Dynamic Stability of Hovercraft in Heave

1970 ◽  
Vol 37 (4) ◽  
pp. 895-900 ◽  
Author(s):  
H. J. Davies ◽  
G. A. Poland
Keyword(s):  
Mathematical Model ◽  
Dynamic Behavior ◽  
Dynamic Stability ◽  
Equilibrium Position ◽  
Forced Oscillation ◽  
Dynamic Equilibrium ◽  
Forced Oscillations ◽  
Two Dimensional ◽  
Oscillation Characteristics ◽  
Nonlinear Nature

The regimes of flow governing the dynamic behavior of a two-dimensional mathematical model of an edge-jet Hovercraft in heaving motion are described and the equations associated with such regimes derived. Both the free and forced-oscillation characteristics are studied. The nonlinear nature of the system manifests itself, in the case of the forced oscillations, as a shift in the dynamic equilibrium position resulting in a loss of mean hoverheight.

scholarly journals ON APPLICATION OF A SIMPLIFIED TWO-DIMENSIONAL MODEL OF FORCED OSCILLATIONS TO THE POWER ANALYSIS OF FLAT STEELWORKS

2020 ◽  
pp. 109-119
Author(s):  
Холодняк Ю.С. ◽  
Подлєсний С.В. ◽  
Капорович С.В. ◽  
Коротенко Є.Д.
Keyword(s):  
Mathematical Model ◽  
Oscillatory System ◽  
Forced Oscillations ◽  
Simultaneous Action ◽  
Oscillatory Process ◽  
Power Calculation ◽  
Two Dimensional ◽  
Resonant Frequencies ◽  
Computational Tools ◽  
The Mathematical Model

Abstract. An analysis of existing methods of power calculation of steelworks under the influence of forced oscillations is performed. When considering the forced oscillations of flat steelworks, two-dimensional models are used, which are complex for wide practical use. Their implementation requires in-depth mathematical training and complex computational tools. The aim of this work is to develop a simplified two-dimensional mathematical model of forced oscillations of flat steelworks with following use of this model in power calculations. The mathematical model proposed in this paper describes oscillations of a weightless steelwork with a point mass of simultaneous action in vertical and horizontal harmonic disturbing forces acting on them. The model is based on the method of forces, establishes a link between the movements of the steelworks and the forces that act on them. Together with the model the dependences for calculating the resonant frequencies of the oscillatory system are obtained. The performed developments allow to determine the dynamic characteristics of the oscillatory process and to calculate a steelwork strength, stiffness and stability.

ANALYSIS OF THE INFLUENCE OF ANGULAR SPEED OF ROTATION OF A PIPELINE WITH LIQUID ON THE DEVELOPMENT OF DYNAMIC PROCESSES

2019 ◽  
pp. 48-51
Author(s):  
O. Limarchenko ◽  
M. Sapon
Keyword(s):  
Mathematical Model ◽  
Dynamic Behavior ◽  
Liquid Flow ◽  
Dynamic Equilibrium ◽  
Longitudinal Axis ◽  
Angular Speed ◽  
System Dynamic ◽  
Dynamic Processes ◽  
Alternative States ◽  
Combined Motion

The article deals with construction of a mathematical model of combined motion of a rigid pipeline conveying liquid. The pipeline performs rotation about the longitudinal axis. For different velocities of liquid flow and pipeline rotation we determine special features of the system dynamic behavior. It was shown that oscillations in the system are developed near rectilinear and two alternative positions of dynamic equilibrium. Characteristics of phenomena manifested on transition to oscillations relative to alternative states are given.

Two Dimensional Unsteady State Mathematical Model for dispersion of Chlorine in Water in a Channel

2011 ◽  
Vol 3 (8) ◽  
pp. 503-505
Author(s):  
Jaipal Jaipal ◽  
◽  
Rakesh Chandra Bhadula ◽  
V. N Kala V. N Kala
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Unsteady State

scholarly journals Damping forced oscillations in power system via interline power flow controller with additional repetitive control

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Shirui Feng ◽  
Xi Wu ◽  
Zhenquan Wang ◽  
Tao Niu ◽  
Qiong Chen
Keyword(s):  
Power Flow ◽  
Forced Oscillation ◽  
Control Method ◽  
Damping Ratio ◽  
Repetitive Control ◽  
Oscillation Amplitude ◽  
Reference Value ◽  
Forced Oscillations ◽  
Flow Controller ◽  
Power Flow Controller

AbstractWith the continuous expansion of power systems and the application of power electronic equipment, forced oscillation has become one of the key problems in terms of system safety and stability. In this paper, an interline power flow controller (IPFC) is used as a power suppression carrier and its mechanism is analyzed using the linearized state-space method to improve the system damping ratio. It is shown that although the IPFC can suppress forced oscillation with well-designed parameters, its capability of improving the system damping ratio is limited. Thus, combined with the repetitive control method, an additional repetitive controller (ARC) is proposed to further dampen the forced power oscillation. The ARC control scheme is characterized by outstanding tracking performance to a system steady reference value, and the main IPFC controller with the ARC can provide higher damping, and further reduce the amplitude of oscillations to zero compared with a supplementary damping controller (SDC). Simulation results show that the IPFC with an ARC can not only greatly reduce the oscillation amplitude, but also actively output the compensation power according to the reference value of the ARC tracking system.

Study on Grinding Force in Two-Dimensional Ultrasonic Grinding Nano-Ceramics

2010 ◽  
Vol 42 ◽  
pp. 204-208 ◽  
Author(s):  
Xiang Dong Li ◽  
Quan Cai Wang
Keyword(s):  
Mathematical Model ◽  
Ultrasonic Vibration ◽  
Contact Time ◽  
Reaction Force ◽  
Grinding Force ◽  
Two Dimensional ◽  
Indentation Fracture ◽  
Ultrasonic Grinding ◽  
The Impact ◽  
Ultrasonic Vibration Assisted Grinding

In this paper, the characteristic of grinding force in two-dimensional ultrasonic vibration assisted grinding nano-ceramic was studied by experiment based on indentation fracture mechanics, and mathematical model of grinding force was established. The study shows that grinding force mainly result from the impact of the grains on the workpiece in ultrasonic grinding, and the pulse power is much larger than normal grinding force. The ultrasonic vibration frequency is so high and the contact time of grains with the workpiece is so short that the pulse force will be balanced by reaction force from workpiece. In grinding workpiece was loaded by the periodical stress field, which accelerates the fatigue fracture.

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

2009 ◽  
Vol 30 (4) ◽  
pp. 455-462
Author(s):  
Gai-ping Zhao ◽  
Er-yun Chen ◽  
Jie Wu ◽  
Shi-xiong Xu ◽  
M. W. Collins ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Discrete Mathematical Model

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

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