共查询到20条相似文献,搜索用时 781 毫秒
1.
The influence of the pendulum parameters and the follower force on the evolution of equilibrium states is analyzed using a
generalized mathematical model of inverted pendulum. Equilibrium curves are plotted using the parameter continuation method.
It is shown that the pendulum with certain values of the angular eccentricity has one or three nonvertical equilibrium positions
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 122–131, March 2007. 相似文献
2.
L. G. Lobas 《International Applied Mechanics》2005,41(6):587-613
The results from studies of the dynamic behavior of a double pendulum under the action of a follower force are analyzed. It
is pointed out that bifurcations and catastrophes of equilibrium states may occur at some values of the parameters. Differential
equations are presented which describe the plane-parallel motion of a pendulum with an arbitrary number of links and angular
and linear eccentricities of the follower force whose orientation depends on one parameter. The basic problems of dynamics
of pendulums with different number of links are formulated
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 3–35, June 2005. 相似文献
3.
V. L. Lobas 《International Applied Mechanics》2005,41(2):197-202
A generalized mathematical model of an inverted double pendulum with asymmetric follower force is developed. The model accounts for all possible types of springs: hard, soft, and linear. The influence of equitype springs on the equilibrium states is examined__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 103–109, February 2005. 相似文献
4.
The effect of the linear eccentricity of the follower force on the equilibrium states of an inverted pendulum is examined.
Bifurcation points and catastrophes associated with changes in pendulum parameters and type of springs are analyzed. Phase
flows are plotted
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 121–129, April 2007. 相似文献
5.
The stability boundaries for the vertical equilibrium position of a triple simple pendulum subject to asymmetric follower
force are analyzed. The effect of the upper spring and the magnitude of the follower force on the roots of the characteristic
equation is studied
Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 122–134, October 2008. 相似文献
6.
The effect of the type of springs on the equilibrium states of an inverted pendulum is examined. The angular and linear eccentricities
of the follower force are taken into account
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 126–137, June 2007. 相似文献
7.
The equilibrium states of an inverted two-link simple pendulum with an asymmetric follower force are classified depending
on the characteristics of the springs (hard, soft, or linear) at the upper end and at the hinges. Phase portraits are plotted.
The bifurcation points on the equilibrium curves are identified. Emphasis is on fold and cusp catastrophes
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 115–128, August 2007. 相似文献
8.
A generalized mathematical theory of a double mathematical pendulum with follower force is used to analyze the stability of the vertical equilibrium position of the pendulum with both linear and nonlinear (hard and soft) elastic elements in the critical case of one zero root of the characteristic equation. The influence of the parameters of these elements on the safe and dangerous sections of the stability boundary is demonstrated__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 133–142, April 2005. 相似文献
9.
The loss of stability of the equilibrium position of a double pendulum with follower force loading and elastic end support is studied. At a special parameter combination the linearized system is characterized by a zero root and a pure imaginary pair of eigenvalues. Therefore, the stability problem is a complicated critical case in the sense of Liapunov and requires a non-linear analysis. A complete post-bifurcation investigation of the coupled divergence and flutter motions is given by means of centre manifold theory, and bifurcation diagrams. Among the different types of motions even the appearance of chaotic behavior is shown. 相似文献
10.
The limit cycles of a double pendulum with hard, soft, or linear springs subject to a follower force are drawn using computer
simulation 相似文献
11.
It is shown that there is a magnitude of the follower force at which two limit cycles, stable and unstable, are born in the
phase space of a double simple pendulum 相似文献
12.
The paper studies the influence of the orientation parameter of the follower force on the behavior of the pendulum with a simple zero eigenvalue in the linearization matrix 相似文献
13.
L. L. Lobas 《International Applied Mechanics》2001,37(12):1618-1623
It is studied how the asymmetry of the follower force influences the stationary states of an inverted two-link mathematical pendulum with viscoelastic hinges and the upper end elastically fixed. It is shown that if the parameters of the system change, bifurcations of the stationary states leading to fold and cusp catastrophes become possible 相似文献
14.
The motion of a double mathematical pendulum under the action of the gravity force and a vibration force whose frequency substantially exceeds the system natural frequencies is considered. An oblique vibration stabilizing the pendulum in an arbitrarily given position is sought. The domain of existence of the pendulum equilibrium points and the vibration parameters corresponding to a given equilibrium of the pendulumare obtained analytically. In the domain of existence of equilibrium points, the subdomain of their stability is distinguished. 相似文献
15.
Local and global bifurcations in the motion of a double pendulum subjected to a follower force have been studied when the follower force and the springs at the joints have structural asymmetries. The bifurcations of the system are examined in the neighborhood of double zero eigenvalues. Applying the center manifold and the normal form theorem to a four-dimensional governing equation, we finally obtain a two-dimensional equation with three unfolding parameters. The local bifurcation boundaries can be obtained for the criteria for the pitchfork and the Hopf bifurcation. The Melnikov theorem is used to find the global bifurcation boundaries for appearance of a homoclinic orbit and coalescence of two limit cycles. Numerical simulation was performed using the original four-dimensional equation to confirm the analytical prediction. 相似文献
16.
L. G. Lobas 《International Applied Mechanics》2005,41(5):566-572
A problem formulation and differential equations are given to describe the plane-parallel motion of an inverted multilink pendulum with an asymmetric follower force acting at the elastically restrained upper end. The physical nonlinearities of the springs are taken into account. The possible mechanisms of energy dissipation are described__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 5, pp. 124–130, May 2005. 相似文献
17.
L. G. Lobas 《International Applied Mechanics》2001,37(1):38-65
General theorems on the stability of stationary states of mechanical systems subjected to nonconservative position forces are presented. Specific mechanical problems on gyroscopic systems, a double-link pendulum with a follower force and elastically fixed upper tip, multilink pneumowheel vehicles, a monorail car, and rail-guided vehicles are analyzed. Methods for investigation of divergent bifurcations and catastrophes of stationary states are described 相似文献
18.
I. E. Glagolev 《Moscow University Mechanics Bulletin》2013,68(6):133-138
In accordance with the Kirchhoff analogy, the equilibrium equations of an elastic thread on a plane are equivalent to the equations of motion of a simple pendulum. This analogy is generalized to the case when the thread is situated on a smooth curved surface. The equilibrium equations for the threads in the general case and in the particular cases of flat, cylindrical, and spherical surfaces are derived. For these surfaces the Kirchhoff analogy is generalized to the case of a simple pendulum in an additional force field. There are also considered the electromagnetic and nonholonomic analogies for the equilibrium equations of an elastic thread. 相似文献
19.
L. G. Lobas 《International Applied Mechanics》2007,43(5):560-567
This paper formulates a problem for and gives the differential equations of plane-parallel motion of an inverted n-link pendulum subject to an asymmetric follower force applied at the upper end via a spring. The physical nonlinearities
of springs are taken into account. The possible mechanisms of energy dissipation are described
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 106–114, May 2007. 相似文献
20.
Charles F. Kalmbach Earl H. Dowell Francis C. Moon 《International Journal of Solids and Structures》1974,10(3):361-381
A theoretical and experimental study is made to determine the feasibility of controlling a thin cantilevered beam subject to a (nonconservative) follower force. A theoretical model is developed using the equations for a thin beam under initial stress and Galerkin's method. An experiment is constructed with the capability of using a variety of feedback loops to control a thin aluminum beam with a tip jet mounted parallel to the chord. A particular control system is chosen for study and an increase of follower force required to destabilize the beam of over 65 per cent is recorded. The theoretical results show good correlation with the experimentally determined stability boundaries and frequency variations with follower force. 相似文献