Non-Linear Constraints and Stiffness Representations in Simple Flexible-Body Dynamic Beam Formulations

2003 ◽  
Vol 9 (8) ◽  
pp. 911-929 ◽  
Author(s):  
William Haering
Keyword(s):  
Linear Constraint ◽  
Linear Constraints ◽  
Model Verification ◽  
Lumped Parameter Model ◽  
Flexible Body ◽  
Flexible Beam ◽  
Lumped Parameter ◽  
Non Linear ◽  
Linear Spring ◽  
Insight Into

Abstract: A simple discrete four-degree-of-freedom (lumped parameter) model representing a flexible beam undergoing large overall planar prescribed motion has been developed. It serves as a simple tool to investigate two previously studied problems involving flexible-body beam dynamics, namely those involving bending and membrane stiffness dominated behavior. The tool is used to investigate the requirements to accurately solve these problems using non-linear constraints and a non-linear spring representation. The validity of this model is demonstrated by comparing results to those previously published for continuous flexible-body beam formulations. One of these continuous representations is modified to include a non-linear tether spring representation. This allows additional model verification as well as insight into the non-linear constraint and stiffness representations. Taken in its entirety, this investigation demonstrates the utility of these simple lumped parameter models, by showing their ability to provide rapid insight into the behavior of the more complicated continuous models, as well as the system in general.

Non-linear dynamic simulation of mechanical periodicity of end-diastolic volume of left ventricle under the influence of baroreflex

2006 ◽  
Vol 220 (3) ◽  
pp. 357-366 ◽  
Author(s):  
Q Wang ◽  
S Xu ◽  
D Chen ◽  
M Collins
Keyword(s):  
Left Ventricle ◽  
Vascular System ◽  
Element Model ◽  
Baroreceptor Reflex ◽  
Lumped Parameter Model ◽  
Linear Dynamic ◽  
End Diastolic Volume ◽  
Lumped Parameter ◽  
Non Linear ◽  
Mechanical Periodicity

Mechanical periodicity (MP) of the end-diastolic volume (EDV) of the left ventricle (LV) is closely associated with cardiovascular pathophysiology. On the basis of the Starling's law of the LV and Burattini and Gnudi's four-element model of the vascular system, and considering baroreceptor reflex, a non-linear dynamic lumped-parameter model is proposed. This simulates the MP phenomena of the EDV by solving a series of one-dimensional discrete non-linear dynamic equations. The results demonstrate that excessive deviations of some physiological parameters often induce MP - the unstable phenomena of EDV - and verify that the effects of baroreceptor reflex enhance the ability of the human physiological system to maintain stability.

A Lumped Parameter Model to Analyse the Dynamic Load Sharing in Planetary Gears with Planet Errors

2011 ◽  
Vol 86 ◽  
pp. 374-379 ◽  
Author(s):  
Xiao Yu Gu ◽  
Philippe Velex
Keyword(s):  
High Speed ◽  
Load Sharing ◽  
Lumped Parameter Model ◽  
Mesh Stiffness ◽  
Planetary Gears ◽  
Position Errors ◽  
Load Distributions ◽  
Lumped Parameter ◽  
Non Linear ◽  
Dynamic Load Sharing

A non-linear dynamic model of planetary gears is presented which accounts for planet position errors, time-varying non-linear mesh stiffness along with the interactions between deflections and instantaneous meshing conditions. The quasi-static load distributions agree well with the experimental results in the literature thus validating the contact simulation. Extensions towards high-speed behaviour are presented which show how dynamic effects may impact the instantaneous load sharing amongst the planets.

scholarly journals Theoretical Analysis and Optimization of a Gloved Hand-arm System

2021 ◽  
Author(s):  
Oreoluwa Alabi ◽  
Sunit Kumar Gupta ◽  
Oumar Barry
Keyword(s):  
Harmonic Balance ◽  
Equations Of Motion ◽  
Biomechanical Model ◽  
Lumped Parameter Model ◽  
Human Hand ◽  
Governing Equations ◽  
Lumped Parameter ◽  
Hand Tool ◽  
Modeling Techniques ◽  
Linear Spring

Abstract Studies have shown that isolators in the form of anti-vibration gloves effectively reduce the transmission of unwanted vibration from vibrating equipment to the human hand. However, as most of these studies are based on experimental or modeling techniques, the level of effectiveness and optimum glove properties for better performance remains unclear. To fill this gap, hand-arm system dynamics with and without gloves are studied analytically in this work. In the current work, we use a lumped parameter model of the hand-arm system, with hand-tool interaction modeled as a linear spring-damper system. The resulting governing equations of motion are solved analytically using the method of harmonic balance. Parametric analysisis performed on the biomechanical model of the hand-armsystem with and without a glove to identify key design pa-rameters. It is observed that the effect of glove parameters on its performance is not repetitive and changes in the studied different frequency ranges. This observation further motivates us to optimize the glove parameters to minimize the overall transmissibility in different frequency ranges.

Large Amplitude Free Vibration Analysis of a Rotating Beam with Non-linear Spring and Mass System

2005 ◽  
Vol 11 (12) ◽  
pp. 1511-1533 ◽  
Author(s):  
S. K. Das ◽  
P. C. Ray ◽  
G. Pohit
Keyword(s):  
Free Vibration Analysis ◽  
Linear Constraint ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Rotating Beam ◽  
Mass System ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Out Of Plane ◽  
Linear Spring

The free, out-of-plane vibration of a rotating beam with a non-linear spring-mass system has been investigated. The non-linear constraint appears in the boundary condition. The solution is obtained by applying the method of multiple time-scales directly to the non-linear partial differential equations and the boundary conditions. The results of the linear frequencies match well with those obtained in the literature. Subsequent non-linear study indicates that there is a pronounced effect of the spring and its mass. The influence of the spring-mass location on frequencies is also investigated for the non-linear frequencies of the rotating beam.

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