The Effects of Flare and Overhangs on the Motions of a Yacht in Head Seas

1993 ◽  
Author(s):  
John C. Kuhn ◽  
Eric C. Schlageter
Keyword(s):  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Order Effects ◽  
Third Order ◽  
Numerical Work ◽  
Strip Theory ◽  
Hull Forms ◽  
The Time Domain ◽  
The Impact

The coupled heave and pitch motions of hull forms with flare and overhangs are examined numerically. The presence of flare and overhangs is numerically modelled with nonlinear hydrostatic and Froude-Krylov forces based on integrals over the instantaneous wetted surface. Forces due to radiation and diffraction are computed with a linear strip-theory. These forces are combined in two coupled nonlinear differential equations of motion that are solved in the time domain with a fourth-order Runge-Kutta integration method. An assessment of the impact of flare and overhangs on motions is obtained by comparing these nonlinear solutions with solutions of the traditional linear equations of motion, which do not contain forces due to flare and overhangs. For an example based on an International America's Cup Class yacht design, it is found that the nonlinear heave and pitch motions are smaller than the linear motions. This is primarily due to reduced first-order response components, which are coupled with nonlinear response components. Comparisons of these results with towing tank data demonstrate that the nonlinear procedure improves prediction quality relative to linear results. In support of this numerical work, the hydrostatic and Froude­Krylov force integrals are expanded in Taylor series with respect to wave elevation. These results indicate how hydrostatic and Froude-Krylov forces change with changing flare and overhang angles, revealing that sectional slope has second and third-order effects on forces while sectional curvature and overhang angles produce third-order effects.

scholarly journals Generalized eigenfunction method for floating bodies

2011 ◽  
Vol 667 ◽  
pp. 544-554 ◽  
Author(s):  
COLM J. FITZGERALD ◽  
MICHAEL H. MEYLAN
Keyword(s):  
Time Domain ◽  
Water Waves ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Two Dimensions ◽  
Floating Body ◽  
Floating Bodies ◽  
Abstract Wave Equation ◽  
Generalized Eigenfunction ◽  
The Time Domain

We consider the time domain problem of a floating body in two dimensions, constrained to move in heave and pitch only, subject to the linear equations of water waves. We show that using the acceleration potential, we can write the equations of motion as an abstract wave equation. From this we derive a generalized eigenfunction solution in which the time domain problem is solved using the frequency-domain solutions. We present numerical results for two simple cases and compare our results with an alternative time domain method.

Aeroelastic Stability and Response of Composite Swept Wings in Subsonic Flow Using Indicial Aerodynamics

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
S. A. Sina ◽  
T. Farsadi ◽  
H. Haddadpour
Keyword(s):  
Compressible Flow ◽  
Structural Model ◽  
Equations Of Motion ◽  
Aeroelastic Stability ◽  
Aeroelastic System ◽  
Aeroelastic Instability ◽  
Eigen Analysis ◽  
Strip Theory ◽  
The Time Domain ◽  
Composite Wing

In this study, the aeroelastic stability and response of an aircraft swept composite wing in subsonic compressible flow are investigated. The composite wing was modeled as an anisotropic thin-walled composite beam with the circumferentially asymmetric stiffness structural configuration to establish proper coupling between bending and torsion. Also, the structural model consists of a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, nonuniform torsional model, and rotary inertia. The finite state form of the unsteady aerodynamic loads have been modeled based on the indicial aerodynamic theory and strip theory in the subsonic compressible flow. Novel Mach dependent exponential approximations of the indicial aerodynamic functions have been developed. The extended Galerkin’s method was used to construct the mass, stiffness, and damping matrices of the nonconservative aeroelastic system. Eigen analysis of the system was performed to obtain the aeroelastic instability (divergence and flutter) boundaries. Also, solving the equations of motion in the time domain leads to the aeroelastic response of wing in different flight speeds. The obtained results are compared with the available results in the literature, which reveals an excellent agreement. The numerical results obtained in this article seek to clarify the effects of geometrical and material couplings and flight Mach number on the aeroelastic instability and response of composite wings in subsonic compressible flow.

Numerical Simulation of Flutter of Suspension Bridges

1997 ◽  
Vol 50 (11S) ◽  
pp. S174-S179 ◽  
Author(s):  
S. Preidikman ◽  
D. T. Mook
Keyword(s):  
Control Systems ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Suspension Bridges ◽  
Governing Equations ◽  
Nonlinear Springs ◽  
Linear Equations Of Motion ◽  
The Time Domain ◽  
Present Simulation ◽  
Post Onset

A method for simulating the spontaneous, wind-excited vibrations of suspension bridges is described. The approach is based on a numerical model that treats the bridge and flowing air as elements of a single dynamic system; and all of the governing equations are integrated numerically, simultaneously, and interactively. It is shown that the present simulation predicts the same onset of flutter as the analysis of Fung. Unlike Fung’s analysis, the present analysis provides the solution in the time domain, is not restricted to periodic motions or linear equations of motion, and provides post-onset behavior as long as the effective angles of attack are not large enough to produce stall. As a consequence, the present analysis can be a very effective tool for the design of flutter-suppressing control systems. Because the equations are solved numerically, nonlinear supports do not present a problem. In the present work, it is shown how the nonlinear springs lead to limit-cycle responses.

Characteristic Parameter Estimation of AMB Supported Coupled Rotor System

2017 ◽  
Author(s):  
Sampath Kumar Kuppa ◽  
Mohit Lal
Keyword(s):  
Frequency Domain ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Characteristic Parameter ◽  
Estimation Of Parameters ◽  
Characteristic Parameters ◽  
Full Spectrum ◽  
Lagrange’S Equation ◽  
Amb System ◽  
The Time Domain

In this article, a rotor–bearing–coupling system supported by Active Magnetic Bearings (AMBs) is numerically simulated to estimate the characteristic parameters of AMB, residual unbalance, and misalignment parameters. The system is modeled with two rigid massless rotors each having a rigid disc and an AMB at its mid-span, mounted on flexible bearings and connected together with a flexible coupling. Proportional–Differential–Integrator (PID) is used to control the controlling current in AMB. Lagrange’s equation is used to obtain the linear equations of motion (EOMs) of the system. The developed EOM is solved by the fourth order Runga–Kutta method to generate the displacement and current responses. The time domain responses are converted into frequency domain by using Fast Fourier Transform (FFT) and full spectrum analysis is carried out to estimate the characteristic parameters of rotor AMB system. The estimation of parameters is performed based on least squares approach in frequency domain. The proposed methodology is tested against different levels of measurement error and modelling error to check the robustness of the algorithm.

Ship Motion Computations Using a High Froude Number Time Domain Strip Theory

2006 ◽  
Vol 50 (01) ◽  
pp. 15-30
Author(s):  
D. S. Holloway ◽  
M. R. Davis
Keyword(s):  
Froude Number ◽  
Time Domain ◽  
High Speed ◽  
Equations Of Motion ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Viscous Effects ◽  
Strip Theory ◽  
Large Amplitude Motions ◽  
The Time Domain

High-speed strip theories are discussed, and a time domain formulation making use of a fixed reference frame for the two-dimensional fluid motion is described in detail. This, and classical (low-speed) strip theory, are compared with the experimental results of Wellicome et al. (1995) up to a Froude number of 0.8, as well as with our own test data for a semi-SWATH, demonstrating the marked improvement of the predictions of the former at high speeds, while the need to account for modest viscous effects at these speeds is also argued. A significant contribution to time domain computations is a method of stabilizing the integration of the ship's equations of motion, which are inherently unstable due to feedback from implicit added mass components of the hydrodynamic force. The time domain high-speed theory is recommended as a practical alternative to three-dimensional methods. It also facilitates the investigation of large-amplitude motions with stern or bow emergence and forms a simulation base for the investigation of ride control systems and local or global loads.

Nonlinear Response of a Sandwich Plate Subjected to Blast Load

2007 ◽  
Author(s):  
Ali Bas¸ ◽  
Zafer Kazancı ◽  
Zahit Mecitog˘lu
Keyword(s):  
Sandwich Plate ◽  
Virtual Work ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Blast Load ◽  
Thin Plates ◽  
Inertia Effects ◽  
The Time Domain ◽  
The Galerkin Method

Present work includes in-plane stiffness and inertia effects on the motion of a sandwich plate under blast load. The geometric nonlinearity effects are taken into account with the von Ka´rma´n large deflection theory of thin plates. All edges clamped boundary conditions are considered in the analyses. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solutions are assumed for the space domain and substituted into the equations of motion. Then the Galerkin Method is used to obtain the nonlinear differential equations in the time domain. The finite difference method is applied to solve the system of coupled nonlinear equations. The results of theoretical analyses are obtained.

Modeling, Simulation, and Modal Analysis of a Hydraulic Valve Lifter With Oil Compressibility Effects

1991 ◽  
Vol 113 (1) ◽  
pp. 46-54 ◽  
Author(s):  
C. T. Hatch ◽  
A. P. Pisano
Keyword(s):  
Differential Equations ◽  
Modal Analysis ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Check Valve ◽  
Third Order ◽  
Bulk Oil ◽  
Special Cases ◽  
Linear Differential ◽  
Hydraulic Valve

A two-degree-of-freedom (2-DOF), analytical model of a hydraulic valve lifter is derived. Special features of the model include the effects of bulk oil compressibility, multimode behavior due to plunger check valve modeling, and provision for the inclusion of third and fourth body displacements to aid in the use of the model in extended, multi-DOF systems. It is shown that motion of the lifter plunger and body must satisfy a coupled system of third-order, nonlinear differential equations of motion. It is also shown that the special cases of zero oil compressibility and/or 1-DOF motion of lifter plunger can be obtained from the general third-order equations. For the case of zero oil compressibility, using Newtonian fluid assumptions, the equations of motion are shown to reduce to a system of second-order, linear differential equations. The differential equations are numerically integrated in five scenarios designed to test various aspects of the model. A modal analysis of the 2-DOF, compressible model with an external contact spring is performed and is shown to be in excellent agreement with simulation results.

scholarly journals Impact of a Multiple Pendulum with a Non-Linear Contact Force

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1202
Author(s):  
Dan B. Marghitu ◽  
Jing Zhao
Keyword(s):  
Kinetic Energy ◽  
Contact Force ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Kinematic Chain ◽  
Double Pendulum ◽  
Lagrange Equations ◽  
Non Linear ◽  
Impact Kinetic Energy ◽  
The Impact

This article presents a method to solve the impact of a kinematic chain in terms of a non-linear contact force. The nonlinear contact force has different expressions for elastic compression, elasto-plastic compression, and elastic restitution. Lagrange equations of motion are used to obtain the non-linear equations of motion with friction for the collision period. The kinetic energy during the impact is compared with the pre-impact kinetic energy. During the impact of a double pendulum the kinetic energy of the non-impacting link is increasing and the total kinetic energy of the impacting link is decreasing.

Parametric Rolling Simulations of Container Ships

2013 ◽  
Author(s):  
Anton Turk ◽  
Jasna Prpić-Oršić ◽  
Carlos Guedes Soares
Keyword(s):  
Time Domain ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Full Range ◽  
Ship Motions ◽  
Computationally Efficient ◽  
Parametric Roll ◽  
Parametric Rolling ◽  
Strip Theory ◽  
The Time Domain

A hybrid nonlinear time domain seakeeping analysis is applied to the study of a container ship advancing at different headings and encounter frequencies. A time-domain nonlinear strip theory in six degrees-of-freedom has been extended to predict ship motions by solving the unsteady hydrodynamic problem in the frequency domain and the equations of motion in the time domain which allows introducing nonlinearities in the linear model. The code is used to make parametric roll predictions for various speeds and headings and the results are summarized in a very intuitive 2D and 3D polar plots showing the full range of the parametric rolling realizations. The method developed is fairly accurate, robust, very computationally efficient, and can predict nonlinear ship motions. It is well suited to be used as a tool in ship design or as part of a path optimization model.

Use of an Electro-Optical-Mechanical Mooring Cable for Oceanographic Buoys: Modeling and Validation

2005 ◽  
Author(s):  
Andrew Hamilton ◽  
Mark Chaffey
Keyword(s):  
Numerical Modeling ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Data Communication ◽  
Monterey Bay ◽  
Test Results ◽  
Sea Floor ◽  
New Locations ◽  
Mooring Cable ◽  
The Time Domain

This paper presents results of numerical modeling of an oceanographic mooring system and makes comparisons to loads measured on a deployed test mooring near Monterey Bay, California. The numerical modeling solves the non-linear equations of motion of the cable in the time-domain. The deployed system is instrumented to monitor environmental loading and the resulting tensions in the mooring cable below the buoy and above the anchor. Comparison of the numerical results to the measured results is useful to refine the accuracy of the model, allowing its use in determining fatigue life of the system and for designing similar systems to be deployed in new locations. This study is part of a project to develop and improve mooring systems for oceanographic use that include an electro-optical-mechanical mooring cable that delivers power and data communication to a network of sea-floor instrumentation. The modeling and test results highlight the engineering challenges associated with designing these systems for long lifetimes.

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