scholarly journals A longer stance is more stable for a standing horse

2021 ◽  
Author(s):  
Karen Gellman ◽  
Andy Ruina
Keyword(s):  
Equilibrium Configuration ◽  
Static Model ◽  
Spring Stiffness ◽  
Domestic Horses ◽  
The Stability ◽  
Muscular Effort

What is the effect of posture on the stability of a standing horse? We address this with a 2D quasi-static model. The model horse has 3 rigid parts: a trunk, a massless fore-limb and a massless rear limb, and has hinges at the shoulder, hip, and hooves. The postural parameter lg is the distance between the hooves. For a given lg, statics finds an equilibrium configuration which, with no muscle stabilization, is unstable. To measure the neuro-muscular effort to maintain stability, we add springs at the shoulder and hip; the larger the springs needed to stabilize the model, the more the neuro-muscular effort needed for stabilization. We find that a canted-in posture (small lg), observed in some pathological domestic horses, requires about twice the spring stiffness (representing twice the neuromuscular effort) as is needed for postures with vertical or slightly splayed-out (large lg ) legs.

scholarly journals ANÁLISE DA INTEGRIDADE E DA INSTABILIDADE DINÂMICA DE UM SISTEMA MECÂNICO SUJEITO A BIFURAÇÃO DO TIPO BUTTERFLY

2021 ◽  
Vol 12 (3) ◽  
pp. 14-22
Author(s):  
Michael Dowglas de Gois Silva ◽  
Fábio Roberto Chavarette ◽  
Milton Batista Ferreira Junior ◽  
Rodrigo Francisco Borges Lourenco
Keyword(s):  
Static Load ◽  
Structural Systems ◽  
Spring Stiffness ◽  
Bifurcation Diagrams ◽  
Model Uncertainties ◽  
Geometric Imperfections ◽  
Attraction Basin ◽  
Linear Buckling ◽  
Lower Load ◽  
The Stability

Slender structural systems susceptible to unstable buckling generally losestability at lower load levels than the linear buckling load of the perfect structure. This is mainly due to the geometric imperfections present in real structures. The objective of this work is to determine the integrity measures, together with the stability of the post-critical solutions of a mechanical system subject to unstable symmetrical buckling, Burtterfly-type bifurcation, using a discrete degree of freedom model. Uncertainties in the order of 10% will be considered in its deterministic parameters, to obtain lower and reliable limits for the project. The proposed uncertainty in the spring stiffness parameters does not change the type of bifurcation and the value of the critical load, only the value of the minimum post-critical of the bifurcation diagrams. The results showed the erosion of the attraction basin and the decrease of the factors of integrity, local and global, for the trivial solutions with the increase of the static load, for the investigated bifurcation.

Periodic Motions in an Autonomous System With a Discontinuous Vector Field

2020 ◽  
Author(s):  
Siyu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Parameter Study ◽  
Spring Stiffness ◽  
Algebraic Equations ◽  
Periodic Motions ◽  
Mapping Structures ◽  
The Stability

Abstract In this paper, periodic motions in an autonomous system with a discontinuous vector field are discussed. The periodic motions are obtained by constructing a set of algebraic equations based on motion mapping structures. The stability of periodic motions is investigated through eigenvalue analysis. The grazing bifurcations are presented by varying the spring stiffness. Once the grazing bifurcation occurs, periodic motions switches from the old motion to a new one. Numerical simulations are conducted for motion illustrations. The parameter study helps one understand autonomous discontinuous dynamical systems.

NONLINEAR VIBRATION ANALYSIS FOR AN AIRFLOW-EXCITED TRANSLATING STRING

2012 ◽  
Vol 09 (04) ◽  
pp. 1250051 ◽  
Author(s):  
YUEFANG WANG ◽  
LEFENG LÜ ◽  
LIHUA HUANG
Keyword(s):  
Nonlinear Vibration ◽  
Harmonic Balance ◽  
Equilibrium Configuration ◽  
Excitation Frequency ◽  
Transverse Motion ◽  
Hopf Bifurcations ◽  
Flip Bifurcation ◽  
Wind Force ◽  
Incremental Harmonic Balance ◽  
The Stability

The nonlinear vibration of transverse motion of a translating string excited by steady wind force is investigated in this paper. The stability of the equilibrium configuration is analyzed and the generation of limit cycles via multiple Hopf bifurcations is presented. Single-, double-, and quadruple-Hopf bifurcations are determined in the parametric space. The limit-cycle response is solved through the method of Incremental Harmonic Balance, with its stability determined by Floquet multipliers. For the forced vibration, the coexistence of periodic and quasiperiodic motions is found with varying excitation frequency and amplitude. The Neimark–Sacker (NS) bifurcation and the flip bifurcation are demonstrated in an example. The continuation software MATCONT is adopted to identify the fold and NS bifurcations of periodic motions, as well as other codim-2 bifurcations of NS–NS, the Chenciner and the 1:1, 1:3, and 1:4 resonances. These bifurcations present the complexity of the string dynamics induced by steady wind excitations.

scholarly journals Influence of “J”-Curve Spring Stiffness on Running Speeds of Segmented Legs during High-Speed Locomotion

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Runxiao Wang ◽  
Wentao Zhao ◽  
Shujun Li ◽  
Shunqi Zhang
Keyword(s):  
High Speed ◽  
Mathematical Formulation ◽  
Legged Robots ◽  
Slip Model ◽  
Spring Stiffness ◽  
Running Speed ◽  
Fast Running ◽  
J Curve ◽  
The Stability ◽  
Leg Spring

Both the linear leg spring model and the two-segment leg model with constant spring stiffness have been broadly used as template models to investigate bouncing gaits for legged robots with compliant legs. In addition to these two models, the other stiffness leg spring models developed using inspiration from biological characteristic have the potential to improve high-speed running capacity of spring-legged robots. In this paper, we investigate the effects of “J”-curve spring stiffness inspired by biological materials on running speeds of segmented legs during high-speed locomotion. Mathematical formulation of the relationship between the virtual leg force and the virtual leg compression is established. When the SLIP model and the two-segment leg model with constant spring stiffness and with “J”-curve spring stiffness have the same dimensionless reference stiffness, the two-segment leg model with “J”-curve spring stiffness reveals that (1) both the largest tolerated range of running speeds and the tolerated maximum running speed are found and (2) at fast running speed from 25 to 40/92 m s−1both the tolerated range of landing angle and the stability region are the largest. It is suggested that the two-segment leg model with “J”-curve spring stiffness is more advantageous for high-speed running compared with the SLIP model and with constant spring stiffness.

Two-dimensional problems of electrohydrostatic stability

1972 ◽  
Vol 272 (1224) ◽  
pp. 331-359 ◽  
Keyword(s):  
Final Section ◽  
Equilibrium Configuration ◽  
Global Analysis ◽  
Conducting Fluid ◽  
Geometrical Parameters ◽  
Approximate Theory ◽  
Cylindrical Conductor ◽  
The Third ◽  
General Terms ◽  
The Stability

The main intention of this paper is to study the breakdown of equilibrium of a conducting fluid surface such as a membrane when placed in the field of a charged cylindrical conductor. The work is presented in four sections. The first section outlines an approximate theory relevant when the gap between the cylinder and surface is small in comparison with the radius of the cylinder. In the second section, this theory is applied to a number of related problems notably the stability of conducting fluid filaments suspended on parallel wires. In the third section we introduce an extension of the asymptotic analysis of the preceding sections which removes the restriction of the small gap requirement and may be applied to problems of section two which possess symmetry about a centre plane. In the final section, we present a global analysis of the stability of a membrane in the field of a cylindrical conductor. Here the problem is studied in general terms without restrictions on geometrical parameters, and the resulting general equations determining the equilibrium configuration of the membrane are solved numerically.

scholarly journals Snapping of a Planar Elastica With Fixed End Slopes

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Jen-San Chen ◽  
Yong-Zhi Lin
Keyword(s):  
Theoretical Prediction ◽  
Static Load ◽  
Natural Frequencies ◽  
Equilibrium Configuration ◽  
The Other ◽  
Deflection Curve ◽  
Slope Difference ◽  
The Stability ◽  
Fixed End ◽  
Load Deflection Curve

In this paper, we study the deformation and stability of a planar elastica. One end of the elastica is clamped and fixed in space. The other end of the elastica is also clamped, but the clamp itself is allowed to slide along a linear track with a slope different from that of the fixed clamp. The elastica deforms after it is subjected to an external pushing force on the moving clamp. It is observed that when the pushing force reaches a critical value, snapping may occur as the elastica jumps from one configuration to another remotely away from the original one. In the theoretical investigation, we calculate the static load-deflection curve for a specified slope difference between the fixed clamp and the moving clamp. To study the stability of the equilibrium configuration, we superpose the equilibrium configuration with a small perturbation and calculate the natural frequencies of the deformed elastica. An experimental setup is designed to measure the load-deflection curve and the natural frequencies of the elastica. The measured load-deflection relation agrees with the theoretical prediction very well. On the other hand, the measured natural frequencies do not agree very well with the theoretical prediction, unless the mass of the moving clamp is taken into account.

Vibration characteristics and thermoelastic analysis of the supersonic composite laminated panel with arbitrary elastic boundaries

2018 ◽  
Vol 233 (7) ◽  
pp. 2503-2517 ◽  
Author(s):  
Huagang Lin ◽  
Dengqing Cao ◽  
Yuqian Xu
Keyword(s):  
Ritz Method ◽  
Vibration Characteristics ◽  
Spring Stiffness ◽  
Aerodynamic Stability ◽  
Coupled Mode ◽  
Elastic Boundary ◽  
Laminated Panels ◽  
The Stability ◽  
New Phenomena ◽  
Admissible Functions

The novelty of this study is to present a theoretical approach to investigate the dynamic behaviors of the laminated panels under arbitrary elastic boundary conditions. The motion equations of panels considering the first order piston theory are derived using Hamilton principle. A solution of computing the vibration characteristics of a panel with arbitrary elastic boundaries is proposed based on the Rayleigh–Ritz method, in which the admissible functions are constructed by a set of characteristic orthogonal polynomials employing the Gram–Schmidt process; the support boundary is modeled by introducing the technology of artificial springs. The effects of spring stiffness and different boundaries on the dynamic characteristics and thermal aeroelastic behaviors are presented in detail. Numerical results show that the small ply angle and large spring stiffness are helpful to improve the aerodynamic stability. Multiple new phenomena have been observed, e.g. the phenomena of mode jumping and the alterations of coupled mode orders. Moreover, the thermal loads and aerodynamic loads play an opposite effect on the stability of composite panels.

scholarly journals Investigation for Synchronization of a Rotor-Pendulum System considering the Multi-DOF Vibration

2016 ◽  
Vol 2016 ◽  
pp. 1-22 ◽  
Author(s):  
Yongjun Hou ◽  
Pan Fang
Keyword(s):  
Lagrange Equation ◽  
Transformation Method ◽  
Spring Stiffness ◽  
Balance Equations ◽  
Pendulum System ◽  
Dimensionless Equation ◽  
Coupling Relationship ◽  
The Stability ◽  
Synchronous Behavior ◽  
Laplace Transformation Method

This work is a continuation for our published literature for vibration synchronization. A new mechanism, two rotors coupled with a pendulum rod in a multi-DOF vibration system, is proposed to implement coupling synchronization, and the dynamics equation of mechanism is derived by Lagrange equation. In addition, the coupling relationship between the vibrobody and the pendulum rod is ascertained with the Laplace transformation method, based on the dimensionless equation of the dynamics system. The Poincare method is employed to study the synchronization state between the two unbalanced rotors, which is converted into that of existence and the stability of solutions for synchronization-balance equations. The obtained results are supported by computer simulations. It is demonstrated that the values of the spring stiffness coefficient, the length of the pendulum, and the angular installation of the pendulum are important parameters with respect to the synchronous behavior in the rotor-pendulum system.

On some exact solutions in magnetohydrodynamics with astrophysical applications

1972 ◽  
Vol 51 (1) ◽  
pp. 33-38 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Free Surface ◽  
Angular Velocity ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Equilibrium Configuration ◽  
Constant Angular Velocity ◽  
Magnetohydrodynamic Equations ◽  
The Stability

Some exact solutions of the steady magnetohydrodynamic equations for a perfectly conducting inviscid self-gravitating incompressible fluid are discussed. It is shown that there exist solutions for which the free surface of the liquid is that of a planetary ellipsoid and rotates with constant angular velocity about its axis. The stability of the equilibrium configuration is not investigated.

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