Americo Cunha, Yasar Yanik, Carlo Olivieri, Samuel da Silva
Abstract This tutorial examines the failure theories of Tresca and von Mises, both of which are crucial for designing metallic structures. Conventionally, Tresca is regarded as more conservative than von Mises from a deterministic perspective. This tutorial, however, introduces a different viewpoint, presenting a scenario where von Mises theory may appear more conservative when variability in the mechanical system parameters is considered. This often overlooked aspect is not extensively addressed in standard textbooks on solid mechanics and the strength of materials. The tutorial aims to shed light on the non-negligible probability where von Mises criterion yields a smaller equivalent stress than Tresca, thus being more conservative. It underscores the importance of integrating probabilistic considerations into stress analyses of solids, offering valuable insights for the education of structural mechanics.
{"title":"Tresca vs. von Mises: Which failure criterion is more conservative in a probabilistic context?","authors":"Americo Cunha, Yasar Yanik, Carlo Olivieri, Samuel da Silva","doi":"10.1115/1.4063894","DOIUrl":"https://doi.org/10.1115/1.4063894","url":null,"abstract":"Abstract This tutorial examines the failure theories of Tresca and von Mises, both of which are crucial for designing metallic structures. Conventionally, Tresca is regarded as more conservative than von Mises from a deterministic perspective. This tutorial, however, introduces a different viewpoint, presenting a scenario where von Mises theory may appear more conservative when variability in the mechanical system parameters is considered. This often overlooked aspect is not extensively addressed in standard textbooks on solid mechanics and the strength of materials. The tutorial aims to shed light on the non-negligible probability where von Mises criterion yields a smaller equivalent stress than Tresca, thus being more conservative. It underscores the importance of integrating probabilistic considerations into stress analyses of solids, offering valuable insights for the education of structural mechanics.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134908574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anh Tay Nguyen, Houlin Xu, Karel Matous, Zdenek P. Bazant
Abstract A preceding 2023 study argued that the resistance of a heterogeneous material to the displacement field curvature is the physically most realistic localization limiter for softening damage. The curvature was characterized by the second gradient of the displacement vector field, which includes the material rotation gradient, and was named the ‘sprain’ tensor, while the term ‘spress’ is here proposed as the force variable work-conjugate to ‘sprain’. In this study, the computational obstacles using nodal sprain forces in the previous study are overcome by using finite elements with linear shape functions for both the displacement vector and for an approximate displacement gradient tensor. The actual gradient calculated from the nodal displacement vectors is constrained to the approximate gradient by means of a Lagrange multiplier tensor. The gradient tensor of the approximate gradient tensor then represents the third-order approximate displacement curvature tensor (or Hessian) of the displacement field. Importantly, the Lagrange multiplier behaves as an externally applied generalized moment density that, similar to gravity, does not affect the total strain-plus-sprain energy density of material. The conditions of stationary values of the total free energy of the structure with respect all these unknowns yields the set of equilibrium equations of the structure for each loading step. Examples of crack growth in fracture specimens are given. It is demonstrated that the simulation results are independent of the orientation of a regular square mesh, and capture the width variation of the crack band, and converge as the finite elements are refined.
{"title":"Smooth Lagrangian Crack Band Model (slCBM) Based on Spress-Sprain Relation and Lagrange Multiplier Constraint of Displacement Gradient","authors":"Anh Tay Nguyen, Houlin Xu, Karel Matous, Zdenek P. Bazant","doi":"10.1115/1.4063896","DOIUrl":"https://doi.org/10.1115/1.4063896","url":null,"abstract":"Abstract A preceding 2023 study argued that the resistance of a heterogeneous material to the displacement field curvature is the physically most realistic localization limiter for softening damage. The curvature was characterized by the second gradient of the displacement vector field, which includes the material rotation gradient, and was named the ‘sprain’ tensor, while the term ‘spress’ is here proposed as the force variable work-conjugate to ‘sprain’. In this study, the computational obstacles using nodal sprain forces in the previous study are overcome by using finite elements with linear shape functions for both the displacement vector and for an approximate displacement gradient tensor. The actual gradient calculated from the nodal displacement vectors is constrained to the approximate gradient by means of a Lagrange multiplier tensor. The gradient tensor of the approximate gradient tensor then represents the third-order approximate displacement curvature tensor (or Hessian) of the displacement field. Importantly, the Lagrange multiplier behaves as an externally applied generalized moment density that, similar to gravity, does not affect the total strain-plus-sprain energy density of material. The conditions of stationary values of the total free energy of the structure with respect all these unknowns yields the set of equilibrium equations of the structure for each loading step. Examples of crack growth in fracture specimens are given. It is demonstrated that the simulation results are independent of the orientation of a regular square mesh, and capture the width variation of the crack band, and converge as the finite elements are refined.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134908717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Flexible batteries are gaining momentum in several fields, including wearable medical devices and biomedical sensors, flexible displays, and smartwatches. These energy storage devices are subjected to electro-chemo-mechanical effects. Here, we present a theoretical framework that couples electromechanical theory incorporating flexoelectricity with diffusion. As an example, we investigate the effect of flexoelectricity on the ionic conductivity in soft materials. Our analytical results for a thin film made of a soft material reveal that the ionic conductivity is significantly higher at the nanoscale and decreases exponentially to approach the bulk value with increasing film thickness. Furthermore, we find that flexoelectricity reduces the ionic conductivity dramatically at film thickness smaller than the length scale associated with flexoelectricity. This behavior is attributed to the opposite directions of polarization induced by flexoelectricity and the flow of ions driven by the chemical potential. These findings shed light on the interplay between flexoelectricity and diffusion which would be paramount in designing miniaturized energy storage devices.
{"title":"An electro-chemo-mechanical theory with flexoelectricity: application to ionic conductivity of soft solid electrolytes","authors":"Anand Mathew, Yashashree Kulkarni","doi":"10.1115/1.4063897","DOIUrl":"https://doi.org/10.1115/1.4063897","url":null,"abstract":"Abstract Flexible batteries are gaining momentum in several fields, including wearable medical devices and biomedical sensors, flexible displays, and smartwatches. These energy storage devices are subjected to electro-chemo-mechanical effects. Here, we present a theoretical framework that couples electromechanical theory incorporating flexoelectricity with diffusion. As an example, we investigate the effect of flexoelectricity on the ionic conductivity in soft materials. Our analytical results for a thin film made of a soft material reveal that the ionic conductivity is significantly higher at the nanoscale and decreases exponentially to approach the bulk value with increasing film thickness. Furthermore, we find that flexoelectricity reduces the ionic conductivity dramatically at film thickness smaller than the length scale associated with flexoelectricity. This behavior is attributed to the opposite directions of polarization induced by flexoelectricity and the flow of ions driven by the chemical potential. These findings shed light on the interplay between flexoelectricity and diffusion which would be paramount in designing miniaturized energy storage devices.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"67 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134908086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guest Editorial 2022 Timoshenko Medal Acceptance Lecture: A Trip the Light Fantastic Accepted Manuscript Michael A. Sutton Michael A. Sutton 300 South Main Street Room A129 Columbia, SC 29208 Email: sutton@sc.edu Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information Michael A. Sutton 300 South Main Street Room A129 Columbia, SC 29208 Email: sutton@sc.edu Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. J. Appl. Mech. 1-12 (12 pages) Paper No: JAM-23-1255 https://doi.org/10.1115/1.4063864 Published Online: October 20, 2023 Article history Received: July 2, 2023 Revised: October 16, 2023 Accepted: October 19, 2023 Published: October 20, 2023
{"title":"2022 Timoshenko Medal Acceptance Lecture: A Trip the Light Fantastic","authors":"Michael A. Sutton","doi":"10.1115/1.4063864","DOIUrl":"https://doi.org/10.1115/1.4063864","url":null,"abstract":"Guest Editorial 2022 Timoshenko Medal Acceptance Lecture: A Trip the Light Fantastic Accepted Manuscript Michael A. Sutton Michael A. Sutton 300 South Main Street Room A129 Columbia, SC 29208 Email: sutton@sc.edu Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information Michael A. Sutton 300 South Main Street Room A129 Columbia, SC 29208 Email: sutton@sc.edu Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. J. Appl. Mech. 1-12 (12 pages) Paper No: JAM-23-1255 https://doi.org/10.1115/1.4063864 Published Online: October 20, 2023 Article history Received: July 2, 2023 Revised: October 16, 2023 Accepted: October 19, 2023 Published: October 20, 2023","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135569699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Nondestructive evaluation (NDE) techniques that use nonlinear wave–damage interactions have gained significant attention recently due to their improved sensitivity in detecting incipient damage. This study presents the use of finite element (FE) simulation with the experimental investigation to quantify the effects of guided waves’ propagation through multiple delaminations in unidirectional glass fiber-reinforced polymer (GFRP) composites. Further, it utilizes the outcomes of nonlinear interactions between guided waves and delaminations to locate the latter. This is achieved through probabilistic Bayesian updating with a structural reliability approach. Guided waves interacting with delaminations induce nonlinear acoustic signatures that can be quantified by the nonlinearity index (NLI). The study found that the NLI changes with the interrogation frequency, as confirmed by numerical and experimental observations. By using the numerical outcomes obtained from the nonlinear responses, a Bayesian model-based approach with subset simulation is proposed and subsequently used to locate multiple delaminations. The results indicate that both the log-likelihood and log-evidence are key factors in determining the localization phenomenon. The proposed method successfully localizes multiple delaminations and evaluates their number, interlaminar position, width, and type.
{"title":"Probabilistic Bayesian approach for delamination localization in GFRP composites using nonlinear guided waves","authors":"Akhilendra Gangwar, D M Joglekar","doi":"10.1115/1.4063503","DOIUrl":"https://doi.org/10.1115/1.4063503","url":null,"abstract":"Abstract Nondestructive evaluation (NDE) techniques that use nonlinear wave–damage interactions have gained significant attention recently due to their improved sensitivity in detecting incipient damage. This study presents the use of finite element (FE) simulation with the experimental investigation to quantify the effects of guided waves’ propagation through multiple delaminations in unidirectional glass fiber-reinforced polymer (GFRP) composites. Further, it utilizes the outcomes of nonlinear interactions between guided waves and delaminations to locate the latter. This is achieved through probabilistic Bayesian updating with a structural reliability approach. Guided waves interacting with delaminations induce nonlinear acoustic signatures that can be quantified by the nonlinearity index (NLI). The study found that the NLI changes with the interrogation frequency, as confirmed by numerical and experimental observations. By using the numerical outcomes obtained from the nonlinear responses, a Bayesian model-based approach with subset simulation is proposed and subsequently used to locate multiple delaminations. The results indicate that both the log-likelihood and log-evidence are key factors in determining the localization phenomenon. The proposed method successfully localizes multiple delaminations and evaluates their number, interlaminar position, width, and type.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"204 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135945124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Data-driven equation identification for dynamical systems has achieved great progress, which for static systems, however, has not kept pace. Unlike dynamical systems, static systems are time invariant, so we cannot capture discrete data along the time stream, which requires identifying governing equations only from scarce data. This work is devoted to this topic, building a data-driven method for extracting the differential-variational equations that govern static behaviors only from scarce, noisy data of responses, loads, as well as the values of system attributes if available. Compared to the differential framework typically adopted in equation identification, the differential-variational framework, due to its spatial integration and variation arbitrariness, brings some advantages, such as high robustness to data noise and low requirements on data amounts. The application, efficacy, and all the aforementioned advantages of this method are demonstrated by four numerical examples, including three continuous systems and one discrete system.
{"title":"Automated Identification of Differential-Variational Equations for Static Systems","authors":"Chunjiang Li, Zhanchao Huang, Zhilong Huang, Yong Wang, Hanqing Jiang","doi":"10.1115/1.4063641","DOIUrl":"https://doi.org/10.1115/1.4063641","url":null,"abstract":"Abstract Data-driven equation identification for dynamical systems has achieved great progress, which for static systems, however, has not kept pace. Unlike dynamical systems, static systems are time invariant, so we cannot capture discrete data along the time stream, which requires identifying governing equations only from scarce data. This work is devoted to this topic, building a data-driven method for extracting the differential-variational equations that govern static behaviors only from scarce, noisy data of responses, loads, as well as the values of system attributes if available. Compared to the differential framework typically adopted in equation identification, the differential-variational framework, due to its spatial integration and variation arbitrariness, brings some advantages, such as high robustness to data noise and low requirements on data amounts. The application, efficacy, and all the aforementioned advantages of this method are demonstrated by four numerical examples, including three continuous systems and one discrete system.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The buoyancy adjustment capability is crucial for underwater robots. Dielectric elastomer (DE) is promising to be designed as inflatable actuators to achieve quiet, fast, and effective buoyancy adjustment. However, the buoyancy adjustment of DE actuators is limited by voltage amplification and controllability. This paper presents to solve the limitation of the DE buoyancy adjustment actuator by magnetic enhancement. An actuator is designed with a two-stage buoyancy adjustment capability. The two-stage adjustment strategy allows the actuator to achieve higher buoyancy adjustment at low voltage and controllable buoyancy adjustment at high voltage, where the switch between the two stages is achieved by tuning the snap of the magnet. A theoretical model is developed to assess the performance of the actuator in the two stages and describe the snap behavior. The experiment results agree with the simulation, and the actuator demonstrates the ability to adjust attitude by changing buoyancy at high voltages and rapidly ascending at low voltages. The multiple buoyancy adjustment capabilities of this actuator have the potential to enable the underwater robot to fulfill various complex task demands.
{"title":"A two-stage magnetically enhanced buoyancy adjustment actuator based on dielectric elastomer","authors":"Xunuo Cao, Jiangshan Zhuo, Weifeng Zou, Xinge Li, Dongrui Ruan, Xuxu Yang, Fanghao Zhou, Tiefeng Li","doi":"10.1115/1.4063399","DOIUrl":"https://doi.org/10.1115/1.4063399","url":null,"abstract":"Abstract The buoyancy adjustment capability is crucial for underwater robots. Dielectric elastomer (DE) is promising to be designed as inflatable actuators to achieve quiet, fast, and effective buoyancy adjustment. However, the buoyancy adjustment of DE actuators is limited by voltage amplification and controllability. This paper presents to solve the limitation of the DE buoyancy adjustment actuator by magnetic enhancement. An actuator is designed with a two-stage buoyancy adjustment capability. The two-stage adjustment strategy allows the actuator to achieve higher buoyancy adjustment at low voltage and controllable buoyancy adjustment at high voltage, where the switch between the two stages is achieved by tuning the snap of the magnet. A theoretical model is developed to assess the performance of the actuator in the two stages and describe the snap behavior. The experiment results agree with the simulation, and the actuator demonstrates the ability to adjust attitude by changing buoyancy at high voltages and rapidly ascending at low voltages. The multiple buoyancy adjustment capabilities of this actuator have the potential to enable the underwater robot to fulfill various complex task demands.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136077385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract An analytical solution for the bending problem of micropolar plates is derived based on the symplectic approach. By applying Legendre's transformation, we obtain the Hamiltonian canonical equation for the bending problem of a micropolar plate. Utilizing the method of separation of variables, the homogeneous Hamiltonian canonical equation can be transformed into an eigenvalue problem of the Hamiltonian operator matrix. We derive the eigensolutions of the eigenvalue problem for the simply supported, free, and clamped boundary conditions at the two opposite sides. Based on the adjoint symplectic orthogonal relation of the eigensolutions, the solution of the bending problem of the micropolar plate is expressed as a series expansion of eigensolutions. Numerical results confirm the validity of the present approach for the bending problem of micropolar plates under various boundary conditions and demonstrate the capability of the proposed approach to capture the size-dependent behavior of micropolar plates.
{"title":"Analytical solution for the bending problem of micropolar plates based on the symplectic approach","authors":"Qiong Wu, Long Chen, Qiang Gao","doi":"10.1115/1.4063398","DOIUrl":"https://doi.org/10.1115/1.4063398","url":null,"abstract":"Abstract An analytical solution for the bending problem of micropolar plates is derived based on the symplectic approach. By applying Legendre's transformation, we obtain the Hamiltonian canonical equation for the bending problem of a micropolar plate. Utilizing the method of separation of variables, the homogeneous Hamiltonian canonical equation can be transformed into an eigenvalue problem of the Hamiltonian operator matrix. We derive the eigensolutions of the eigenvalue problem for the simply supported, free, and clamped boundary conditions at the two opposite sides. Based on the adjoint symplectic orthogonal relation of the eigensolutions, the solution of the bending problem of the micropolar plate is expressed as a series expansion of eigensolutions. Numerical results confirm the validity of the present approach for the bending problem of micropolar plates under various boundary conditions and demonstrate the capability of the proposed approach to capture the size-dependent behavior of micropolar plates.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136077386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xiaohao Sun, Kun Zhou, Frederic Demoly, Ruike Renee Zhao, H. Jerry Qi
Abstract 3D/4D printing offers significant flexibility in manufacturing complex structures with a diverse range of mechanical responses, while also posing critical needs in tackling challenging inverse design problems. The rapidly developing machine learning (ML) approach offers new opportunities and has attracted significant interest in the field. In this perspective paper, we highlight recent advancements of utilizing ML for designing printed structures with desired mechanical responses. First, we provide an overview of common forward and inverse problems, relevant types of structures, and design space and responses in 3D/4D printing. Second, we review recent works that have employed a variety of ML approaches for the inverse design of different mechanical responses, ranging from structural properties to active shape changes. Finally, we briefly discuss the main challenges, summarize existing and potential ML approaches, and extend the discussion to broader design problems in the field of 3D/4D printing. This paper is expected to provide foundational guides and insights into the application of ML for 3D/4D printing design.
{"title":"Perspective: Machine learning in design for 3D/4D printing","authors":"Xiaohao Sun, Kun Zhou, Frederic Demoly, Ruike Renee Zhao, H. Jerry Qi","doi":"10.1115/1.4063684","DOIUrl":"https://doi.org/10.1115/1.4063684","url":null,"abstract":"Abstract 3D/4D printing offers significant flexibility in manufacturing complex structures with a diverse range of mechanical responses, while also posing critical needs in tackling challenging inverse design problems. The rapidly developing machine learning (ML) approach offers new opportunities and has attracted significant interest in the field. In this perspective paper, we highlight recent advancements of utilizing ML for designing printed structures with desired mechanical responses. First, we provide an overview of common forward and inverse problems, relevant types of structures, and design space and responses in 3D/4D printing. Second, we review recent works that have employed a variety of ML approaches for the inverse design of different mechanical responses, ranging from structural properties to active shape changes. Finally, we briefly discuss the main challenges, summarize existing and potential ML approaches, and extend the discussion to broader design problems in the field of 3D/4D printing. This paper is expected to provide foundational guides and insights into the application of ML for 3D/4D printing design.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134976039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper explores the decomposition of linear, multi-degree-of-freedom, conservative gyroscopic dynamical systems into uncoupled subsystems through the use of real congruences. Two conditions, both of which are necessary and sufficient, are provided for the existence of a real linear coordinate transformation that uncouples the dynamical system into independent canonical subsystems, each subsystem having no more than two-degrees-of-freedom. New insights and conceptual simplifications of the behavior of such systems are provided when these conditions are satisfied, thereby improving our understanding of their complex dynamical behavior. Several analytical results useful in science and engineering are obtained as consequences of these twin conditions. Many of the analytical results are illustrated by several numerical examples to show their immediate applicability to naturally occurring and engineered systems.
{"title":"Decomposition and Uncoupling of Multi-degree-of-freedom Gyroscopic Conservative Systems","authors":"Ranislav Bulatovic, Firdaus Udwadia","doi":"10.1115/1.4063504","DOIUrl":"https://doi.org/10.1115/1.4063504","url":null,"abstract":"Abstract This paper explores the decomposition of linear, multi-degree-of-freedom, conservative gyroscopic dynamical systems into uncoupled subsystems through the use of real congruences. Two conditions, both of which are necessary and sufficient, are provided for the existence of a real linear coordinate transformation that uncouples the dynamical system into independent canonical subsystems, each subsystem having no more than two-degrees-of-freedom. New insights and conceptual simplifications of the behavior of such systems are provided when these conditions are satisfied, thereby improving our understanding of their complex dynamical behavior. Several analytical results useful in science and engineering are obtained as consequences of these twin conditions. Many of the analytical results are illustrated by several numerical examples to show their immediate applicability to naturally occurring and engineered systems.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135535373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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