Dynamic Analysis of Three-Dimensional Mechanisms in “Natural” Coordinates

1987 ◽  
Vol 109 (4) ◽  
pp. 460-465 ◽  
Author(s):  
J. Garci´a de Jalo´n ◽  
J. Unda ◽  
A. Avello ◽  
J. M. Jime´nez
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Equilibrium ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Natural Coordinates ◽  
Constant Mass ◽  
Equilibrium Equations ◽  
Constraint Equations ◽  
Comparative Results ◽  
Value Decomposition

In this paper a new method for the dynamic analysis of three-dimensional mechanisms is presented. This method is based on the use, as mechanism coordinates, of Cartesian coordinates and components of some points and vectors rigidly attached to every element. With these coordinates the constraint equations are very easily formulated. A constant mass matrix has been derived for an element with two points and two vectors. Two simple and efficient methods to establish the dynamic equilibrium equations are presented. The use of the singular value decomposition is also included. Finally some comparative results are presented.

scholarly journals A GIS-based three-dimensional landslide generated waves height calculation method

2019 ◽  
Author(s):  
Guo Yu ◽  
Mowen Xie ◽  
Lei Bu ◽  
Asim Farooq
Keyword(s):  
Spatial Data ◽  
Calculation Method ◽  
Dynamic Equilibrium ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analysis Model ◽  
Equilibrium Equations ◽  
Gis Environment ◽  
Spatial State ◽  
Surge Height

Abstract. Combined with the spatial data processing capability of geographic information systems (GIS), a three-dimensional (3D) landslide surge height calculation method is proposed based on grid column units. First, the data related to the landslide are rasterized to form grid columns, and a force analysis model of 3D landslides is established. Combining the vertical strip method with Newton's laws of motion, dynamic equilibrium equations are established to solve for the surge height. Moreover, a 3D landslide surge height calculation expansion module is developed in the GIS environment, and the results are compared with those of the two-dimensional Pan Jiazheng method. Comparisons show that the maximum surge height obtained by the proposed method is 24.6 % larger than that based on the Pan Jiazheng method. Compared with the traditional two-dimensional method, the 3D method proposed in this paper better represents the actual spatial state of the landslide and is more suitable for risk assessment.

Formulation of Three-Dimensional Rigid-Flexible Multibody Systems

2007 ◽  
Author(s):  
Daniel Garci´a-Vallejo ◽  
Jose´ L. Escalona ◽  
Juana M. Mayo ◽  
Jaime Domi´nguez
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Three Dimensional ◽  
Natural Coordinates ◽  
Flexible Multibody System ◽  
Absolute Nodal Coordinates ◽  
Constraint Equations ◽  
Flexible Multibody ◽  
The Matrix ◽  
Nodal Coordinates

Multibody systems generally contain solids the deformations of which are appreciable and which decisively influence the dynamics of the system. These solids have to be modeled by means of special formulations for flexible solids. At the same time, other solids are of such a high stiffness that they may be considered rigid, which simplifies their modeling. For these reasons, for a rigid-flexible multibody system, two types of formulations co-exist in the equations of the system. Among the different possibilities provided in bibliography on the material, the formulation in natural coordinates and the formulation in absolute nodal coordinates are utilized in this article to model the rigid and flexible solids, respectively. This article contains a mixed formulation based on the possibility of sharing coordinates between a rigid solid and a flexible solid. In addition, the fact that the matrix of the global mass of the system is shown to be constant and that many of the constraint equations obtained upon utilizing these formulations are linear and can be eliminated. In this work, the formulation presented is utilized to simulate a mechanism with both rigid and flexible components.

Describing Rigid-Flexible Multibody Systems Using Natural and Absolute Nodal Coordinates

2003 ◽  
Author(s):  
D. Garci´a-Vallejo ◽  
J. L. Escalona ◽  
J. Mayo ◽  
J. Domi´nguez ◽  
A. A´lvarez
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Linear Constraint ◽  
Rigid Bodies ◽  
Natural Coordinates ◽  
Flexible Bodies ◽  
Absolute Nodal Coordinate ◽  
Constraint Equations ◽  
Non Linear ◽  
The Absolute

This paper deals with the dynamic description of interconnected rigid and flexible bodies. The absolute nodal coordinate formulation is used to describe the motion of flexible bodies and natural coordinates are used to describe the motion of the rigid bodies. The absolute nodal coordinate formulation is a non-incremental finite element procedure specially suitable for the dynamic analysis of flexible bodies exhibiting rigid body motion and large deformations. Nodal coordinates, that include global position vectors and global slopes, are all defined in a global inertial coordinate system. The advantages of using the absolute nodal coordinate formulation include constancy in the mass matrix, and the need for only a minimal set of non-linear constraint equations when connecting different flexible bodies with kinematic joints. When bodies within the system can be considered rigid, the above-mentioned advantages of the equations of motion can be preserved provided natural coordinates are used. In the natural coordinates method, the coordinates used to describe rigid bodies include global position vectors of basic points and global unit vectors. As in the absolute nodal coordinate formulation, rotational coordinates are avoided and the mass matrix is also constant. This paper provides computer implementation of this formulation that only uses absolute coordinates for general two-dimensional multibody systems. The constraint equations needed to define kinematic joints between different bodies can be linear or non-linear. The linear constraint equations, that include those needed to define rigid connections and revolute joints, are used to define constant connectivity matrices that reduce the size of the system coordinates. These constant connectivity matrices are also used to obtain the system mass matrix and the system generalized forces. However, the non-linear constraint equations that account for sliding joints, require the use of the Lagrange multipliers technique. Numerical examples are provided and compared to the results of other existing formulations.

Study of Flat Belt Drive Mechanics

2009 ◽  
Vol 419-420 ◽  
pp. 265-268 ◽  
Author(s):  
Da Yu Zheng ◽  
Xiang Yi Guan ◽  
Xin Chen ◽  
Zhong Lin Zhang
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Equilibrium ◽  
Inertial Force ◽  
Slip Angle ◽  
Belt Drive ◽  
Equilibrium Equations ◽  
Calculation Results ◽  
Geometric Boundary ◽  
Boundary Equations ◽  
Maximum Transmission

The Mechanics between belt and pulley in flat belt drive running is complicated. Since no inertial force or only partial inertial force was taken into account before, it is necessary to add in the inertial affection fully for more accurate dynamic analysis modeling of the flat belt drive. In the assumption that belt material is deformed in linear elasticity and the flat belt drive is running in steady state, the dynamic equilibrium equations of radial and tangent directions are presented and simplified through the belt infinitesimal element processing and the equations associated with mechanical coefficients and dimensions are also derived. After building up the relations of constitutive equations and geometric boundary equations, the solutions to the dynamic differential equations have been found. The sample flat belt drive is introduced for performing method application and obtained adequate calculation results. It is concluded that the presented method calculation results make the maximum transmission momentum tends to be smaller and the slip angle tends to be bigger than the traditional one. And the fluctuation range is mainly depending on the belt speed and the belt stiffness. This method is valuable for dynamic analysis and the design methodology of belt drive.

scholarly journals Dynamic Equilibrium Equations in Unified Mechanics Theory

2021 ◽  
Vol 2 (1) ◽  
pp. 63-80
Author(s):  
Noushad Bin Jamal Bin Jamal M ◽  
Hsiao Wei Lee ◽  
Chebolu Lakshmana Rao ◽  
Cemal Basaran
Keyword(s):  
Energy Loss ◽  
Entropy Generation ◽  
Equilibrium Equation ◽  
Dynamic Equilibrium ◽  
Free Vibration Analysis ◽  
Newtonian Mechanics ◽  
Equilibrium Equations ◽  
Time Coordinate ◽  
Proposed Model ◽  
Laws Of Thermodynamics

Traditionally dynamic analysis is done using Newton’s universal laws of the equation of motion. According to the laws of Newtonian mechanics, the x, y, z, space-time coordinate system does not include a term for energy loss, an empirical damping term “C” is used in the dynamic equilibrium equation. Energy loss in any system is governed by the laws of thermodynamics. Unified Mechanics Theory (UMT) unifies the universal laws of motion of Newton and the laws of thermodynamics at ab-initio level. As a result, the energy loss [entropy generation] is automatically included in the laws of the Unified Mechanics Theory (UMT). Using unified mechanics theory, the dynamic equilibrium equation is derived and presented. One-dimensional free vibration analysis with frictional dissipation is used to compare the results of the proposed model with that of a Newtonian mechanics equation. For the proposed entropy generation equation in the system, the trend of predictions is comparable with the reported experimental results and Newtonian mechanics-based predictions.

Consistent Hydrodynamic Mass for Parallel Prismatic Beams in a Fluid-Filled Container

1984 ◽  
Vol 106 (3) ◽  
pp. 270-275
Author(s):  
J. F. Loeber
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Incompressible Fluid ◽  
Finite Element Methods ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Beam Length ◽  
Step Process ◽  
Beam Bending

In this paper, representation of the effects of incompressible fluid on the dynamic response of parallel beams in fluid-filled containers is developed using the concept of hydrodynamic mass. Using a two-step process, first the hydrodynamic mass matrix per unit (beam) length is derived using finite element methods with a thermal analogy. Second, this mass matrix is distributed in a consistent mass fashion along the beam lengths in a manner that accommodates three-dimensional beam bending plus torsion. The technique is illustrated by application to analysis of an experiment involving vibration of an array of four tubes in a fluid-filled cylinder.

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