Generalized Equations of Motion for the Dynamic Analysis of Elastic Mechanism Systems

1984 ◽  
Vol 106 (4) ◽  
pp. 243-248 ◽  
Author(s):  
D. A. Turcic ◽  
Ashok Midha
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Single Type ◽  
Generalized Equations ◽  
Element Analysis ◽  
Beam Elements ◽  
Elastic Mechanism ◽  
Element Type

Until recently, vibration effects have generally been neglected in the design of high-speed machines and mechanisms. This has been primarily due to the complexity of the mathematical analysis of mechanisms with elastic links. With the advent of high-speed computers and structural dynamics techniques, such as finite element analysis, this is no longer regarded as such a formidable task. To date, with few exceptions, the analysis of elastic mechanism systems have been limited to a single type of mechanism (i.e., a four-bar or slider-crank) modeled with a small number of simple finite elements (usually beam elements). This paper develops the generalized equations of motion for elastic mechanism systems by utilizing finite element theory. The derivation and final form of the equations of motion provide the capability to model a general two- or three-dimensional complex elastic mechanism, to include the nonlinear rigid-body and elastic motion coupling terms in a general representation, and to allow any finite element type to be utilized in the model. A discussion of a solution method, applications, as well as an experimental investigation of an elastic four-bar mechanism will be presented in subsequent publications.

Mechanical and Optimization Analyses for Novel Wound Composite Axial Impeller

2009 ◽  
Author(s):  
Jifeng Wang ◽  
Qubo Li ◽  
Norbert Mu¨ller
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
High Speed ◽  
High Performance ◽  
Low Cost ◽  
Three Dimensional ◽  
Von Mises Stress ◽  
Loading Conditions ◽  
Element Analysis ◽  
Wound Composite

A mechanical and optimal analyses procedure is developed to assess the stresses and deformations of Novel Wound Composite Axial-Impeller under loading conditions particular to centrifuge. This procedure is based on an analytical method and Finite Element Analysis (FEA, commercial software ANSYS) results. A low-cost, light-weight, high-performance, composite turbomachinery impeller from differently designed patterns will be evaluated. Such impellers can economically enable refrigeration plants using water as a refrigerant (R718). To create different complex patterns of impellers, MATLAB is used for creating the geometry of impellers, and CAD software UG is used to build three-dimensional impeller models. Available loading conditions are: radial body force due to high speed rotation about the cylindrical axis and fluid forces on each blade. Two-dimensional plane stress and three-dimensional stress finite element analysis are carried out using ANSYS to validate these analytical mechanical equations. The von Mises stress is investigated, and maximum stress and Tsai-Wu failure criteria are applied for composite material failure, and they generally show good agreement.

scholarly journals New Analytical Model Used in Finite Element Analysis of Solids Mechanics

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1401 ◽  
Author(s):  
Sorin Vlase ◽  
Adrian Eracle Nicolescu ◽  
Marin Marin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Elastic Solid ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Element Analysis ◽  
Elastic Multibody System

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

Three-dimensional analyses of two high-speed trains crossing on a bridge

2003 ◽  
Vol 217 (2) ◽  
pp. 99-110
Author(s):  
H-T Lin ◽  
S-H Ju
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
High Speed ◽  
Three Dimensional ◽  
Dynamic Effect ◽  
Response Ratio ◽  
Element Analysis ◽  
Dynamic Finite Element Analysis ◽  
High Speed Trains ◽  
The One

This paper investigates the dynamic characteristics of the three-dimensional vehicle-bridge system when two high-speed trains are crossing on a bridge. Multispan bridges with slender piers and simply supported beams were used in the dynamic finite element analysis. A response ratio (RR) was defined in this study to represent the ratio of the vehicle-bridge interaction of two-way trains to that of a one-way train. The finite element results indicate that this ratio increases significantly when two-way trains run near the same speed, and the maximum value is approximately equal to or smaller than two for the vertical dynamic response. This means that the maximum dynamic response of the two-way trains is at most twice that of the one-way train. When the two-way train speeds are sufficiently different, the response ratio approaches one on average, which means that the dynamic effect of the two-way train is similar to that of the one-way train. Finite element results also indicate that the averaged response ratio in the three global directions is about 1.65 when the two-way trains run at the same speed.

Analysis of a High-Speed Flexible Four-Bar Linkage: Part I—Formulation and Solution

1989 ◽  
Vol 111 (1) ◽  
pp. 35-41 ◽  
Author(s):  
F. W. Liou ◽  
A. G. Erdman
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Equations Of Motion ◽  
Computer Code ◽  
Element Analysis ◽  
Virtual Displacement ◽  
Axial Forces ◽  
Direct Integration Method ◽  
Analysis Computer ◽  
Four Bar Linkage

Derived from the principle of virtual displacement, a general finite element analysis computer code (FEMAP) of the flexible four-bar linkage is developed on the Apollo computer. In this part, virtual displacement method is presented as a basic theory for the general formulation of the equations of motion. Based on these results, a general finite element computer code of planar four-bar linkage is developed. All the links of the mechanism are considered to be flexible. The nonlinear terms such as coupling between the rigid body and elastic deformation terms and the effect of the axial forces are included. The Newmark direct integration method is used as solution scheme.

A Finite Element Analysis of the Navier-Stokes Equations Applied to High Speed Thin Film Lubrication

1987 ◽  
Vol 109 (1) ◽  
pp. 71-76 ◽  
Author(s):  
J. O. Medwell ◽  
D. T. Gethin ◽  
C. Taylor
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Thin Film Lubrication ◽  
Element Analysis ◽  
Navier Stokes Equations ◽  
Film Lubrication

The performance of a cylindrical bore bearing fed by two axial grooves orthogonal to the load line is analyzed by solving the Navier-Stokes equations using the finite element method. This produces detailed information about the three-dimensional velocity and pressure field within the hydrodynamic film. It is also shown that the method may be applied to long bearing geometries where recirculatory flows occur and in which the governing equations are elliptic. As expected the analysis confirms that lubricant inertia does not affect bearing performance significantly.

A Static and Dynamic Model of Geared Transmissions by Combining Substructures and Elastic Foundations—Applications to Thin-Rimmed Gears

2006 ◽  
Vol 129 (2) ◽  
pp. 184-194 ◽  
Author(s):  
M. N. Bettaïeb ◽  
P. Velex ◽  
M. Ajmi
Keyword(s):  
Finite Element ◽  
Contact Stiffness ◽  
Equations Of Motion ◽  
Hybrid Approach ◽  
Three Dimensional ◽  
Element Model ◽  
3D Finite Element ◽  
Elastic Foundations ◽  
Beam Elements ◽  
Set Up

The present work is aimed at predicting the static and dynamic behavior of geared transmissions comprising flexible components. The proposed model adopts a hybrid approach, combining classical beam elements, elastic foundations for the simulation of tooth contacts, and substructures derived from three-dimensional (3D) finite element grids for thin-rimmed gears and their supporting shafts. The pinion shaft and body are modeled via beam elements which simulate bending, torsion and traction. Tooth contact deflections are described using time-varying elastic foundations (Pasternak foundations) connected by independent contact stiffness. In order to account for thin-rimmed gears, a 3D finite element model of the gear (excluding teeth) is set up and a pseudo-modal reduction technique is used prior to solving the equations of motion. Depending on the gear structure, the results reveal a potentially significant influence of thin rims on both quasi-static and dynamic tooth loading.

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