate that the WSINDy algorithm exhibits high accuracy and robustness in the parameter identification process of galloping models with varying DOF, surpassing the performance of the SINDy and ISINDy algorithms. The identification models play a crucial role in validating anti-galloping designs and formulating anti-galloping plans in engineering applications.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"140 ","pages":"Article 115899"},"PeriodicalIF":4.4,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}