New Generic Equation for Interaction Effects on a Moored Containership Due to a Passing Tanker

2006 ◽  
Vol 50 (03) ◽  
pp. 278-287 ◽  
Author(s):  
K. S. Varyani ◽  
M. Vantorre
Keyword(s):  
Horizontal Plane ◽  
Hydrodynamic Interaction ◽  
Equations Of Motion ◽  
Test Program ◽  
Ship Maneuvering ◽  
Interaction Forces ◽  
Captive Model Test ◽  
The Mathematical Model ◽  
Generic Equation ◽  
Systematic Database

In order to improve the formulation of moored-passing ship interaction forces and moments in the mathematical model of a ship maneuvering simulator, a comprehensive captive model test program was carried out and a theoretical calculation method was developed. At present, semiempirical approaches, resulting in an estimation of forces and moments in the horizontal plane caused by hydrodynamic interaction on a moored ship due to a passing ship, are not available in literature. The present research intends to enhance the theoretical approach by validating the calculated peak forces and moments with experimental data. The numerical method is subsequently applied to generate a systematic database for the development of a new set of generic formulae for estimating the effect of passing vessels on moored ships in the equations of motion for surge, sway, and yaw applied in maneuvering and moor-ing simulators.

scholarly journals A Fast Algorithm for the Prediction of Ship-Bank Interaction in Shallow Water

2020 ◽  
Vol 8 (11) ◽  
pp. 927
Author(s):  
Jin Huang ◽  
Chen Xu ◽  
Ping Xin ◽  
Xueqian Zhou ◽  
Serge Sutulo ◽  
...  
Keyword(s):  
Shallow Water ◽  
Hydrodynamic Interaction ◽  
Surface Boundary ◽  
Complex Flow ◽  
Ship Maneuvering ◽  
Interaction Forces ◽  
Rankine Source ◽  
Bank Effect ◽  
Sinkage And Trim ◽  
Navigation Safety

The hydrodynamic interaction induced by the complex flow around a ship maneuvering in restricted waters has a significant influence on navigation safety. In particular, when a ship moves in the vicinity of a bank, the hydrodynamic interaction forces caused by the bank effect can significantly affect the ship’s maneuverability. An efficient algorithm integrated in onboard systems or simulators for capturing the bank effect with fair accuracy would benefit navigation safety. In this study, an algorithm based on the potential-flow theory is presented for efficient calculation of ship-bank hydrodynamic interaction forces. Under the low Froude number assumption, the free surface boundary condition is approximated using the double-body model. A layer of sources is dynamically distributed on part of the seabed and bank in the vicinity of the ship to model the boundary conditions. The sinkage and trim are iteratively solved via hydrostatic balance, and the importance of including sinkage and trim is investigated. To validate the numerical method, a series of simulations with various configurations are carried out, and the results are compared with experiment and numerical results obtained with RANSE-based and Rankine source methods. The comparison and analysis show the accuracy of the method proposed in this paper satisfactory except for extreme shallow water cases.

A Unified Frequency Equation and the Motion Analysis of a Moving Flexible Beam Carrying a Concentrated Mass

1999 ◽  
Author(s):  
S. Park ◽  
J. W. Lee ◽  
Y. Youm ◽  
W. K. Chung
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Open Loop ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Lumped Mass ◽  
Concentrated Mass ◽  
Forcing Function ◽  
The Mathematical Model

Abstract In this paper, the mathematical model of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying an intermediate lumped mass is derived. The equations of motion of the beam-mass-cart system is analyzed utilizing unconstrained modal analysis, and a unified frequency equation which can be generally applied to this kind of system is obtained. The change of natural frequencies and mode shapes with respect to the change of the mass ratios of the beam, the lumped mass and the cart and to the position of the lumped mass is investigated. The open-loop responses of the system by arbitrary forcing function are also obtained through numerical simulations.

Dynamics of MEMS-Based Angular Rate Sensors Excited via External Electrostatic Forces

2020 ◽  
Author(s):  
Ibrahim F. Gebrel ◽  
Ligang Wang ◽  
Samuel F. Asokanthan
Keyword(s):  
Dynamic Behavior ◽  
Electrostatic Force ◽  
Angular Rate ◽  
Equations Of Motion ◽  
Ring Structure ◽  
Dynamic Responses ◽  
Actuator Dynamics ◽  
Vibratory Gyroscopes ◽  
Thin Ring ◽  
The Mathematical Model

Abstract This paper investigates the dynamic behavior of rotating MEMS-based vibratory gyroscopes which employs a thin ring as the vibrating flexible element. The mathematical model for the MEMS ring structure as well as a model for the nonlinear electrostatic excitation forces are formulated. Galerkin’s procedure is employed to reduce the equations of motion to a set of ordinary differential equations. Understanding the effects of nonlinear actuator dynamics is considered important for characterizing the dynamic behavior of such devices. A suitable theoretical model to generate nonlinear electrostatic force that acts on the MEMS ring structure is formulated. Dynamic responses in the driving and the sensing directions are examined via time responses, phase diagram, and Poincare’ map plots when the input angular motion and the nonlinear electrostatic force are considered simultaneously. The analysis is envisaged to aid fabrication of this class of devices as well as for providing design improvements in MEMS Ring-based Gyroscopes.

Effects of Hull and Control Surface Roughness on Ship Maneuvering

2020 ◽  
pp. 1-10
Author(s):  
John C. Daidola
Keyword(s):  
Surface Roughness ◽  
Equations Of Motion ◽  
Control Surface ◽  
Ship Maneuvering ◽  
Single Screw ◽  
Operation And Maintenance ◽  
Hydrodynamic Derivatives ◽  
Turning Maneuver ◽  
And Control ◽  
Surface Vessel

The effects of hull roughness on ship maneuvering characteristics are investigated. The hydrodynamic derivatives in the equations of motion for surface vessel maneuvering are modified to incorporate roughness of the hull and rudder. Vessel lifetime roughness profiles are postulated based on construction, coatings, operation, and maintenance for a vessel life of 25 years. These are then applied to the turning maneuver for single screw cargo ships with block coefficients from .60 to .80. The implications for naval missions are discussed.

scholarly journals Free Interfaces at the Tips of the Cilia in the One-Dimensional Periciliary Layer

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1961
Author(s):  
Kanognudge Wuttanachamsri
Keyword(s):  
Mathematical Model ◽  
Exact Solution ◽  
Free Boundary ◽  
Horizontal Plane ◽  
Numerical Solutions ◽  
Numerical Results ◽  
Brinkman Equation ◽  
Average Height ◽  
Free Interface ◽  
The Mathematical Model

Cilia on the surface of ciliated cells in the respiratory system are organelles that beat forward and backward to generate metachronal waves to propel mucus out of lungs. The layer that contains the cilia, coating the interior epithelial surface of the bronchi and bronchiolesis, is called the periciliary layer (PCL). With fluid nourishment, cilia can move efficiently. The fluid in this region is named the PCL fluid and is considered to be an incompressible, viscous, Newtonian fluid. We propose there to be a free boundary at the tips of cilia underlining a gas phase while the cilia are moving forward. The Brinkman equation on a macroscopic scale, in which bundles of cilia are considered rather than individuals, with the Stefan condition was used in the PCL to determine the velocity of the PCL fluid and the height/shape of the free boundary. Regarding the numerical methods, the boundary immobilization technique was applied to immobilize the moving boundaries using coordinate transformation (working with a fixed domain). A finite element method was employed to discretize the mathematical model and a finite difference approach was applied to the Stefan problem to determine the free interface. In this study, an effective stroke is assumed to start when the cilia make a 140∘ angle to the horizontal plane and the velocitiesof cilia increase until the cilia are perpendicular to the horizontal plane. Then, the velocities of the cilia decrease until the cilia make a 40∘ angle with the horizontal plane. From the numerical results, we can see that although the velocities of the cilia increase and then decrease, the free interface at the tips of the cilia continues increasing for the full forward phase. The numerical results are verified and compared with an exact solution and experimental data from the literature. Regarding the fixed boundary, the numerical results converge to the exact solution. Regarding the free interface, the numerical solutions were compared with the average height of the PCL in non-cystic fibrosis (CF) human tissues and were in excellent agreement. This research also proposes possible values of parameters in the mathematical model in order to determine the free interface. Applications of these fluid flows include animal hair, fibers and filter pads, and rice fields.

Theoretical and Experimental Study of the Dynamics of the Tripod-Ball Sliding Joint With Clearance

2001 ◽  
Author(s):  
Jia Xiaohong ◽  
Ji Linhong ◽  
Jin Dewen ◽  
Zhang Jichuan
Keyword(s):  
Mathematical Model ◽  
Equations Of Motion ◽  
Experimental Studies ◽  
Active System ◽  
New Concepts ◽  
Sliding Joint ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model ◽  
Kane Method

Abstract Clearance is inevitable in the kinematic joints of mechanisms. In this paper the dynamic behavior of a crank-slider mechanism with clearance in its tripod-ball sliding joint is investigated theoretically and experimentally. The mathematical model of this new-type joint is established, and the new concepts of basal system and active system are put forward. Based on the mode-change criterion established in this paper, the consistent equations of motion in full-scale are derived by using Kane method. The experimental rig was set up to measure the effects of the clearance on the dynamic response. Corresponding experimental studies verify the theoretical results satisfactorily. In addition, due to the nonlinear elements in the improved mathematical model of the joint with clearance, the chaotic responses are found in numerical simulation.

Electrostatically Actuated Coupled MEMS Resonators

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Kyle N. Taylor
Keyword(s):  
Nonlinear Response ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
System Structure ◽  
Lagrange Equations ◽  
Electrostatically Actuated ◽  
Beam System ◽  
Mems Resonators ◽  
The Mathematical Model ◽  
Steady State Solutions

This paper deals with the nonlinear response of an electrostatically actuated cantilever beam system composed of two micro beam resonators near natural frequency. The mathematical model of the system is obtained using Lagrange equations. The equations of motion are nondimensionalized and then the method of multiple scales is used to find steady state solutions. Both AC and DC actuation voltages of the first beam are considered, while the influence on the system of DC on the second beam is explored. Graphical representations of the influence of the detuning parameters are provided for a typical micro beam system structure.

Hydrodynamic Interaction Forces on Ship Hulls Equipped With Propulsors

2012 ◽  
Author(s):  
Serge Sutulo ◽  
C. Guedes Soares
Keyword(s):  
Pressure Distribution ◽  
Hydrodynamic Interaction ◽  
Potential Interaction ◽  
Interaction Forces ◽  
Ship Hulls ◽  
Actuator Disk ◽  
Close Proximity ◽  
Body Potential ◽  
Yaw Moment ◽  
Accelerating Motion

Typically, study of hydrodynamic interaction between vessels navigating in close proximity to each other is limited to hydrodynamics of bare hulls. Meanwhile, ship propulsors, especially heavily loaded, which may happen in accelerating motion, can alter substantially the flow and distribution of pressure on the hulls which can be viewed as generalization of the thrust deduction phenomenon. The 3D doubled body potential interaction code based on the source panel method developed earlier by the authors has been enhanced to include the effect of a propeller on each of the interacting ships under the assumption that the propeller jets (slipstreams) are not involved into the interaction. Each propeller is simulated by a disk of sinks further approximated with a polygon composed of identical triangular panels with identical constant sink density linked to the thrust of the propulsor according to the actuator disk theory. Comparative computations were carried out for two identical tanker vessels in the close-proximity overtaking manoeuvre at various values of the loading coefficient of each propeller. The loading coefficient is not supposed to be necessarily defined by the steady propulsion point. Numerical results demonstrate that a heavily loaded propeller substantially modifies the pressure distribution on both hulls resulting in alteration of the hydrodynamic interaction loads, especially of the surge force and yaw moment.

Melnikov-based analysis for chaotic dynamics of spin-orbit motion of a gyrostat satellite

2019 ◽  
Vol 233 (4) ◽  
pp. 931-941
Author(s):  
Seyed Mahdi Abtahi
Keyword(s):  
Equations Of Motion ◽  
Time History ◽  
Melnikov Method ◽  
Spin Orbit ◽  
Attitude Dynamics ◽  
Inertia Moment ◽  
Coupled Equations ◽  
Highly Nonlinear ◽  
Complex Spin ◽  
The Mathematical Model

Interactions of the orbital motion on attitude dynamics of the gyrostat satellite are considered in this paper. The mathematical model is derived using the Hamiltonian method for the spin-orbit motion of the spacecraft followed by the reduction of the coupled equations of motion using the extended Deprit canonical transformation. The analytical Melnikov method is used innovatively to study chaos on the complex Spin-Orbit dynamics of the gyrostat satellite. Also, the numerical methods such as Lyapunov exponent criterion, Poincaré section, trajectories of phase portrait, and the time–history responses can be proved the heteroclinic bifurcation and chaotic vibrations in the highly nonlinear system. Using the results based on the Melnikov integral, the parameters of the spacecraft including the mass and inertia moment of satellite with respect to the altitude of orbit can be designed in order to control the bifurcation with a view to prevention of chaos in the system in the absence of an active control system.

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