scholarly journals Modeling and Stability Analysis for the Vibrating Motion of Three Degrees-of-Freedom Dynamical System Near Resonance

2021 ◽  
Vol 11 (24) ◽  
pp. 11943
Author(s):  
Wael S. Amer ◽  
Tarek S. Amer ◽  
Seham S. Hassan
Keyword(s):  
Dynamical System ◽  
Degrees Of Freedom ◽  
Multiple Scales ◽  
Positive Influence ◽  
Theoretical Physics ◽  
Physical Parameters ◽  
The Third ◽  
Near Resonance ◽  
The Stability ◽  
Three Degrees Of Freedom

The focus of this article is on the investigation of a dynamical system consisting of a linear damped transverse tuned-absorber connected with a non-linear damped-spring-pendulum, in which its hanged point moves in an elliptic path. The regulating system of motion is derived using Lagrange’s equations, which is then solved analytically up to the third approximation employing the approach of multiple scales (AMS). The emerging cases of resonance are categorized according to the solvability requirements wherein the modulation equations (ME) have been found. The stability areas and the instability ones are examined utilizing the Routh–Hurwitz criteria (RHC) and analyzed in line with the solutions at the steady state. The obtained results, resonance responses, and stability regions are addressed and graphically depicted to explore the positive influence of the various inputs of the physical parameters on the rheological behavior of the inspected system. The significance of the present work stems from its numerous applications in theoretical physics and engineering.

scholarly journals Analyzing the Stability for the Motion of an Unstretched Double Pendulum Near Resonance

2021 ◽  
Vol 11 (20) ◽  
pp. 9520
Author(s):  
Tarek S. Amer ◽  
Roman Starosta ◽  
Adelkarim S. Elameer ◽  
Mohamed A. Bek
Keyword(s):  
Degrees Of Freedom ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Double Pendulum ◽  
Nonlinear Dynamical ◽  
Near Resonance ◽  
Wide Range ◽  
The Stability ◽  
The Impact

This work looks at the nonlinear dynamical motion of an unstretched two degrees of freedom double pendulum in which its pivot point follows an elliptic route with steady angular velocity. These pendulums have different lengths and are attached with different masses. Lagrange’s equations are employed to derive the governing kinematic system of motion. The multiple scales technique is utilized to find the desired approximate solutions up to the third order of approximation. Resonance cases have been classified, and modulation equations are formulated. Solvability requirements for the steady-state solutions are specified. The obtained solutions and resonance curves are represented graphically. The nonlinear stability approach is used to check the impact of the various parameters on the dynamical motion. The comparison between the attained analytic solutions and the numerical ones reveals a high degree of consistency between them and reflects an excellent accuracy of the used approach. The importance of the mentioned model points to its applications in a wide range of fields such as ships motion, swaying buildings, transportation devices and rotor dynamics.

scholarly journals Galloping Stability and Wind Tunnel Test of Iced Quad Bundled Conductors considering Wake Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xiaohui Liu ◽  
Ming Zou ◽  
Chuan Wu ◽  
Mengqi Cai ◽  
Guangyun Min ◽  
...  
Keyword(s):  
Wind Tunnel ◽  
Transmission Lines ◽  
Degrees Of Freedom ◽  
Wind Tunnel Test ◽  
Aerodynamic Coefficients ◽  
Wake Effect ◽  
Aerodynamic Coefficient ◽  
Set Up ◽  
The Stability ◽  
Three Degrees Of Freedom

A new quad bundle conductor galloping model considering wake effect is proposed to solve the problem of different aerodynamic coefficients of each subconductor of iced quad bundle conductor. Based on the quasistatic theory, a new 3-DOF (three degrees of freedom) galloping model of iced quad bundle conductors is established, which can accurately reflect the energy transfer and galloping of quad bundle conductor in three directions. After a series of formula derivations, the conductor stability judgment formula is obtained. In the wind tunnel test, according to the actual engineering situation, different variables are set up to accurately simulate the galloping of iced quad bundle conductor under the wind, and the aerodynamic coefficient is obtained. Finally, according to the stability judgment formula of this paper, calculate the critical wind speed of conductor galloping through programming. The dates of wind tunnel test and calculation in this paper can be used in the antigalloping design of transmission lines.

scholarly journals Stability-preserving model order reduction for linear stochastic Galerkin systems

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Roland Pulch
Keyword(s):  
Dynamical System ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Electric Circuit ◽  
Physical Parameters ◽  
Science And Engineering ◽  
Model Order ◽  
Linear Dynamical Systems ◽  
Stochastic Galerkin ◽  
The Stability

Abstract Mathematical modeling often yields linear dynamical systems in science and engineering. We change physical parameters of the system into random variables to perform an uncertainty quantification. The stochastic Galerkin method yields a larger linear dynamical system, whose solution represents an approximation of random processes. A model order reduction (MOR) of the Galerkin system is advantageous due to the high dimensionality. However, asymptotic stability may be lost in some MOR techniques. In Galerkin-type MOR methods, the stability can be guaranteed by a transformation to a dissipative form. Either the original dynamical system or the stochastic Galerkin system can be transformed. We investigate the two variants of this stability-preserving approach. Both techniques are feasible, while featuring different properties in numerical methods. Results of numerical computations are demonstrated for two test examples modeling a mechanical application and an electric circuit, respectively.

A 3D passive dynamic biped with yaw and roll compensation

Robotica ◽  
2001 ◽  
Vol 19 (3) ◽  
pp. 275-284 ◽  
Author(s):  
M. Wisse ◽  
A. L. Schwab ◽  
R. Q. vd. Linde
Keyword(s):  
Degrees Of Freedom ◽  
High Energy ◽  
Roll Motion ◽  
Multibody Model ◽  
The Third ◽  
High Energy Efficiency ◽  
Dynamic Compensator ◽  
Third Dimension ◽  
The Stability ◽  
Natural Dynamics

Autonomous walking bipedal machines, possibly useful for rehabilitation and entertainment purposes, need a high energy efficiency, offered by the concept of ‘Passive Dynamic Walking' (exploitation of the natural dynamics of the robot). 2D passive dynamic bipeds have been shown to be inherently stable, but in the third dimension two problematic degrees of freedom are introduced: yaw and roll.We propose a design for a 3D biped with a pelvic body as a passive dynamic compensator, which will compensate for the undesired yaw and roll motion, and allow the rest of the robot to move as if it were a 2D machine. To test our design, we perform numerical simulations on a multibody model of the robot. With limit cycle analysis we calculate the stability of the robot when walking at its natural speed.The simulation shows that the compensator, indeed, effectively compensates for both the yaw and the roll motion, and that the walker is stable.

scholarly journals Carter's constant and superintegrability

2018 ◽  
Vol 27 (07) ◽  
pp. 1850066
Author(s):  
Payel Mukhopadhyay ◽  
K. Rajesh Nayak
Keyword(s):  
Dynamical System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Superintegrable System ◽  
Simple Observation ◽  
Superintegrable Systems ◽  
Axisymmetric Spacetime ◽  
Three Degrees Of Freedom

Carter's constant is a nontrivial conserved quantity of motion of a particle moving in stationary axisymmetric spacetime. In the version of the theorem originally given by Carter, due to the presence of two Killing vectors, the system effectively has two degrees of freedom. We propose an extension to the first version of Carter's theorem to a system having three degrees of freedom to find two functionally independent Carter-like integrals of motion. We further generalize the theorem to a dynamical system with [Formula: see text] degrees of freedom. We further study the implications of Carter's constant to superintegrability and present a different approach to probe a superintegrable system. Our formalism gives another viewpoint to a superintegrable system using the simple observation of separable Hamiltonian according to Carter's criteria. We then give some examples by constructing some two-dimensional superintegrable systems based on this idea and also show that all three-dimensional simple classical superintegrable potentials are also Carter separable.

Analysis of Vehicle Dynamic Equilibrium Points with 3-DOF Based on Genetic Algorithm

2014 ◽  
Vol 608-609 ◽  
pp. 721-725
Author(s):  
Rong Li ◽  
Wei Min Li
Keyword(s):  
Genetic Algorithm ◽  
Vehicle Dynamics ◽  
Optimization Design ◽  
Degrees Of Freedom ◽  
Dynamic Equilibrium ◽  
Equilibrium Points ◽  
Vehicle Handling ◽  
Dynamic Modification ◽  
The Stability ◽  
Three Degrees Of Freedom

To further study the stability of vehicle dynamics, a vehicle handling stability’s nonlinear model (including longitudinal, lateral and yaw movement three degrees of freedom) was established. Genetic algorithm was proposed for the vehicle dynamics system’s equilibrium points with 3-DOF. This algorithm solves the problem that cannot be solved through the traditional analytic algorithms and numerical methods. Comparing with the existing research results, the feasibility of solving the equilibrium point by the genetic algorithm is verified. It provides the theoretical foundation for dynamic modification and optimization design of powertrain.

scholarly journals On the Number of Isolating Integrals in Systems with Three Degrees of Freedom

1971 ◽  
Vol 10 ◽  
pp. 110-117
Author(s):  
Claude Froeschle
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Model Problem ◽  
Energy Integral ◽  
Dimensional Mapping ◽  
Three Degrees Of Freedom

AbstractDynamical systems with three degrees of freedom can be reduced to the study of a four-dimensional mapping. We consider here, as a model problem, the mapping given by the following equations: We have found that as soon as b ≠ 0, i.e. even for a very weak coupling, a dynamical system with three degrees of freedom has in general either two or zero isolating integrals (besides the usual energy integral).

scholarly journals Design and Verification of Heading and Velocity Coupled Nonlinear Controller for Unmanned Surface Vehicle

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3427 ◽  
Author(s):  
Jiucai Jin ◽  
Jie Zhang ◽  
Deqing Liu
Keyword(s):  
Degrees Of Freedom ◽  
Lyapunov Theory ◽  
Velocity Control ◽  
Nonlinear Controller ◽  
Experiment Data ◽  
Unmanned Surface Vehicle ◽  
Autonomous Operation ◽  
The Stability ◽  
Velocity Tracking ◽  
Three Degrees Of Freedom

Unmanned Surface Vehicle (USV) is a novel multifunctional platform for ocean observation, and its heading and velocity control are essential and important for autonomous operation. A coupled heading and velocity controller is designed using backstepping technology for an USV called ‘USBV’ (Unmanned Surface Bathymetry Vehicle). The USBV is an underactuated catamaran, where the heading and velocity are controlled together by two thrusters at the stern. The three degrees-of-freedom equations are used for USBV’s modeling, which is identified using experiment data. The identified model, with two inputs, induces heading and velocity tracking, which are coupled. Based on the model, a nonlinear controller for heading and velocity are acquired using backstepping technology. The stability of the controller is proved by Lyapunov theory under some assumptions. The verification is presented by lake and sea experiments.

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