Monolithic Coupling of the Pressure and Rigid Body Motion Equations in Computational Marine Hydrodynamics

In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume(FV) framework,where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach(i.e. "strongly coupled" approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy.

Relevance of zero lift drag coefficient and lift coefficient to Mach number for large aspect ratio winged rigid body

Synthetic analysis is conducted to the wind tunnel experiment results of zero lift drag coefficient and lift coefficient for large aspect ratio winged rigid body.By means of wind tunnel experiment data,the dynamics model of the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body is amended.The research indicates that the change trends of zero lift drag coefficient and lift coefficient to Mach number are similar.The calculation result and wind tunnel experiment data all verify the validity of the amended dynamics model by which to estimate the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body,and thus providing some technical reference to aerodynamics character analysis of the same types of winged rigid body.

Implementation of configuration dependent stiffness proportional damping for the dynamics of rigid multi-block systems

The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid muhi-block systems.The stiff- ness proportional damping is constructed for the prescribed damping ratio,based on the non-zero fundamental frequency ef- fective during the time interval while the boundary conditions remain essentially constant.At this time interval,the funda- mental frequency can be estimated without complete eigenvalue analysis.The damping coefficients will vary while the damp- ing ratio remains the same throughout the entire analysis.A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases.These procedures were implemented in the development of the dis- tinet element method for the dynamic analyses of piled multi-block systems.The analysis results |or the single-block and two-block systems were in a good agreement with the analytic predictions.Applications to the seismic analyses of piled four- block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.

Numerical Solution of Constrained Mechanical System Motions Equations and Inverse Problems of Dynamics

In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined.

Augmented Eigenvector and Its Orthogonality of Linear Multi-rigid-flexibel-body System

The orthogonality of eigenvector is a precondition to compute the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method. For a linear multi-rigid-flexible-body system, the eigenfunction does not satisfy the orthogonality under ordinary meaning. A new concept--augmented eigenvector is introduced, which is used to overcome the orthogonality problem of eigenvectors of linear multi-rigid-flexible-body system. The constitution method and the orthogonality of augmented eigenvector are expatiated. After the orthogonality of augmented eigenvector is acquired, the coupling of coordinates in dynamics equations can be released, which makes it possible to analyze exactly the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method.

A SYMPLECTIC ALGORITHM FOR DYNAMICS OF RIGID BODY

For the dynamics of a rigid body with a fixed point based on the quaternion and the corresponding generalized momenta, a displacement-based symplectic integration scheme for differential-algebraic equations is proposed and applied to the Lagrange＇s equations based on dependent generalized momenta. Numerical experiments show that the algorithm possesses such characters as high precision and preserving system invariants. More importantly, the generalized momenta based Lagrange＇s equations show unique advantages over the traditional Lagrange＇s equations in symplectic integrations.

A TENSOR METHOD FOR THE DERIVATION OF THE EQUATIONS OF RIGID BODY DYNAMICS

A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor with zero corotational rate is used to prove the equivalences of five methods, namely, Lagrange's equations, Nielsen's equations, Gibbs-Appell's equations, Kane's equations and the generalized momentum type of Kane's equations. Some differential identities on angular velocity and angular acceleration are given.

MODELING AND ANALYSIS OF A COUPLED RIGID_FLEXIBLE SYSTEM

Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of 'centrifugal potential field', which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius' method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.

Research on the Structural Rigidity Characteristics of a Reconfigurable TBM Thrust Mechanism

To improve the adaptability of TBMs in diverse geological environments,this paper proposes a reconfigurable Type-V thrust mechanism(V-TM)with rearrangeable working states,in which structural stiffness can be automatically altered during operation.Therefore,millions of configurations can be obtained,and thousands of instances of working status per configuration can be set respectively.Nonetheless,the complexity of configurations and diversity of working states contributes to further complications for the structural stiffness algorithm.This results in challenges such as difficulty calculating the payload compliance index and the environment adaptability index.To solve this problem,we use the configuration matrix to describe the relationship between propelling jacks under reconfiguration and adopt pattern vectors to describe the working state of each hydraulic cylinder.Then,both the dynamic compatible equation between propeller forces of the hydraulic cylinders and driving forces,and the kinematic harmonizing equation between the hydraulic cylinder displacements and their deformations are established.Next,we derive the stiffness analytical equation using Hooke’s law and the Jacobian Matrix.The proposed approach provides an effective algorithm to support structural rigidity analysis,and lays a solid theoretical foundation for calculating the performance indexes of the V-TM.We then analyze the rigidity characteristics of typical configurations under different working states,and obtain the main factors affecting structural stiffness of the V-TM.The results show the deviation degree of structural parameters in hydraulic cylinders within the same group,and the working status of propelling jacks.Finally,our constructive conclusions contribute valuable information for matching and optimization by drawing on the factors that affect the structural rigidity of the V-TM.

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.

Dynamic model for landsliding monitoring under rigid body assumption

Based on the assumption that the slope bodies are rigid, the dynamic model of the landsiding (forward model) was put forward. According to the dynamic model, the system equations of Kalman filter were constituted. The mechanical status of a slope was hence combined with the monitoring data by Kalman filter. The model uncertainties or model errors could also be considered through some fictitious observation equations. Different from existed methods, the presented method can make use for not only the statistic information contained in the data but also the information provided by the mechanical and geological aspect of slopes. At last a numerical example was given out to show the feasibility of the method. [

DYNAMIC MODELING AND SIMULATION OF FLEXIBLE CABLE WITH LARGE SAG

Discrete model of flexible cable with large sag is established by using multiple rigid body-spherical hinge model, and dynamic equation of that discrete model is derived according to dynamics theory of multiple rigid body system. Displacement and velocity of system are revised to eliminate violation phenomenon of the differential-algebra equation in numerical simulation based of the theory of generalized inverse of matrices. Numerical simulation proves the validity of our method.

THE INVARIANT MANIFOLD METHOD AND THE CONTROLLABILITY OF NONLINEAR CONTROL SYSTEM

The problem of controllability of nonlinear control system is a significant field which has an extensive prospect of application. A. M. Kovalev of Ukraine Academy of Science applied the oriented manifold method developed in dynamics:of rigid body to nonlinear control system for the first time,and obtained a series of efficient results. Based on Kovalev's oriented manifold method, firstly, by invariant manifold method the problem of controllability of nonlinear control system was studied and the necessary condition of the controllability of a kind of affine nonlinear system was given out. Then the realization of the necessary condition wars discussed. At last, the motion of a rigid body with two rotors,vas, investigated and the necessary condition which is satisfied by this system,vas proved.

Dynamic Analysis on the Main Transmission Device of Wooden Ice Cream Sticks Branding Machine

In order to reduce the labor intensity,improve the production efficiency and enhance the equipment stability and the branding accuracy of the pattern,we have completed a double-row high-efficiency wooden ice cream stick branding machine structural design.The rigid-flexible coupling dynamics model is established and the movement and stress of the first-stage chain drive are calculated and analyzed.The comparison of the theoretical calculation results shows that the dynamic modeling and the structural design of the equipment are reasonable and the result of dynamic calculation also provides the basis of load data for dynamic strength calculation of structural components.

Development and Proof-of-Concept Study of a Novel Intraoperative Surgical Planning Tool for Robotic Arm-Assisted Total Knee Arthroplasty

Background: Intraoperative surgical planning tools (ISPTs) used in current-generation robotic arm-assisted total knee arthroplasty (RTKA) systems (such as Navio® and MAKO®) involve employment of postoperative passive joint balancing. This results in improper ligament tension, which may negatively impact joint stability, which, in turn, may adversely affect patient function after TKA. Methods: A simulation-enhanced ISPT (SEISPT) that provides insights relating to postoperative active joint mechanics was developed. This involved four steps: 1) validation of a multi-body musculoskeletal model;2) optimization of the validated model;3) use of the validated and optimized model to derive knee performance equations (KPEs), which are equations that relate implant component characteristics to implant component biomechanical responses;and 4) optimization of the KPEs with respect to these responses. In a proof-of-concept study, KPEs that involved two com- ponent biomechanical responses that have been shown to strongly correlate with poor proprioception (a common patient complaint post-TKA) were used to calculate optimal positions and orientations of the femoral and tibial components in the TKA design implanted in one subject (as reported in a publicly-available dataset). Results: The differences between the calculated implant positions and orientations and the corresponding achieved values for the implant components in the subject were not similar to component position and orientation errors reported in biomechanical literature studies involving Navio® and MAKO®. Also, we indicate how SEISPT could be incorporated into the surgical workflow of Navio® with minimal disruption and increase in cost. Conclusion: SEISPT is a plausible alternative to current-gen- eration ISPTs.

采用基础激励下力反作用的大挠性结构动力学建模研究

以中心刚体和挠性梁为例,针对缺乏占质量和惯量强势成分中心刚体的刚柔耦合系统进行动力学建模研究.建立了基于基础激励输入和力反作用输出的离散动力学模型,以仿真计算对本文提出的模型进行验证,仿真结果表明,建立的模型解释了动力学刚化现象产生的原因并计算出不同转速下的系统频率,能够准确地解释刚柔耦合系统的动力刚化现象.同时考虑了中心刚体的运动,发现刚体质量和惯量对系统机动后姿态角振动频率有影响.

刚体转动惯量实验的改进

动力学法测刚体转动惯量是通过测量砝码脱落前后2π~6π角位移区间的角加速度平均值得到转动惯量,该实验要求砝码脱落前后系统为匀变速运动,但该前提条件并不能得到很好保证,从而引入了系统误差.本文利用黑白条码纸带、光纤放大器、数据采集卡等对实验装置进行了改进,同时优化了数据处理方法,减弱了对匀变速运动这一前提的要求.对照实验测量结果表明:改进后的实验装置的测量误差减小,对平行轴定理的验证效果得到了提升.

纵置板簧式非独立悬架与整体式转向系统的运动学分析与优化

针对汽车悬架系统与转向系统在汽车行驶过程中存在运动干涉、轮胎磨损等问题,本文基于汽车前悬架与整体式转向系统刚体运动学模型,采用三维空间坐标变换法对系统关键点以及重要杆系的位置参数变化进行了分析与计算,并以实际内、外前轮转角关系与理想阿克曼转角关系存在差值最小为目标,基于iSIGHT与MATLAB集成仿真技术,进行设计变量DOE分析与优化计算,经过比较分析,优化后的设计方案可有效降低轮胎磨损,提升汽车的行驶性能。

舰载机及其尾钩的动力学建模与分析

为了研究舰载机尾钩的动力学特性对阻拦结果的影响,建立了舰载机的平面运动刚体动力学模型和考虑尾钩纵向缓冲作用的尾钩空间运动刚体动力学模型。使用拉格朗日第一类方程建立了舰载机及其尾钩之间的转动副模型,进而构建了舰载机及其尾钩组成的系统动力学模型,将该模型与阻拦装置的系统模型联合组成了完整的阻拦动态仿真模型。开展了飞机的阻拦试验,并将试验结果与仿真结果进行对比分析,结果验证了舰载机及其尾钩动力学模型的有效性和准确性,揭示了尾钩特性对舰载机阻拦过载的重要影响。

花键约束下变形摩擦片角向摆动的数值分析

为了揭示离合器分离状态下摩擦元件变形前后的动力学特性差异,本文研究了花键约束下不同变形程度摩擦片的角向摆动特性,分析了花键界面和翘曲变形对摆动的影响。本文对平直摩擦片进行了力学分析,并建立了平直片角向摆动的动力学模型。在此基础上,对平直片引入薄板的变形函数,考虑几何差异推导出了变形摩擦片的摆动模型。同时,与经典边界条件对比,在摩擦片内径的花键约束处采用了摩擦边界,并且基于几何结构推导出了最大允许摆动角。通过数值仿真,在时域和频域分析了各影响因素对摆动的影响。结果表明:旋转的摩擦片受扰动后,角向摆动频率随转速的增加而增加,而翘曲变形会降低摆动频率。此外,最大摆动角度在低转速时会延长摩擦片摆动的时间,摩擦力则会降低摆动的时间。