{"title":"Semi-Implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics With Hysteresis","authors":"Bidhayak Goswami, Anindya Chatterjee","doi":"10.1115/1.4057042","DOIUrl":"https://doi.org/10.1115/1.4057042","url":null,"abstract":"Abstract Structural damping is often empirically rate-independent wherein the dissipative part of the stress depends on the history of deformation but not its rate of change. Hysteresis models are popular for rate-independent dissipation; and a popular hysteresis model is the Bouc-Wen model. If such hysteretic dissipation is incorporated in a refined finite element model, then the model involves the usual structural dynamics equations along with nonlinear nonsmooth ordinary differential equations for a large number of internal hysteretic states at Gauss points used within the virtual work calculation. For such systems, numerical integration is difficult due to both the distributed nonanalytic nonlinearity of hysteresis as well as large natural frequencies in the finite element model. Here, we offer two contributions. First, we present a simple semi-implicit integration approach where the structural part is handled implicitly based on the work of Piché, while the hysteretic part is handled explicitly. A cantilever beam example is solved in detail using high mesh refinement. Convergence is good for lower damping and a smoother hysteresis loop. For a less smooth hysteresis loop and/or higher damping, convergence is noted to be roughly linear on average. Encouragingly, the time-step needed for stability is much larger than the time period of the highest natural frequency of the structural model. Subsequently, data from several simulations conducted using the above semi-implicit method are used to construct reduced order models of the system, where the structural dynamics is projected onto a few modes and the number of hysteretic states is reduced significantly as well. Convergence studies of error against the number of retained hysteretic states show very good results.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"439 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135035243","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}
{"title":"Equivalent Beam Model and Improved Structure Design of Large Space Antenna Truss with Geometric Nonlinearity","authors":"Jiang Shi, Cai Guo-Ping","doi":"10.1115/1.4057043","DOIUrl":"https://doi.org/10.1115/1.4057043","url":null,"abstract":"\u0000 This paper proposes a extend linear equivalent method that can extend the linear equivalent micropolar beam model to the nonlinear equivalent micropolar beam model to analyze nonlinear vibration for large space truss structure, and also proposes a lattice enhancement method to improve the cantilever truss for the buckling problem that exists in space cantilever truss structures. The nonlinear equivalent model is obtained by introducing a co-rotating coordinate system into the linear equivalent beam model. Since the instability of the fixed root end of the cantilever truss is the main reason for buckling, the method of strengthening the longeron of the truss lattice by lattice is proposed. The accuracy of the equivalent geometric nonlinear model and the effectiveness of the improved cantilever truss structure are verified by four numerical simulation examples. The methods proposed in this paper provide some reference for studying the dynamics analysis of large space trusses and the design of structures.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"240 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77414319","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}
{"title":"A 2D Corotational Beam Formulation Based On the Local Frame of Special Euclidean Group SE(2)","authors":"Pu You, Zhuyong Liu, Ziqi Ma","doi":"10.1115/1.4057044","DOIUrl":"https://doi.org/10.1115/1.4057044","url":null,"abstract":"\u0000 The corotational frame method is widely used in the simulation of flexible multibody dynamics. Its core idea is to separate the rigid motion from the flexible deformation so that it can make fully exploit a large number of excellent local finite elements. The essence of the conventional corotational frame method is the projection relationship between the element frame and the global frame. This paper explores another coordinate projection method for 2D corotational beam element. The projection relationship between the element frame and the local frame in the framework of Lie algebra se(2) has been proposed. Based on the description of SE(2), the formulation of corotational beam element and integration algorithm is presented. The local frame description greatly reduces the nonlinearity of the formula by eliminating the effect of the rigid body motion on the projection matrix, internal force and inertial force. Several examples of large deformation and or large rotation are performed, and it is found that the step-size convergence and iterative convergence of SE(2) description are improved compared with ℝ3 description. In additionMoreover, some examples are used given to verify that the frame invariance brought by SE(2)the coordinate transformation is valuable for improving computing efficiency. The presented transformation method can easily extend to other 2D corotational elements.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"90 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90690328","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}
{"title":"Define the Lyapunov Exponents for ψ-Fractional Differential System","authors":"N'Gbo N'Gbo, Jianhua Tang","doi":"10.1115/1.4057041","DOIUrl":"https://doi.org/10.1115/1.4057041","url":null,"abstract":"\u0000 In this article, we focus on the relations between the asymptotics of solutions and the sensitivity to initial values of fractional differential systems. To investigate this problem, we consider the ψ-fractional calculus, which is considered to be a generalization of those of Riemann-Liouville and Hadamard. For this purpose, we define Lyapunov exponents for ψ-fractional differential systems and estimate their upper bounds. Examples are also presented to demonstrate the efficiency of our results.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"49 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85030312","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}
{"title":"Unconditionally Stable Numerical Scheme for Heat Transfer of Mixed Convective Darcy-Forchheimer Flow of Micropolar Fluid Over Oscillatory Moving Sheet","authors":"Y. Nawaz, M. Arif, K. Abodayeh","doi":"10.1115/1.4056969","DOIUrl":"https://doi.org/10.1115/1.4056969","url":null,"abstract":"\u0000 A third-order numerical scheme is proposed for the time discretization of time-dependent partial differential equations (PDEs). This third-order proposed scheme is further modified, and the new scheme is obtained with second-order accuracy in time and is unconditionally stable. The stability of the new scheme is proved by employing von Neumann stability analysis. For spatial discretization, a compact fourth-order scheme is adopted. Moreover, a mathematical model for heat transfer of Darcy-Forchheimer flow of Micropolar fluid is modified with an oscillatory sheet, nonlinear mixed convection, thermal radiation and viscous dissipation. The suitable transformations are considered to transform the dimensional system of PDEs into dimensionless PDEs and further solve this system using the proposed numerical scheme. It is found that velocity and angular velocity have dual behaviour by incrementing coupling parameters. The proposed second-order accurate in-time scheme is compared with the existing Crank-Nicolson scheme. The proposed scheme is shown to have faster convergence than the existing scheme with the same accuracy. We anticipated this would help investigators address outstanding challenges in industrial and engineering enclosures.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"11 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84261310","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}
{"title":"Predicting Nonlinear Modal Properties by Measuring Free Vibration Responses","authors":"Shih-Chun Huang, Hao-Wen Chen, Meng-Hsuan Tien","doi":"10.1115/1.4056949","DOIUrl":"https://doi.org/10.1115/1.4056949","url":null,"abstract":"\u0000 Identifying dynamical system models from measurements is a central challenge in the structural dynamics community. Nonlinear system identification, in particular, is of great challenge since there are combinatorically many possible model structures which requires expert knowledge for constructing an appropriate model. Furthermore, traditional nonlinear system identification methods require a steady excitation input that is not always available in many practical applications. Recently, a technique referred to as the sparse identification of nonlinear dynamics (SINDy) algorithm was developed for discovering mathematical models of general nonlinear systems. The SINDy method is able to find a generalized linear state-space model for the autonomous nonlinear system by analyzing the collected response data. In this work, the SINDy method is adapted and combined with the shooting method and numerical continuation technique to form a system identification platform that is capable of predicting the nonlinear modal properties of mechanical oscillators. The proposed platform is able to predict the nonlinear normal modes (NNMs) of these systems by processing the noised data of their free vibration response. Also, the NNMs and internal resonance of the nonlinear systems at a high energy level can be captured using the proposed technique by processing the response data at a lower energy level. The proposed method is numerically demonstrated on a two degree of freedom mechanical oscillator. Furthermore, the effects of measurement error and excitation condition on the NNMs prediction are investigated. The NNM prediction platform presented in this paper is applicable to a variety of nonlinear systems.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"66 5 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87755948","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}
{"title":"Feasibility Study of Upper Limb Control Method Based On EMG-Angle Relation","authors":"Bianca Lento, Y. Aoustin, T. Zielińska","doi":"10.1115/1.4056918","DOIUrl":"https://doi.org/10.1115/1.4056918","url":null,"abstract":"\u0000 The method of inferring the human upper limb angles basis on EMG signals with the use of fuzzy logic neural network is discussed. The planar motion in sagittal plane is taken into account, and two EMG signals are analyzed. An artificial neural network with fuzzy logic is used to process EMG signals. The network predicts angular trajectories. On the basis of the difference between the current and the intended angular position, the driving torques are determined using simplified dynamic model. To verify the method, the real and predicted angles are compared. The difference between the torques evaluated using predicted angular trajectories and simplified dynamics, and the torques delivered by the OpenSim simulator using the true data is also studied. Obtained results confirm the correctness of the concept and its usefulness for controlling prostheses or exoskeletons.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"2 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90632625","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}
{"title":"Energy-Efficient Actuator Design Principles For Robotic Leg Prostheses And Exoskeletons: A Review Of Series Elasticity And Backdrivability","authors":"Brokoslaw Laschowski, J. McPhee","doi":"10.1115/1.4056919","DOIUrl":"https://doi.org/10.1115/1.4056919","url":null,"abstract":"\u0000 Robotic leg prostheses and exoskeletons have traditionally been designed using highly-geared motor-transmission systems that minimally exploit the passive dynamics of human locomotion, resulting in inefficient actuators that require significant energy consumption and thus provide limited battery-powered operation or require large onboard batteries. Here we review two of the leading energy-efficient actuator design principles for legged and wearable robotic systems: series elasticity and backdrivability. As shown by inverse dynamic simulations of walking, there are periods of negative joint work that can increase efficiency by recycling some of the otherwise dissipated energy using series elastic actuators and/or backdriveable actuators with energy regeneration. Series elastic actuators can improve shock tolerance during foot-ground impacts and reduce the peak power and energy consumption of the motor via mechanical energy storage and return. However, actuators with series elasticity tend to have lower output torque, increased mass and architecture complexity due to the added physical spring, and limited force and torque control bandwidth. High torque density motors with low-ratio transmissions, known as quasi-direct drives, can likewise achieve low output impedance and high backdrivability, allowing for safe and compliant human-robot physical interactions, in addition to energy regeneration. However, torque-dense motors tend to have higher Joule heating losses, greater motor mass and inertia, and require specialized motor drivers for real-time control. While each actuator design has advantages and drawbacks, designers should consider the energy-efficiency of robotic leg prostheses and exoskeletons during various locomotor activities of daily living.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"6 11","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72481781","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}
Jagdev Singh, A. Alshehri, Sushila Rathore, Devendra Kumar
{"title":"Computational Analysis of Fractional Liénard's Equation with Exponential Memory","authors":"Jagdev Singh, A. Alshehri, Sushila Rathore, Devendra Kumar","doi":"10.1115/1.4056858","DOIUrl":"https://doi.org/10.1115/1.4056858","url":null,"abstract":"\u0000 The fractional model of Liénard's equations is very useful in the study of oscillating circuits. The main aim of this article is to investigate a fractional extension of Liénard's equation by using a fractional operator with exponential kernel. A user friendly analytical algorithm is suggested to obtain the solutions of fractional model of Liénard's equation. The considered computational technique is a combination of q-homotopy analysis method and a relatively new integral transform. The outcomes of the investigation presented in graphical and tabular forms, which reveal that the suggested computational scheme is very accurate and useful for handling such type of fractional order nonlinear mathematical models.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"87 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88166826","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}