Ship Motions From Unsteady Maneuvering in Two-Dimensional Waves: Part II—Analysis of Data

2011 ◽  
Author(s):  
Joseph T. Klamo ◽  
Ray-Qing Lin
Keyword(s):  
Wave Field ◽  
Degrees Of Freedom ◽  
Nonlinear Effects ◽  
Ship Motions ◽  
Two Dimensional ◽  
Linear Superposition ◽  
One Dimensional ◽  
Model Response ◽  
Experimental Laboratory ◽  
Dimensional Wave

An experimental test has been conducted to measure the six degrees-of-freedom motions of a remote-controlled model attempting to hold heading while at forward speed in a two-dimensional wave field. During testing, the two underlying components of the wave field were always orthogonal to each other but various relative headings of the model to the dominant wave were explored. Of particular interest is understanding the nonlinear effects of the two distinct underlying wave encounter frequencies on the model response and the severity to which it causes the response in the two-dimensional wave field to differ from the linear summation of responses from equivalent one-dimensional waves. Since the experimental data contains the full wave-wave and wave-ship interactions of the two-dimensional wave field, we will use numerical results from the Digital, Self-consistent Ship Experimental Laboratory (DiSSEL) to generate the necessary one-dimensional wave results. This allows us to compare the predicted ship response motions from linear superposition of two one-dimensional wave field responses to the measured motions in a two-dimensional wave field for various relative wave heading combinations. It will be shown that for waves forward of beam, the predicted pitch results from superposition are fairly accurate while the roll prediction is not. However, for waves aft of beam, the motion predictions from linear superposition of pitch and roll are both poor. In such aft of beam cases, the disagreement can be quite large due to deviations in the ship heading caused by drift forces.

Ship Motions From Unsteady Maneuvering in Two-Dimensional Waves: Part I—Numerical Simulations

2011 ◽  
Author(s):  
Ray-Qing Lin ◽  
Joseph T. Klamo
Keyword(s):  
Solid Body ◽  
Degrees Of Freedom ◽  
Rapid Change ◽  
Ship Motions ◽  
Two Dimensional ◽  
Wave Interactions ◽  
Challenging Tasks ◽  
Experimental Laboratory ◽  
Nonlinear Ship Motion ◽  
Dimensional Wave

Numerically simulating the six-degrees-of-freedom response motions of a ship executing an unsteady maneuver in a two-dimensional wave environment is one of the most challenging tasks in seakeeping. Mathematical difficulties may occur for several reasons. For example, the rapid change in encounter frequencies may cause a numerical dynamics imbalance. Furthermore, in order to predict the ship’s track (ship heading) accurately, the rudder forces and two-dimensional drift forces must be predicted accurately; otherwise, erroneously predicted headings can ultimately lead to obtaining entirely different ship motions. To overcome these problems, we added a well-behaved, pre-conditional iterative method into the hybrid flow-based, fully-nonlinear ship motion model, DiSSEL (Digital, Self-consistent Ship Experimental Laboratory), in a two-dimensional wave environment. DiSSEL includes two components: a ship-wave interactions model (Lin et al., 2005[1], Lin and Kuang, 2006[2]), and a solid body motions interactions model (Lin and Kuang 2010[3]). The rudder and appendage forces (Lin et al, 2010[4]) are included in the solid body motions component. This refined model is able to overcome the mathematical dynamics imbalance when the encounter frequency rapidly changes as well as accurately calculate the forces on the hull and rudders. Finally the simulations of ship response motions at various relative headings and at various forward speeds in a two-dimensional seaway will be benchmarked against experimental model data for the test cases.

scholarly journals Nonlinear processes in the bunched electron beams of high-power klystrons and the limits of analytical and one-dimensional numerical models applicability for their analysis.

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
V.Y. Rodyakin ◽  
◽  
V.M. Pikunov ◽  
V.N. Aksenov ◽  
◽  
...  
Keyword(s):  
Electron Beam ◽  
High Power ◽  
Numerical Models ◽  
Nonlinear Effects ◽  
Analytical Models ◽  
Modulation Amplitude ◽  
Two Dimensional ◽  
One Dimensional ◽  
Charge Parameter ◽  
Program Data

We present the results of a comparative theoretical analysis of the electron beam bunching in a single-stage klystron amplifier using analytical models, a one-dimensional disk program, and a two-dimensional program. Data on the influence of various one-dimensional and two-dimensional nonlinear effects on the efficiency of electron beam bunching at different values of the space charge parameter and the modulation amplitude are presented. The limits of applicability of analytical and one-dimensional numerical models for electron beam bunching analysis in high-power klystron amplifiers are found.

Three-Dimensional Periodic Fully Nonlinear Potential Waves

2013 ◽  
Author(s):  
Dmitry Chalikov ◽  
Alexander V. Babanin
Keyword(s):  
Wave Field ◽  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Transform Method ◽  
Fully Nonlinear ◽  
Stokes Waves ◽  
Nonlinear Potential ◽  
The Fourier Transform

An exact numerical scheme for a long-term simulation of three-dimensional potential fully-nonlinear periodic gravity waves is suggested. The scheme is based on a surface-following non-orthogonal curvilinear coordinate system and does not use the technique based on expansion of the velocity potential. The Poisson equation for the velocity potential is solved iteratively. The Fourier transform method, the second-order accuracy approximation of the vertical derivatives on a stretched vertical grid and the fourth-order Runge-Kutta time stepping are used. The scheme is validated by simulation of steep Stokes waves. The model requires considerable computer resources, but the one-processor version of the model for PC allows us to simulate an evolution of a wave field with thousands degrees of freedom for hundreds of wave periods. The scheme is designed for investigation of the nonlinear two-dimensional surface waves, for generation of extreme waves as well as for the direct calculations of a nonlinear interaction rate. After implementation of the wave breaking parameterization and wind input, the model can be used for the direct simulation of a two-dimensional wave field evolution under the action of wind, nonlinear wave-wave interactions and dissipation. The model can be used for verification of different types of simplified models.

A General Continuum Theory With Microstructure for Wave Propagation in Elastic Laminated Composites

1974 ◽  
Vol 41 (1) ◽  
pp. 101-105 ◽  
Author(s):  
G. A. Hegemier ◽  
T. C. Bache
Keyword(s):  
Wave Propagation ◽  
Continuum Model ◽  
Laminated Composites ◽  
Continuum Theory ◽  
Velocity Spectrum ◽  
Two Dimensional ◽  
One Dimensional ◽  
General Continuum ◽  
Hierarchy Of Models ◽  
Dimensional Wave

A continuum theory with microstructure for wave propagation in laminated composites, proposed in previous works concerning propagation normal and parallel to the laminates, is extended herein to the general two-dimensional case. Continuum model construction is based upon an asymptotic scheme in which dominant signal wavelengths are assumed large compared to typical composite microdimensions. A hierarchy of models is defined by the order of truncation of the obtained asymptotic sequence. Particular attention is given to the lowest order dispersive theory. The phase velocity spectrum of the general theory is investigated for one-dimensional wave propagation at various propagation angles with respect to the laminates. Retention of all terms in the asymptotic sequence is found to yield the exact elasticity spectrum, while spectral collation of the lowest order dispersive theory with the first three modes of the exact theory gives excellent agreement.

scholarly journals Robustness of Polynomial Stability of Damped Wave Equations

2022 ◽  
Author(s):  
Dmytro Baidiuk ◽  
Lassi Paunonen
Keyword(s):  
Boundary Condition ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Polynomial Stability ◽  
One Dimensional ◽  
Acoustic Boundary Condition ◽  
The Stability ◽  
Perturbed Equation ◽  
Dimensional Wave

AbstractIn this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional wave equations on rectangular domains, a one-dimensional weakly damped Webster’s equation, and a wave equation with an acoustic boundary condition. In the case of Webster’s equation, we use our results to compute explicit numerical bounds that guarantee the polynomial stability of the perturbed equation.

Nonlinear Spectral Properties of Elastic Waves Propagating Along a Pantographic Metamaterial With Local Inertia Amplifiers

2021 ◽  
Author(s):  
Valeria Settimi ◽  
Marco Lepidi ◽  
Andrea Bacigalupo
Keyword(s):  
Elastic Waves ◽  
Degrees Of Freedom ◽  
Invariant Manifolds ◽  
Nonlinear Effects ◽  
Harmonic Waves ◽  
Nonlinear Dispersion ◽  
Asymptotic Approach ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Atomic Cell

Abstract Pantographic mechanisms can be introduced in the cellular periodic microstructure of architected metamaterials to achieve functional effects of local inertia amplification. The paper presents a one-dimensional pantographic metamaterial, characterized by an inertially amplified tetra-atomic cell. An internally constrained two-degrees-of-freedom model is formulated to describe the undamped free propagation of harmonic waves in the weakly nonlinear regime. A general asymptotic approach is employed to analytically determine the linear and nonlinear dispersion properties. Analytical, although asymptotically approximate, functions are obtained for the nonlinear wavefrequencies and waveforms, which show significant nonlinear effects including softening/hardening bending of the backbone curves and synclastic/anticlastic curvatures of the invariant manifolds.

scholarly journals Derivation of Second Order Partial Differential Equation Indicating Wave and Heat Equation through the Use of the Navier Stoke’s Equation for Unsteady and Incompressible Flow

2021 ◽  
Vol 2 (3) ◽  
pp. 19-21
Author(s):  
M. G. A. Hayder Chowdhury ◽  
N. Akhtar
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Incompressible Flow ◽  
Order Partial Differential Equation ◽  
Two Dimensional ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Strong Relation ◽  
Dimensional Wave ◽  
Do So

In this paper, we have tried to approach the concepts of two-dimensional wave equation and one dimensional heat equation through the means of the Navier Stoke’s equation for unsteady and incompressible flow. Our pursuit to do so has been supported with ample justifications and analytic discussions. The strong relation shared by the fluid dynamics, wave mechanics and heat flow has been brought to light through our attempts.

Sign in / Sign up

Export Citation Format

Share Document