Modeling the Climber Fall Arrest Dynamics

2005 ◽  
Author(s):  
Lionel Manin ◽  
Jarir Mahfoudh ◽  
Matthieu Richard ◽  
David Jauffres
Keyword(s):  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Close Approximation ◽  
Non Linear ◽  
The Future ◽  
Safety Recommendations ◽  
Improved Design ◽  
Fall Arrest

Sports and mountaineering activities are becoming more and more popular. Equipment constructors seek to develop products and devices that are easy to use and that take into account all safety recommendations. PETZL and INSA have collaborated to develop a model for the simulation of displacements and efforts involved during the fall of a climber in the “safety chain”. The model is based on the classical equations of motion, in which climber and belayer are considered as rigid masses, while the rope is considered as a series of non-linear stiffness passing through several devices as brakes and runners. The main goal is to predict the forces in the rope and on the return anchor at the first rebound of the fall. Experiments were first performed in order to observe and determine the dynamic characteristics of the rope, and then to validate results stemming from simulations. Several fall configurations are simulated, and the model performs satisfactorily. It also provides a close approximation of the phenomena observed experimentally. The model enables the assessment of the existing equipments and the improved design of the future one.

scholarly journals Dynamic Quality of an Aerostatic Thrust Bearing with a Microgroove and Support Center on Elastic Suspension

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1492
Author(s):  
Vladimir Kodnyanko ◽  
Stanislav Shatokhin ◽  
Andrey Kurzakov ◽  
Lilia Strok ◽  
Yuri Pikalov ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Negative Impact ◽  
Aerostatic Bearing ◽  
Elastic Suspension ◽  
Variable Parameters ◽  
Aerostatic Bearings ◽  
Improved Design ◽  
Dynamic Quality ◽  
Bearing Layer

The disadvantage of aerostatic bearings is their low dynamic quality. The negative impact on the dynamic characteristics of the bearing is exerted by the volume of air contained in the bearing gap, pockets, and microgrooves located at the outlet of the feeding diaphragms. Reducing the volume of air in the flow path is a resource for increasing the dynamic quality of the aerostatic bearing. This article presents an improved design of an axial aerostatic bearing with simple diaphragms, an annular microgroove, and an elastic suspension of the movable center of the supporting disk. A mathematical model is presented and a methodology for calculating the static characteristics of a bearing and dynamic quality indicators is described. The calculations were carried out using dimensionless quantities, which made it possible to reduce the number of variable parameters. A new method for solving linearized and Laplace-transformed boundary value problems for transformants of air pressure dynamic functions in the bearing layer was applied, which made it possible to obtain a numerical solution of problems sufficient for practice accuracy. The optimization of the criteria for the dynamic quality of the bearing was carried out. It is shown that the use of an elastic suspension of the support center improves its dynamic characteristics by reducing the volume of compressed air in the bearing layer and choosing the optimal volume of the microgroove.

GPR-based novel approach for non-linear aerodynamic modelling from flight data

2018 ◽  
Vol 123 (1259) ◽  
pp. 79-92
Author(s):  
A. Kumar ◽  
A. K. Ghosh
Keyword(s):  
Aerodynamic Force ◽  
Equations Of Motion ◽  
Gaussian Process Regression ◽  
Likelihood Estimation ◽  
Flight Data ◽  
Novel Approach ◽  
Non Linear ◽  
Research Aircraft ◽  
Novel Method ◽  
Aerodynamic Modelling

ABSTRACTIn this paper, a Gaussian process regression (GPR)-based novel method is proposed for non-linear aerodynamic modelling of the aircraft using flight data. This data-driven regression approach uses the kernel-based probabilistic model to predict the non-linearity. The efficacy of this method is examined and validated by estimating force and moment coefficients using research aircraft flight data. Estimated coefficients of aerodynamic force and moment using GPR method are compared with the estimated coefficients using maximum-likelihood estimation (MLE) method. Estimated coefficients from the GPR method are statistically analysed and found to be at par with estimated coefficients from MLE, which is popularly used as a conventional method. GPR approach does not require to solve the complex equations of motion. GPR further can be directed for the generalised applications in the area of aeroelasticity, load estimation, and optimisation.

scholarly journals Is our perception of the spread of COVID-19 inherently inaccurate?

2021 ◽  
Author(s):  
Alexander Maier
Keyword(s):  
Decision Making ◽  
Subjective Perception ◽  
Logarithmic Function ◽  
Original Formulation ◽  
Global Crisis ◽  
New Information ◽  
The World ◽  
Non Linear ◽  
The Future ◽  
Linear Nature

One of the most fundamental insights into the nature of our subjective perception of the world around us is that it is not veridical. In other words, we tend to not perceive information about the world around us accurately. Instead, our brains interpret new information through a host of innate and learned mechanisms that can introduce bias and distortions One of the best studied mechanisms that guide – and distort – our perception is the psychophysical Weber-Fechner law. According to this empirically derived, mathematically formulated law we tend to put more emphasis on smaller deviations in size while underestimating larger changes. The original formulation of the Weber-Fechner law takes the shape of a logarithmic function and is commonly applied to somatosensory perception such as the weight of an object. However, later work showed that the Weber-Fechner law can be generalized and describe a large variety of perceived changes in magnitude that even go beyond the sensory domain. Here we investigate the hypothesis that our perception of data associated with the spread of COVID-19 and similar pandemics is governed by the same psychophysical laws. Based on several recently published studies, we demonstrate that the Weber-Fechner law can be shown to directly affect the decision-making of officials in response to this global crisis as well as the greater public at large. We discuss how heightened awareness of the non-linear nature of subjective perception could help alleviate problematic judgements in similar situations in the future.

The Static Aeroelasticity of Slender Configurations

1963 ◽  
Vol 14 (1) ◽  
pp. 75-104 ◽  
Author(s):  
G. J. Hancock
Keyword(s):  
Static Stability ◽  
Aerodynamic Forces ◽  
Flexible Aircraft ◽  
The Past ◽  
Plate Models ◽  
Non Linear ◽  
The Future ◽  
Static Aeroelasticity ◽  
Definition Of ◽  
Image Position

SummaryThe validity and applicability of the static margin (stick fixed) Kn,where as defined by Gates and Lyon is shown to be restricted to the conventional flexible aircraft. Alternative suggestions for the definition of static margin are put forward which can be equally applied to the conventional flexible aircraft of the past and the integrated flexible aircraft of the future. Calculations have been carried out on simple slender plate models with both linear and non-linear aerodynamic forces to assess their static stability characteristics.

Non-Linear Vibrations of Plates Under Thermal and Mechanical Loads

2005 ◽  
Author(s):  
P. Ribeiro
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Implicit Time ◽  
Linear Elastic ◽  
Time Integration Method ◽  
Thermal Fields ◽  
Non Linear ◽  
Linear Vibrations ◽  
The Time Domain ◽  
Constitutive Material

The geometrically non-linear vibrations of plates under the combined effect of thermal fields and mechanical excitations are analyzed. With this purpose, an accurate model based on a p-version, hierarchical, first-order shear deformation finite element is employed. The constitutive material of the plates is linear elastic and isotropic. The equations of motion are solved in the time domain by an implicit time integration method. The temperature and the amplitude of the mechanical excitation are varied, and transitions from periodic to non-periodic motions are found.

scholarly journals The future of theh-index: Can bending an already non-linear metric work?

BioEssays ◽  
2012 ◽  
Vol 34 (10) ◽  
pp. 821-822
Author(s):  
Andrew Moore
Keyword(s):  
Non Linear ◽  
The Future

Non-Linear Dynamic Analysis of a Cable-Stayed Beam

2005 ◽  
Author(s):  
Carlos E. N. Mazzilli ◽  
Franz Rena´n Villarroel Rojas
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Multiple Scale ◽  
Local Mode ◽  
Numerical Application ◽  
Global Mode ◽  
Lower Mode ◽  
Reduced Equations ◽  
External Resonance ◽  
Non Linear

The dynamic behaviour of a simple clamped beam suspended at the other end by an inclined cable stay is surveyed in this paper. The sag due to the cable weight, as well as the non-linear coupling between the cable and the beam motions are taken into account. The formulation for in-plane vibration follows closely that of Gattulli et al. [1] and confirms their findings for the overall features of the equations of motion and the system modal properties. A reduced non-linear mathematical model, with two degrees of freedom, is also developed, following again the steps of Gattulli and co-authors [2,3]. Hamilton’s Principle is evoked to allow for the projection of the displacement field of both the beam and the cable onto the space defined by the first two modes, namely a “global” mode (beam and cable) and a “local” mode (cable). The method of multiple scales is then applied to the analysis of the reduced equations of motion, when the system is subjected to the action of a harmonic loading. The steady-state solutions are characterised in the case of internal resonance between the local and the global modes, plus external resonance with respect to either one of the modes considered. A numerical application is presented, for which multiple-scale results are compared with those of numerical integration. A reasonable qualitative and quantitative agreement is seen to happen particularly in the case of external resonance with the higher mode. Discrepancies should obviously be expected due to strong non-linearities present in the reduced equations of motion. That is specially the case for external resonance with the lower mode.

Formulation of Multiple Belt System and its Dynamic Analysis

1993 ◽  
Author(s):  
Takuzo Iwatsubo ◽  
Shiro Arii ◽  
Kei Hasegawa ◽  
Koki Shiohata
Keyword(s):  
Computer Program ◽  
Dynamic Analysis ◽  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Transient Responses ◽  
Fundamental Idea ◽  
Linear Equations Of Motion ◽  
Simulation Results ◽  
Belt System

Abstract This paper presents a method for analyzing the dynamic characteristics of driving systems consisting of multiple belts and pulleys. First, the algorithm which derives the linear equations of motion of arbitrary multi-coupled belt systems is shown. Secondly, by using the algorithm, the computer program which formulates the equations of motion and calculates the transient responses of the belt system is presented. The fundamental idea of the algorithm is as follows: Complicated belt systems consisting of multiple belts and pulleys are regarded as combinations of simple belt systems consisting of a single belt and some pulleys. Therefore, the equations of motion of the belt systems can be derived by the superposition of the equations of motion of the simple belt systems. By means of this method, the responses of arbitrary multi-coupled belt systems can be calculated. Finally, to verify the usefulness of this method, the simulation results are compared with the experimental results.

The Role of Modal Coupling on the Non-Linear Response of Cylindrical Shells Subjected to Dynamic Axial Loads

2000 ◽  
Author(s):  
Paulo B. Gonçalves ◽  
Zenón J. G. N. Del Prado
Keyword(s):  
Dynamic Instability ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Parametric Instability ◽  
Compressive Load ◽  
Basins Of Attraction ◽  
Dynamic Component ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Low Dimensional

Abstract This paper discusses the dynamic instability of circular cylindrical shells subjected to time-dependent axial edge loads of the form P(t) = P0+P1(t), where the dynamic component p1(t) is periodic in time and P0 is a uniform compressive load. In the present paper a low dimensional model, which retains the essential non-linear terms, is used to study the non-linear oscillations and instabilities of the shell. For this, Donnell’s shallow shell equations are used together with the Galerkin method to derive a set of coupled non-linear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. To study the non-linear behavior of the shell, several numerical strategies were used to obtain Poincaré maps, stable and unstable fixed points, bifurcation diagrams and basins of attraction. Particular attention is paid to two dynamic instability phenomena that may arise under these loading conditions: parametric instability and escape from the pre-buckling potential well. The numerical results obtained from this investigation clarify the conditions, which control whether or not instability may occur. This may help in establishing proper design criteria for these shells under dynamic loads, a topic practically unexplored in literature.

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