scholarly journals Modeling and Analysis of a Large-Scale Double-Level Guyed Mast for Membrane Antennas

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Bingyan Li ◽  
Yuxuan Liu ◽  
Rongqiang Liu ◽  
Hongwei Guo ◽  
Qiang Cong ◽  
...  
Keyword(s):  
Large Scale ◽  
Virtual Work ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Principle Of Virtual Work ◽  
Static Stiffness ◽  
Modeling And Analysis ◽  
Stiffness Matrices ◽  
Guyed Mast ◽  
Equivalent Mechanism

This paper proposes a double-level guyed membrane antenna for stiffness improvement of a large-scale tri-prism deployable mast using the collapsible tubular mast (CTM). Initially, the construction of the antenna and the modeling of the CTM boom are illustrated. Afterwards, the central mast with isosceles triangular cross section is mathematically equivalent to a continuum beam, in which the equations of motion and the constitutive relations are derived. Based on the equivalent central beam, the double-level guyed mast for the membrane antenna is modeled as a 2(3-SPS-S) mechanism, and then velocity Jacobian matrices and stiffness matrices of SPS branches are constructed. Additionally, the total stiffness matrix of the equivalent mechanism is derived with the principle of virtual work and then evaluated as an accurate approach. Finally, with the aim to improve the static stiffness of the double-level guyed mast, the numerical analysis using the Genetic Algorithm (GA) is carried out for optimizing the distribution of guys in terms of anchor positions and attachment heights.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

Effect of the Gravity Force on the Propagation of a Rotating Flexible Rod After Impact

1997 ◽  
Author(s):  
Wei-Hsin Gau
Keyword(s):  
Elastic Waves ◽  
Virtual Work ◽  
Impact Load ◽  
Equations Of Motion ◽  
Fourier Method ◽  
Gravity Force ◽  
Principle Of Virtual Work ◽  
Shape Functions ◽  
Concentrated Force ◽  
The Impact

Abstract The aim of this paper is to analyze the effect of the gravity force on the impact-induced elastic waves which propagate on a radially rotating rod. The equations of motion of the system are developed using the principle of virtual work in dynamics. The impact load is included by the use of the generalized impulse momentum equations, involving the coefficient of restitution. The system is solved using the Fourier method. The deformation of the rod is supposed to be at any instant a linear combination of a set of shape functions. These shape functions are, in this investigation, the modes of a cantilever beam. The weight of the rod is modeled as a concentrated force applied at any instant at the center of the rod.

Development of an Active Curved Beam Model—Part II: Kinetics and Internal Activation

2017 ◽  
Vol 84 (6) ◽  
Author(s):  
Hidenori Murakami
Keyword(s):  
Large Deformation ◽  
Timoshenko Beam ◽  
Virtual Work ◽  
Constitutive Relations ◽  
Differential Forms ◽  
Three Dimensional ◽  
Beam Model ◽  
Cauchy Stress ◽  
Principle Of Virtual Work ◽  
Beam Equations

Utilizing the kinematics, presented in the Part I, an active large deformation beam model for slender, flexible, or soft robots is developed from the d'Alembert's principle of virtual work, which is derived for three-dimensional elastic solids from Hamilton's principle. This derivation is accomplished by refining the definition of the Cauchy stress tensor as a vector-valued 2-form to exploit advanced geometrical operations available for differential forms. From the three-dimensional principle of virtual work, both the beam principle of virtual work and beam equations of motion with consistent boundary conditions are derived, adopting the kinematic assumption of rigid cross sections of a deforming beam. In the derivation of the beam model, Élie Cartan's moving frame method is utilized. The resulting large deformation beam equations apply to both passive and active beams. The beam equations are validated with the previously reported results expressed in vector form. To transform passive beams to active beams, constitutive relations for internal actuation are presented in rate form. Then, the resulting three-dimensional beam models are reduced to an active planar beam model. To illustrate the deformation due to internal actuation, an active Timoshenko beam model is derived by linearizing the nonlinear planar equations. For an active, simply supported Timoshenko beam, the analytical solution is presented. Finally, a linear locomotion of a soft inchworm-inspired robot is simulated by implementing active C1 beam elements in a nonlinear finite element (FE) code.

High-Order Mixture Homogenization of Fiber-Reinforced Composites

1991 ◽  
Vol 113 (4) ◽  
pp. 254-263 ◽  
Author(s):  
A. Toledano ◽  
H. Murakami
Keyword(s):  
Virtual Work ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Material Interfaces ◽  
Explicit Finite Element ◽  
Exact Data ◽  
Tangent Moduli

An asymptotic mixture theory of fiber-reinforced composites with periodic microstructure is presented for rate-independent inelastic responses, such as elastoplastic deformation. Key elements are the modeling capability of simulating critical interaction across material interfaces and the inclusion of the kinetic energy of micro-displacements. The construction of the proposed mixture model, which is deterministic, instead of phenomenological, is accomplished by resorting to a variational approach. The principle of virtual work is used for total quantities to derive mixture equations of motion and boundary conditions, while Reissner’s mixed variational principle (1984, 1986), applied to the incremental boundary value problem yields consistent mixture constitutive relations. In order to assess the model accuracy, numerical experiments were conducted for static and dynamic loads. The prediction of the model in the time domain was obtained by an explicit finite element code. DYNA2D is used to furnish numerically exact data for the problems by discretizing the details of the microstructure. On the other hand, the model capability of predicting effective tangent moduli was tested by comparing results with NIKE2D. In all cases, good agreement was observed between the predicted and exact data for plastic, as well as elastic responses.

Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work

Robotica ◽  
2009 ◽  
Vol 27 (2) ◽  
pp. 259-268 ◽  
Author(s):  
Yongjie Zhao ◽  
Feng Gao
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Principle Of Virtual Work ◽  
Constraint Forces ◽  
Dynamical Equations ◽  
Robot System ◽  
Lead Screw ◽  
Moving Platform

SUMMARYIn this paper, the inverse dynamics of the 6-dof out-parallel manipulator is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. The dynamical equations of motion include the rotation inertia of motor–coupler–screw and the term caused by the external force and moment exerted at the moving platform. The approach described here leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure. Numerical simulation for the inverse dynamics of a 6-dof out-parallel manipulator is illustrated. The whole actuating torques and the torques caused by gravity, velocity, acceleration, moving platform, strut, carriage, and the rotation inertia of the lead screw, motor rotor and coupler have been computed.

Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work

1999 ◽  
Vol 122 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Computational Algorithm ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Principle Of Virtual Work ◽  
Dynamical Equations ◽  
Jacobian Matrices ◽  
Systematic Methodology ◽  
Moving Platform

This paper presents a systematic methodology for solving the inverse dynamics of a Stewart-Gough manipulator. Based on the principle of virtual work and the concept of link Jacobian matrices, a methodology for deriving the dynamical equations of motion is developed. It is shown that the dynamics of the manipulator can be reduced to solving a system of six linear equations in six unknowns. A computational algorithm for solving the inverse dynamics of the manipulator is developed and several trajectories of the moving platform are simulated. [S1050-0472(00)00401-3]

A High-Order Mixture Homogenization of Bi-laminated Composites

1990 ◽  
Vol 57 (2) ◽  
pp. 388-397 ◽  
Author(s):  
H. Murakami ◽  
A. Toledano
Keyword(s):  
Virtual Work ◽  
Laminated Composites ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Mixture Theory ◽  
Model Accuracy ◽  
Exact Data ◽  
Inelastic Responses ◽  
Predicted Values ◽  
The Time Domain

An asymptotic mixture theory of bi-laminated composites with periodic microstructure is presented for rate-independent inelastic responses, such as elastic-plastic deformation. Key elements are the modeling capability of simulating critical interaction between adjacent layers and the inclusion of the kinetic energy of microdisplacements. A variational procedure is adopted in order to construct a mixture model, which is deterministic, instead of phenomenological. The principle of virtual work is used for total quantities to construct mixture equations of motion, while Reissner’s mixed variational principle (1984, 1986) applied to rate boundary value problems is used to yield mixture constitutive relations. In order to assess the model accuracy in the time domain, the predicted values were compared with experimental and numerically exact data. Good agreements between the predicted and experimental or numerically exact data for plastic as well as elastic waves were observed.

Dynamic Modeling and Analysis for a Planar Three Degrees-of-Freedom Manipulator Under Prescribed Mount Motion

2019 ◽  
Author(s):  
Takeyuki Ono ◽  
Ryosuke Eto ◽  
Junya Yamakawa ◽  
Hidenori Murakami
Keyword(s):  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Base Plate ◽  
Moving Frame ◽  
Parallel Plates ◽  
Modeling And Analysis ◽  
Three Degrees Of Freedom

Abstract This paper presents dynamic modeling of a planar, three degrees-of-freedom manipulator consisting of two parallel plates, referred to as top and base plates, which are connected by three actuated legs. When a sensitive equipment is carried by a moving robot or vehicle, it becomes necessary to mount the equipment on a platform which achieves precise positioning for stabilization. The objectives of this paper are to derive analytical equations of motion and apply them to control simulations on the stabilizing planar manipulator. In the derivation of analytical equations of motion, the moving frame method is utilized to describe the kinematics of the two-dimensional multibody system. For the manipulator system comprised of jointed bodies, a graph tree is utilized, which visually illustrates how the constituent bodies are connected to each other. For kinetics, the principle of virtual work is employed to derive the analytical equations of motion for the manipulator system. The resulting equations of motion are used to numerically assess the performance of a sliding mode controller (SMC) to stabilize the top plate from the motion of the translating and rotating base plate. In the numerical simulation, the SMC is compared with a simple PID controller to evaluate both the tracking performance and robustness.

A Modified Numerical Substructure Method for Dynamic Analysis of Vehicle–Track–Bridge Systems

2020 ◽  
Vol 20 (12) ◽  
pp. 2050134
Author(s):  
Yongdou Liu ◽  
Quan Gu
Keyword(s):  
Large Scale ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Interaction Force ◽  
Small Scale ◽  
Computational Accuracy ◽  
Substructure Method ◽  
Dynamic Substructuring ◽  
Nonlinear Force ◽  
Track Bridge

This paper presents a modified numerical substructure method for simulating the dynamic response of vehicle–track–bridge (VTB) systems. The method can be used to analyze large-scale VTB systems accurately and efficiently. Based on the principle of virtual work, the equations of motion are derived for two separate subsystems, i.e. a small-scale of finely modeled VTB substructure and a coarsely meshed large main bridge subsystem using different level of refinement. Different from the conventional dynamic substructuring approaches, the bridge spans close to the vehicle are modeled in both the main and substructure models, and the contradiction of repeatedly modeling is solved using a “nonlinear force corrector”. A special wheel–rail interaction (WRI) element is used to simulate the fast-moving interaction force between the vehicle and rail. In this way, the two models remain unchanged while the vehicle moves forward, and the computational accuracy is the same as the large-scale purely refined model, while the efficiency is significantly improved, particularly, for the large-scale long VTB systems. Two examples of realistic VTB systems with either smooth or un-smooth rails are used to verify the proposed method. The results demonstrate that the presented method has remarkable advantages of computational efficiency and accuracy, providing a practically useful tool for analysis of large-scale VTB systems.

Sign in / Sign up

Export Citation Format

Share Document