Stability and Dynamics of Axially Moving Unidirectional Plates Partially Immersed in a Liquid

2014 ◽  
Vol 14 (04) ◽  
pp. 1450010 ◽  
Author(s):  
Yan Qing Wang ◽  
Xing Hui Guo ◽  
Zhen Sun ◽  
Jian Li
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Plate Theory ◽  
Fluid Pressure ◽  
Added Mass ◽  
Chaotic Motions ◽  
Bernoulli’S Equation ◽  
Singular Functions ◽  
Axially Moving ◽  
The Stability

The stability and dynamics of an axially moving unidirectional plate partially immersed in a liquid and subjected to a nonlinear aerodynamic excitation are investigated. The method of singular functions is adopted to study the dynamic characteristics of the unidirectional plates with discontinuous characteristics. Nonlinearities due to large-amplitude plate motions are considered by using the classical nonlinear thin plate theory, with allowance for the effect of viscous structural damping. The velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the unidirectional plate. The effect of fluid on the vibrations of the plate may be equivalent to added mass of the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate–fluid interfaces. The system is discretized by Galerkin's method while a model involving two degrees of freedom, is adopted. Attention is focused on the behavior of the system in the region of dynamic instability, and several motions are found by numerical simulations. The effects of the moving speed and some other parameters on the dynamics of the system are also investigated. It is shown that chaotic motions can occur in this system in several certain regions of parameter space.

Vibrations of Axially Moving Vertical Rectangular Plates in Contact with Fluid

2016 ◽  
Vol 16 (02) ◽  
pp. 1450092 ◽  
Author(s):  
Yan Qing Wang ◽  
Sen Wen Xue ◽  
Xiao Bo Huang ◽  
Wei Du
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Fluid Pressure ◽  
Added Mass ◽  
Vibration Characteristics ◽  
Rectangular Plates ◽  
Moving Plate ◽  
Bernoulli’S Equation ◽  
Aspect Ratios ◽  
Axially Moving

The vibration characteristics of an axially moving vertical plate immersed in fluid and subjected to a pretension are investigated, with a special consideration to natural frequencies, complex mode functions and critical speeds of the system. The classical thin plate theory is adopted for the formulation of the governing equation of motion of the vibrating plates. The effects of free surface waves, compressibility and viscidity of the fluid are neglected in the analysis. The velocity potential and Bernoulli’s equation are used to describe the fluid pressure acting on the moving plate. The effect of fluid on the vibrations of the plate may be regarded as equivalent to an added mass on the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate–fluid interfaces. The effects of some system parameters such as the moving speed, stiffness ratios, location and aspect ratios of the plate and the fluid-plate density ratios on the above-mentioned vibration characteristics of the plate–fluid system are investigated in detail. Various different boundary conditions are considered in the study.

The Influence of Hold-Back Vessels on the Operation of a DP Drilling Rig: Control System and Stability Analysis

2017 ◽  
Author(s):  
Alex S. Huang ◽  
Eduardo Aoun Tannuri ◽  
Asdrubal N. Queiroz Filho ◽  
André S. S. Ianagui ◽  
Douglas G. T. Yuba ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Simplified Model ◽  
Fast Time ◽  
Dynamic Simulations ◽  
Positioning Systems ◽  
Time Dynamic ◽  
Drilling Rig ◽  
The Stability ◽  
Drilling Rigs

Certain maritime operations require the accurate positioning of the vessel, and in order to accomplish that DP (dynamic positioning) systems were developed. It combines the information obtained from sensors with the expected dynamic of the ship to better estimate its actual position and the external forces, and with those information the controller allocates the forces among the available actuators so the vessel keeps a desired position. In situations where drift of the vessel could cause great harm (human, material or environmental losses) it might be necessary to provide additional safeguards. One possible solution is to connect an AHTS (anchor handling tug supply) to the original DP vessel, in order to complement the forces generated by its thrusters. However as shown by Jensen (2008) and IMCA M 185 (2012), this connection could actually degrade the position keeping ability of the vessel, nullifying the purpose of improving the safety of the operation. The objective of the present paper is to confirm the hypothesis that the use of hold-back vessels to support DP drilling rigs may degrade the performance of the DP system, causing dynamic instability, and to determine the boundaries of operation under which this phenomenon occurs: sea state, parameters of the vessels and force transmitted by the hold-back vessel. Firstly, an analytical study of the system was done. It was considered a simplified model of two vessels connected by a cable with two degrees of freedom (one for each vessel), since the force applied by a cable is unidirectional. Using control theory, the limiting stiffness of the cable was determined by analyzing the poles of the system. Considering a catenary model for the connecting cable, it was possible to determine the maximum force that could be transmitted between the vessels without the system becoming unstable. The influence of the Kalman Filter in the stability of the system was also studied. Those results were then compared and confirmed with fast time dynamic simulations of the system, in which the influence of different environmental conditions were also added to the analysis. To complete the study, real time simulations were done on a full mission simulator, equipped with the original Kongsberg DP system for the drilling rig. The simplified model showed consistent results, validated by the simulations, demonstrating it can be a useful tool when analyzing the stability of two connected vessels.

Non-Linear Aeroelastic Stability of Wind Turbines

2013 ◽  
Vol 569-570 ◽  
pp. 531-538 ◽  
Author(s):  
Z.L. Zhang ◽  
M.T. Sichani ◽  
Jie Li ◽  
J.B. Chen ◽  
S.R.K. Nielsen
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Degrees Of Freedom ◽  
Dynamic Instability ◽  
Maximum Lyapunov Exponent ◽  
Moving Frames ◽  
Internal Resonances ◽  
Wind Turbine System ◽  
Non Linear ◽  
The Stability

As wind turbines increase in magnitude without a proportional increase in stiffness, the risk of dynamic instability is believed to increase. Wind turbines are time dependent systems due to the coupling between degrees of freedom defined in the fixed and moving frames of reference, which may trigger off internal resonances. Further, the rotational speed of the rotor is not constant due to the stochastic turbulence, which may also influence the stability. In this paper, a robust measure of the dynamic stability of wind turbines is suggested, which takes the collective blade pitch control and non-linear aero-elasticity into consideration. The stability of the wind turbine is determined by the maximum Lyapunov exponent of the system, which is operated directly on the non-linear state vector differential equations. Numerical examples show that this approach is robust for stability identification of the wind turbine system.

scholarly journals Analytical Study on Inherent Properties of a Unidirectional Vibrating Steel Strip Partially Immersed in Fluid

2013 ◽  
Vol 20 (4) ◽  
pp. 793-807 ◽  
Author(s):  
J. Li ◽  
X.H. Guo ◽  
J. Luo ◽  
H.Y. Li ◽  
Y.Q. Wang
Keyword(s):  
Steel Strip ◽  
Fluid Pressure ◽  
Added Mass ◽  
Mode Shapes ◽  
Fluid Interfaces ◽  
The Finite Element Method ◽  
Bernoulli’S Equation ◽  
Pressure Fields ◽  
Steel Strips ◽  
Different Types

The theory of singuarity functions is introduced to present an analytical approach for the natural properties of a unidirectional vibrating steel strip with two opposite edges simply supported and other two free, partially submerged in fluid and under tension. The velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the steel strip. The effect of fluid on vibrations of the strip may be equivalent to added mass of the strip. The math formula of added mass can be obtained from kinematic boundary conditions of the strip-fluid interfaces. Singularity functions are adopted to solve problems of the strip with discontinuous characteristics. By applying Laplace transforms, analytical solutions for inherent properties of the vibrating steel strip in contact with fluid are finally acquired. An example is given to illustrate that the proposed method matches the numerical solution using the finite element method (FEM) very closely. The results show that fluid has strong effect on natural frequencies and mode shapes of vibrating steel strips partially dipped into a liquid. The influences such as tension, the submergence depth, the position of strip in the container and the dimension of the container on the dynamic behavior of the strip are also investigated. Moreover, the presented method can also be used to study vertical or angled plates with discontinuous characteristics as well as different types of pressure fields around.

scholarly journals Stability of Axially Moving Piezolaminated Viscoelastic Plate Subjected to Follower Force

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yan Wang ◽  
Tao Jing ◽  
Jimei Wu ◽  
Min Xie
Keyword(s):  
Piezoelectric Layer ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Tensile Force ◽  
Viscoelastic Plate ◽  
Follower Force ◽  
Complex Eigenvalue ◽  
Axially Moving ◽  
The Stability ◽  
Moving Speed

The stability of the moving viscoelastic plate with the piezoelectric layer subjected to uniformly distributed tangential follower force is investigated. The force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force. The differential equation of the axially moving viscoelastic rectangular plate with piezoelectric layer subjected to uniformly distributed tangential follower force is formulated on the basis of the Kirchhoff thin plate theory and the two-dimensional viscoelastic differential constitutive relation. The complex eigenvalue equations are established by the differential quadrature method. Via numerical calculation, the curves of real parts and imaginary parts of dimensionless complex frequencies versus uniformly distributed tangential follower force and dimensionless moving speed are obtained. The effects of nonconservative force, dimensionless axially moving speed, and dimensionless applied voltages on the stability of axially moving nonconservative viscoelastic plate with piezoelectric layer are analyzed.

scholarly journals Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Mingyue Shao ◽  
Jimei Wu ◽  
Yan Wang ◽  
Qiumin Wu
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Plate Theory ◽  
Velocity Variation ◽  
Mean Velocity ◽  
Thin Plate Theory ◽  
Time Histories ◽  
Axially Moving ◽  
The Stability ◽  
The Galerkin Method

Nonlinear vibration characteristics of a moving membrane with variable velocity have been examined. The velocity is presumed as harmonic change that takes place over uniform average speed, and the nonlinear vibration equation of the axially moving membrane is inferred according to the D’Alembert principle and the von Kármán nonlinear thin plate theory. The Galerkin method is employed for discretizing the vibration partial differential equations. However, the solutions concerning to differential equations are determined through the 4th order Runge–Kutta technique. The results of mean velocity, velocity variation amplitude, and aspect ratio on nonlinear vibration of moving membranes are emphasized. The phase-plane diagrams, time histories, bifurcation graphs, and Poincaré maps are obtained; besides that, the stability regions and chaotic regions of membranes are also obtained. This paper gives a theoretical foundation for enhancing the dynamic behavior and stability of moving membranes.

Stability of a Spinning Rotor Subjected to a Distributed Traction

2003 ◽  
Author(s):  
Bongsu Kang
Keyword(s):  
Thick Plate ◽  
Dynamic Instability ◽  
Plate Theory ◽  
Transverse Component ◽  
Accurate Estimation ◽  
Plate Model ◽  
Disc Brakes ◽  
The Stability ◽  
Spinning Speed ◽  
Circular Saws

In this paper, the stability of a spinning rotor loaded by a circumferentially distributed frictional traction is examined. Typical engineering applications include automotive and aircraft disc brakes and circular saws. The frictional traction, which is always directed tangent to the instantaneous deflection curve of the rotor, is decomposed into in-plane and transverse components. The in-plan component is equilibrated by the in-plane stresses while the transverse component is a slope-dependent nonconservative followertype force that is the major source of dynamic instability of the rotor in this study. The rotor is modeled as a spinning annular plate that includes the effects of rotary inertia and shear deformations in the context of the Mindlin thick plate theory. A thick plate model is employed to ensure an accurate estimation of the eigenvalues when the rotor vibration involves high circumferential modes (eighth or ninth) that are often observed in unstable automotive disc brakes. The pad or stator is represented as a viscoelastic subgrade that reacts to both transverse and shearing motion of the rotor. The degree of instability is measured by examining the resulting complex eigenvalues. Effects of various system parameters such as frictional traction, geometry of the rotor, pad size, spinning speed, and viscoelastic properties of the pad on the dynamic instability are discussed. Results, when compared with those from the classical thin plate model of the rotor, are significantly different.

Bifurcations of Eigenvalues of Gyroscopic Systems With Parameters Near Stability Boundaries

2000 ◽  
Vol 68 (2) ◽  
pp. 199-205 ◽  
Author(s):  
A. P. Seyranian ◽  
W. Kliem
Keyword(s):  
Degrees Of Freedom ◽  
Stability Boundaries ◽  
Stability And Instability ◽  
Generalized Eigenvectors ◽  
Double Eigenvalues ◽  
Normal Vectors ◽  
Axially Moving ◽  
The Stability ◽  
Derivatives Of ◽  
Gyroscopic Systems

This paper deals with stability problems of linear gyroscopic systems Mx¨+Gx˙+Kx=0 with finite or infinite degrees-of-freedom, where the system matrices or operators depend smoothly on several real parameters. Explicit formulas for the behavior of eigenvalues under a change of parameters are obtained. It is shown that the bifurcation (splitting) of double eigenvalues is closely related to the stability, flutter, and divergence boundaries in the parameter space. Normal vectors to these boundaries are derived using only information at a boundary point: eigenvalues, eigenvectors, and generalized eigenvectors, as well as first derivatives of the system matrices (or operators) with respect to parameters. These results provide simple and constructive stability and instability criteria. The presented theory is exemplified by two mechanical problems: a rotating elastic shaft carrying a disk, and an axially moving tensioned beam.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

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