scholarly journals Vibration of the Translation and the Inclination Motions Coupled System Under the Periodic Base Motion (Auto-parametric Resonance and Influences of Height of Center of Mass, Unbalance of Mass and Difference between Support Stiffness)

2007 ◽  
Vol 1 (4) ◽  
pp. 736-747 ◽  
Author(s):  
Tsuyoshi INOUE ◽  
Yukio ISHIDA ◽  
Shintaro YAMADA
Keyword(s):  
Parametric Resonance ◽  
Center Of Mass ◽  
Coupled System ◽  
Mass Unbalance

Parametric Vibration of a Flexible Structure Excited by Periodic Passage of Moving Oscillators

2020 ◽  
Vol 87 (7) ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Dynamic Stability ◽  
Parametric Resonance ◽  
Flexible Structures ◽  
Coupled System ◽  
Analytical Form ◽  
Stability Criteria ◽  
Analysis Method ◽  
State Equations ◽  
Supporting Structure ◽  
Moving Oscillator

Abstract Flexible structures carrying moving subsystems are found in various engineering applications. Periodic passage of subsystems over a supporting structure can induce parametric resonance, causing vibration with ever-increasing amplitude in the structure. Instead of its engineering implications, parametric excitation of a structure with sequentially passing oscillators has not been well addressed. The dynamic stability in such a moving-oscillator problem, due to viscoelastic coupling between the supporting structure and moving oscillators, is different from that in a moving-mass problem. In this paper, parametric resonance of coupled structure-moving oscillator systems is thoroughly examined, and a new stability analysis method is proposed. In the development, a set of sequential state equations is first derived, leading to a model for structures carrying a sequence of moving oscillators. Through the introduction of a mapping matrix, a set of stability criteria on parametric resonance is then established. Being of analytical form, these criteria can accurately and efficiently predict the dynamic stability of a coupled structure-moving oscillator system. In addition, by the spectral radius of the mapping matrix, the global stability of a coupled system can be conveniently investigated in a parameter space. The system model and stability criteria are illustrated and validated in numerical examples.

scholarly journals Modeling a Controlled-Floating Space Robot for In-Space Services: A Beginner’s Tutorial

2021 ◽  
Vol 8 ◽  
Author(s):  
Asma Seddaoui ◽  
Chakravarthini Mini Saaj ◽  
Manu Harikrishnan Nair
Keyword(s):  
Center Of Mass ◽  
Autonomous Systems ◽  
Coupled System ◽  
Cost Effective ◽  
Space Robot ◽  
Loop Control ◽  
Viable Solution ◽  
Wide Range ◽  
Pose Control ◽  
Orbital Space

Ground-based applications of robotics and autonomous systems (RASs) are fast advancing, and there is a growing appetite for developing cost-effective RAS solutions for in situ servicing, debris removal, manufacturing, and assembly missions. An orbital space robot, that is, a spacecraft mounted with one or more robotic manipulators, is an inevitable system for a range of future in-orbit services. However, various practical challenges make controlling a space robot extremely difficult compared with its terrestrial counterpart. The state of the art of modeling the kinematics and dynamics of a space robot, operating in the free-flying and free-floating modes, has been well studied by researchers. However, these two modes of operation have various shortcomings, which can be overcome by operating the space robot in the controlled-floating mode. This tutorial article aims to address the knowledge gap in modeling complex space robots operating in the controlled-floating mode and under perturbed conditions. The novel research contribution of this article is the refined dynamic model of a chaser space robot, derived with respect to the moving target while accounting for the internal perturbations due to constantly changing the center of mass, the inertial matrix, Coriolis, and centrifugal terms of the coupled system; it also accounts for the external environmental disturbances. The nonlinear model presented accurately represents the multibody coupled dynamics of a space robot, which is pivotal for precise pose control. Simulation results presented demonstrate the accuracy of the model for closed-loop control. In addition to the theoretical contributions in mathematical modeling, this article also offers a commercially viable solution for a wide range of in-orbit missions.

scholarly journals Nonlinear Stability Analysis of a Spinning Top with an Interior Liquid-Filled Cavity

2020 ◽  
Author(s):  
Giovanni Paolo Galdi ◽  
Giusy Mazzone
Keyword(s):  
Nonlinear Stability ◽  
Center Of Mass ◽  
Coupled System ◽  
Vertical Axis ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Nonlinear Stability Analysis ◽  
Spinning Top ◽  
Axis Passing

Consider the  motion of the the coupled system, $\mathscr S$, constituted by a (non-necessarily symmetric) top, $\mathscr B$, with an interior cavity, $\mathscr C$, completely filled up with a Navier-Stokes  liquid, $\mathscr L$. A particular steady-state motion $\bar{\sf s}$ (say) of $\mathscr S$, is when $\mathscr L$ is at rest with respect to $\mathscr B$, and $\mathscr S$, as a whole rigid body, spins with a constant angular velocity $\bar{\V\omega}$ around a vertical axis passing through its center of mass $G$ in its highest position ({\em upright spinning top}). We then provide a completely characterization of the nonlinear stability of $\bar{\sf s}$ by showing, roughly speaking, that $\bar{\sf s}$ is stable if and only if $|\bar{\V\omega}|$ is sufficiently large, all other physical parameters being fixed. Moreover we show that, unlike the case when $\mathscr C$ is empty, under the above stability conditions, the top will eventually return to the unperturbed upright configuration.

Dynamic Analysis and Parametric Excitation of a Multi-Span Beam Structure Coupled With a Sequence of Moving Rigid Bodies

2018 ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Parametric Resonance ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Rigid Bodies ◽  
Time Varying ◽  
Beam Structure ◽  
Assumed Mode Method ◽  
Mode Method

Dynamic analysis of a multi-span beam structure carrying moving rigid bodies is essentially important in various engineering applications. With many rigid bodies having different speeds and varying inter-distances, number of degrees of freedom of the coupled beam-moving rigid body system is time-varying and the beam-rigid body interaction is thus complicated. Developed in this paper is a method of extended solution domain (ESD) that resolves the issue of time-varying number of degrees and delivers a consistent mathematical model for the coupled system. The governing equation of the coupled system is derived with generalized assumed mode method through use of exact eigenfunctions and solved via numerical integration. Numerical simulation shows the accuracy and efficiency of the proposed method. Moreover, a preliminary study on parametric resonance on a beam structure with 10 rigid bodies provides guidance for future development of conditions on parametric resonance induced by moving rigid bodies, which can be useful for operation of certain coupled structure systems.

Dynamic Analysis and Parametric Resonance of a Fast Projection System

2019 ◽  
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Dynamic Response ◽  
Parametric Resonance ◽  
Coupled System ◽  
Rigid Bodies ◽  
Time Varying ◽  
Dynamic Coupling ◽  
Projection System ◽  
System Parameters ◽  
Gun Barrel ◽  
Systematic Solution

Abstract Fast projection systems are seen in various engineering applications, including weaponry systems. This work is concerned with the vibration of coupled gun barrel-bullet systems. The vibration of the muzzle end of a gun barrel (launching structure) is critical to shooting accuracy and launching safety. Under a rapid and repeated launching process, the launching structure may experience parametric resonance that is induced by accelerating projectiles. In this paper, a mathematical model of the coupled gun barrel-bullet is developed. In the development, the gun barrel is modeled by a cantilever beam; the projectiles are modeled as moving rigid bodies with time-varying velocities; and the dynamic coupling between the gun barrel and projectiles are described by pairs of springs and dampers. With this model, the dynamic response of the coupled system is determined through use of an extended solution domain (ESD) technique, which facilitates systematic solution of the dynamic response of the coupled beam-rigid body system. Numerical results show that parametric resonance can be induced in the launching structure, which is highly dependent on system parameters and projectile launching rate.

Dynamic Response of a Beam Structure Excited by Sequentially Moving Rigid Bodies

2020 ◽  
Vol 20 (08) ◽  
pp. 2050093
Author(s):  
Hao Gao ◽  
Bingen Yang
Keyword(s):  
Dynamic Response ◽  
Rigid Body ◽  
Parametric Resonance ◽  
Coupled System ◽  
Rigid Bodies ◽  
Coupled Systems ◽  
Solution Technique ◽  
Beam Structure ◽  
Dynamic Interactions ◽  
Contact Points

A coupled dynamic system consisting of a supporting beam structure and multiple passing rigid bodies is seen in various engineering applications. The dynamic response of such a coupled system is quite different from that of the beam structure subject to moving loads or moving oscillators. The dynamic interactions between the beam and moving rigid bodies are complicated, mainly because of the time-varying number and locations of contact points between the beam and bodies. Due to lack of an efficient modeling and solution technique, previous studies on these coupled systems have been limited to a beam carrying one or a few moving rigid bodies. As such, dynamic interactions between a supporting structure and arbitrarily many moving rigid bodies have not been well investigated, and parametric resonance induced by a sequence of moving rigid bodies, which has important engineering implications, is missed. In this paper, a new semi-analytical method for modeling and analysis of the above-mentioned coupled systems is developed. The method is based on an extended solution domain, by which the number of degrees of freedom of a coupled system is fixed regardless of the number of contact points between the beam and moving rigid bodies at any given time. This feature allows simple and concise description of flexible–rigid body interactions in modeling, and easy and effective implementation of numerical algorithms in solution. The proposed method provides a useful platform for thorough study of flexible–rigid body interactions and parametric resonance for coupled beam–moving rigid body systems. The accuracy and efficiency of the proposed method in computation is demonstrated in several examples.

Coupled Lateral-Torsional Vibration of a Gear-Pair System Supported by a Squeeze Film Damper

1993 ◽  
Author(s):  
Chin-Shong Chen ◽  
S. Natsiavas ◽  
Harold D. Nelson
Keyword(s):  
Steady State ◽  
Coupled System ◽  
Squeeze Film ◽  
Gear Pair ◽  
Torsional Motion ◽  
Squeeze Film Damper ◽  
Gear Mesh ◽  
Mass Unbalance ◽  
Steady State Responses ◽  
State Responses

Abstract This paper investigates the coupled lateral-torsional vibration of a gear-pair system supported by a cavitated squeeze film damper (SFD). Both steady state and transient dynamic characteristics of the system are analyzed. In order to gain insight into the dynamics of the system, the free vibration frequencies and modes of the linearized system are first determined. Then, the response of the nonlinear system is examined under mass unbalance and torque excitation. The trigonometric collocation method (TCM) is employed to obtain periodic steady-state responses. Direct integration is also used in order to verify TCM and capture transient response. A comparison of the steady state responses obtained with the present model by first considering only the lateral vibration and then including torsional effects demonstrates the need to include the coupling between lateral and torsional motion. Then, the effect of parameters such as gear mesh stiffness and damping, clearance-to-diameter ratio of the SFD and gear mass unbalance on the steady state response is also presented. It is found that the mass unbalance excites not only lateral-dominated modes of the coupled system but also torsional-dominated modes. Further numerical results show that the modes of the coupled system which are dominated by lateral motion can be attenuated by using a SFD, while the modes dominated by torsional motion can be substantially suppressed by gear mesh damping. Finally, the presence of multiple solutions and complex response is predicted in some frequency ranges.

The Center of Mass Influences Normal Attentional Orienting

1994 ◽  
Author(s):  
Marcia Grabowecky ◽  
Lynn C. Robertson ◽  
Anne Treisman
Keyword(s):  
Center Of Mass ◽  
Attentional Orienting

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

Sign in / Sign up

Export Citation Format

Share Document