Analysis of a Nonlinear Mechanical System With Three Degrees of Freedom

1959 ◽  
Vol 26 (4) ◽  
pp. 546-548
Author(s):  
S. A. Hovanessian
Keyword(s):  
Steady State ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Amplitude Equations ◽  
Response Curves ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System ◽  
Nonlinear Mechanical Systems ◽  
Steady State Amplitude ◽  
Three Degrees Of Freedom

Abstract In recent years the methods of solution of nonlinear vibratory systems with one degree of freedom have been extended to the solution of nonlinear systems with two degrees of freedom. For these systems, the steady-state amplitude equations can be obtained by several methods, such as perturbation and the iteration method introduced by Duffing. In this paper the amplitude-frequency equations for a nonlinear mechanical system with three degrees of freedom are obtained, using Duffing’s method for obtaining the steady-state amplitude equations [1]. The steady-state response curves of two nonlinear mechanical systems, each having three degrees of freedom, are given.

Analysis of a 2DOF Nonlinear Mechanical System Using the Normal Form Method

2019 ◽  
Author(s):  
David Julian Gonzalez Maldonado ◽  
Peter Hagedorn ◽  
Thiago Ritto ◽  
Rubens Sampaio ◽  
Artem Karev
Keyword(s):  
Normal Form ◽  
Mechanical System ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System ◽  
Normal Form Method

Theoretical and Experimental Study of the Nonlinearly Coupled Heave, Pitch, and Roll Motions of a Ship in Longitudinal Waves

1993 ◽  
Author(s):  
I. G. Oh ◽  
A. H. Nayfeh ◽  
D. T. Mook
Keyword(s):  
Large Amplitude ◽  
Degrees Of Freedom ◽  
Excitation Frequency ◽  
Force Response ◽  
Governing Equations ◽  
Response Curves ◽  
Varying Coefficients ◽  
Jump Phenomena ◽  
Time Varying Coefficients ◽  
Three Degrees Of Freedom

Abstract The loss of dynamic stability and the resulting large-amplitude roll of a vessel in a head or following sea were studied theoretically and experimentally. A ship model with three degrees of freedom (roll, pitch, heave) was considered. The governing equations for the heave and pitch modes were linearized and their harmonic solutions were coupled with the nonlinear equation governing roll. The resulting equation, which has time-varying coefficients, was used to predict the response in roll. The principal parametric resonance was considered in which the excitation frequency is twice the natural frequency in roll. Force-response curves were obtained. The existence of jump phenomena and multiple stable solutions for the case of subcritical instability was observed in the experiments and found to be in good qualitative agreement with the results predicted by the theory. The experiments also revealed that the large-amplitude roll is dependent on the location of the model in the standing waves.

scholarly journals Motion modes of the nonlinear mechanical system of the rotor autobalancer

2019 ◽  
Vol 25 ◽  
pp. 1-6 ◽  
Author(s):  
Alexander Gorbenko ◽  
Guntis Strautmanis ◽  
Gennadiy Filimonikhin ◽  
Mareks Mezitis
Keyword(s):  
Mechanical System ◽  
Motion Modes ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System

A Novel 4D Chaotic System Based on Two Degrees of Freedom Nonlinear Mechanical System

2018 ◽  
Vol 73 (7) ◽  
pp. 595-607 ◽  
Author(s):  
Sezgin Kacar ◽  
Zhouchao Wei ◽  
Akif Akgul ◽  
Burak Aricioglu
Keyword(s):  
Mechanical System ◽  
Chaotic System ◽  
Degrees Of Freedom ◽  
Electronic Circuit ◽  
Chaotic Behaviour ◽  
Two Degrees Of Freedom ◽  
Nonlinear Mechanical System ◽  
Linear Mechanical System ◽  
Low Amplitude ◽  
The Mathematical Model

AbstractIn this study, a non-linear mechanical system with two degrees of freedom is considered in terms of chaos phenomena and chaotic behaviour. The mathematical model of the system was moved to the state space and presented as a four dimensional (4D) chaotic system. The system’s chaotic behaviour was investigated by performing dynamic analyses of the system such as equilibria, Lyapunov exponents, bifurcation analyses, etc. Also, the electronic circuit realisation is implemented as a real-time application. This system exhibited vibration along with noise-like behaviour because of its very low amplitude values. Thus, the system is scaled to increase the amplitude values. As a result, the electronic circuit implementation of the 4D chaotic system derived from the model of a physical system is realised.

Multiobjective Robust Controller Synthesis for Nonlinear Mechanical System

2018 ◽  
Vol 19 (11) ◽  
pp. 691-698 ◽  
Author(s):  
G. L. Degtyarev ◽  
R. N. Faizutdinov ◽  
I. O. Spiridonov
Keyword(s):  
Robust Control ◽  
Control Theory ◽  
Mechanical System ◽  
Controller Design ◽  
Controller Synthesis ◽  
Control Law ◽  
Robust Controller ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System ◽  
Robust Control Theory

In the paper multiobjective robust controller synthesis problem for nonlinear mechanical system described by Lagrange’s equations of the second kind is considered. Such tasks have numerous practical applications, for example in controller design of robotic systems and gyro-stabilized platforms. In practice, we often have to use uncertain mathematical plant models in controller design. Therefore, ensuring robustness in presence of parameters perturbations and unknown external disturbances is an important requirement for designed systems. Much of modern robust control theory is linear. When the actual system exhibits nonlinear behavior, nonlinearities are usually included in the uncertainty set of the plant. A disadvantage of this approach is that resulting controllers may be too conservative especially when nonlinearities are significant. The nonlinear H∞ optimal control theory developed on the basis of differential game theory is a natural extension of the linear robust control theory. Nonlinear theory methods ensure robust stability of designed control systems. However, to determine nonlinear H∞-control law, the partial differential equation have to be solved which is a rather complicated task. In addition, it is difficult to ensure robust performance of controlled processes when using this method. In this paper, methods of linear parameter-varying (LPV) systems are used to synthesize robust control law. It is shown, that Lagrange system may be adequately represented in the form of quasi-LPV model. From the computational point of view, the synthesis procedure is reduced to convex optimization techniques under constraints expressed in the form of linear matrix inequalities (LMIs). Measured parameters are incorporated in the control law, thus ensuring continuous adjustment of the controller parameters to the current plant dynamics and better performance of control processes in comparison with H∞-regulators. Furthermore, the use of the LMIs allows to take into account the transient performance requirements in the controller synthesis. Since the quasi-LPV system depends continuously on the parameter vector, the LMI system is infinite-dimensional. This infinitedimensional system is reduced to a finite set of LMIs by introducing a polytopic LPV representation. The example of multiobjective robust control synthesis for electro-optical device’s line of sight pointing and stabilization system suspended in two-axes inertially stabilized platform is given.

Computational and numerical analysis of a nonlinear mechanical system with bounded delay

2017 ◽  
Vol 91 ◽  
pp. 36-57 ◽  
Author(s):  
Marcos Rabelo ◽  
Luciana Silva ◽  
Romes Borges ◽  
Rosane Gonçalves ◽  
Marcos Henrique
Keyword(s):  
Numerical Analysis ◽  
Mechanical System ◽  
Bounded Delay ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System
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