Linear water waves: the horizontal motion of a structure in the time domain

2012 ◽  
Vol 709 ◽  
pp. 289-312 ◽  
Author(s):  
P. McIver
Keyword(s):  
Time Domain ◽  
Water Waves ◽  
Initial Conditions ◽  
Horizontal Motion ◽  
Floating Structure ◽  
Start Up ◽  
Specific Calculations ◽  
Linearized Theory ◽  
Infinitesimal Disturbance ◽  
The Time Domain

AbstractThe framework of the linearized theory of water waves in the time domain is used to examine the horizontal motion of an unrestrained floating structure. One of the principal assumptions of the theory is that an infinitesimal disturbance of the rest state will lead to an infinitesimal motion of the fluid and structure. It has been known for some time that for some initial conditions the theory predicts an unbounded horizontal motion of the structure that violates this assumption, but the possibility does not appear to have been examined in detail. Here some circumstances that lead to predictions of large motions are identified and, in addition, it is shown that not all non-trivial initial conditions lead to violations of the assumptions. In particular, it is shown that the horizontal motion of a floating structure remains bounded when it is initiated by the start up of a separate wave maker. The general discussion is supported by specific calculations for a vertical circular cylinder.

Experimental Validation of a Dynamic Simulation

1990 ◽  
Author(s):  
K. Harold Yae ◽  
Su-Tai Chern ◽  
Howyoung Hwang
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Simulation ◽  
Time Domain ◽  
Experimental Validation ◽  
Initial Conditions ◽  
Hydraulic Cylinder ◽  
Force Output ◽  
Inverse Dynamic ◽  
Inverse Dynamic Analysis ◽  
The Time Domain

Abstract Using forward and inverse dynamic analysis, the dynamic simulation of a backhoe has been compared with experiments. In the experiment, recorded were the configuration and force histories; that is, velocity and position, and force output from the hydraulic cylinder-all were measured in the time domain. When the experimental force history is used as driving force in the simulation, forward dynamic analysis produces a corresponding motion history. And when the experimental motion history is used as if a prescribed trajectory, inverse dynamic analysis generates a corresponding force history. Therefore, these two sets of motion and force histories — one set from experiment, and the other from the simulation that is driven forward and backward with the experimental data — are compared in the time domain. The comparisons are discussed in regard to the effects of variations in initial conditions, friction, and viscous damping.

scholarly journals Application of nonlinear dynamics methods for quantitative and qualitative evaluation of properties of 2D models of S-chaos

2021 ◽  
Vol 16 (91) ◽  
pp. 125-143
Author(s):  
Aleksei A. Gavrishev ◽  
Keyword(s):  
Nonlinear Dynamics ◽  
Lower Bound ◽  
Time Domain ◽  
Initial Conditions ◽  
Qualitative Evaluation ◽  
Recurrence Analysis ◽  
Combined Application ◽  
Student Version ◽  
The Time Domain ◽  
Property Characteristic

In this article, based on the mathematical, numerical and computer modeling carried out by the combined application of E&F Chaos, Past, Fractan, Visual Recurrence Analysis, Eviews Student Version Lite programs, some of the well-known 2D models of S-chaos are modeled, the data obtained are studied using nonlinear dynamics methods and the fact of their relation or non-relation to chaotic (quasi-chaotic) processes is established. As a result, it was found that the time diagrams obtained for the studied 2D models of S-chaos have a complex noise-like appearance and are continuous in the time domain. The resulting spectral diagrams have both a complex noise-like and regular appearance and are continuous in the spectral regions. The obtained values of BDS-statistics show that some of the time implementations can be attributed to chaotic (quasi-chaotic) processes. Also, the obtained values of BDS-statistics show that the studied 2D models of S-chaos have a property characteristic of classical chaotic (quasi-chaotic) processes: the slightest change in the initial conditions leads to the generation of a new set of signals. The obtained values of the lower bound of the KS-entropy show that the studied models also have the properties of chaotic (quasi-chaotic). Taking into account the conducted research and data from known works [1–5], it is possible to conclude that 2D models of S-chaos can relate to chaotic (quasi-chaotic) processes.

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.

Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

2019 ◽  
Vol 878 ◽  
pp. 190-220 ◽  
Author(s):  
Francesca M. Sogaro ◽  
Peter J. Schmid ◽  
Aimee S. Morgans
Keyword(s):  
Time Domain ◽  
Time Scale ◽  
Initial Conditions ◽  
Normal Modes ◽  
Time Domain Analysis ◽  
Normal Behaviour ◽  
Optimal Perturbation ◽  
Acoustic Modes ◽  
Energy Growth ◽  
The Time Domain

This study analyses the interplay between classical acoustic modes and intrinsic thermoacoustic (ITA) modes in a simple thermoacoustic system. The analysis is performed using a frequency-domain low-order network model as well as a time-domain spatially discretised model. Anti-correlated modal sensitivities are found to arise due to a pairwise interplay between acoustic and ITA modes. The magnitude of the sensitivities increases as the interplay between the modes grows stronger. The results show a global behaviour of the modes linked to the presence of exceptional points in the spectrum. The time-domain analysis results in a delay-differential equation and allows the investigation of non-normal behaviour and its consequences. Pseudospectral analysis reveals that energy amplification is crucially linked to an interplay between acoustic and ITA modes. While higher non-orthogonality between two modes is correlated with peaks in modal sensitivity, transient energy growth does not necessarily involve the most sensitive modes. In particular, growth estimates based on the Kreiss constant demonstrate that transient amplification relies critically on the proximity of the non-normal modes to the imaginary axis. The time scale for transient amplification is identified as the flame time delay, which is further corroborated by determining the optimal initial conditions responsible for the bulk of the non-modal energy growth. The flame is identified as an active and dominant contributor to energy gain. The frequency of the optimal perturbation matches the acoustic time scale, once more confirming an interplay between acoustic and ITA structures. Flame-based amplification factors of two to five are found, which are significant when feeding into the acoustic dynamics and eventually triggering nonlinear limit-cycle behaviour.

scholarly journals Scattering of gravity waves by a periodically structured ridge of finite extent

2019 ◽  
Vol 871 ◽  
pp. 350-376 ◽  
Author(s):  
Agnès Maurel ◽  
Kim Pham ◽  
Jean-Jacques Marigo
Keyword(s):  
Gravity Waves ◽  
Time Domain ◽  
Water Waves ◽  
Classical Result ◽  
Water Channel ◽  
Three Dimensional ◽  
Dimensional Problem ◽  
Homogenized Model ◽  
The Time Domain ◽  
Finite Extent

We study the propagation of water waves over a ridge structured at the subwavelength scale using homogenization techniques able to account for its finite extent. The calculations are conducted in the time domain considering the full three-dimensional problem to capture the effects of the evanescent field in the water channel over the structured ridge and at its boundaries. This provides an effective two-dimensional wave equation which is a classical result but also non-intuitive transmission conditions between the region of the ridge and the surrounding regions of constant immersion depth. Numerical results provide evidence that the scattering properties of a structured ridge can be strongly influenced by the evanescent fields, a fact which is accurately captured by the homogenized model.

A standard finite‐difference scheme for the time‐domain computation of anelastic wavefields

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 290-296 ◽  
Author(s):  
E. S. Krebes ◽  
Gerardo Quiroga‐Goode
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Time Domain ◽  
Finite Difference Scheme ◽  
Initial Conditions ◽  
Homogeneous Medium ◽  
Standard Technique ◽  
Equation Of Motion ◽  
Central Difference ◽  
The Time Domain

We show that the finite‐differencing technique based on the consecutive application of the central difference operator to spatial derivatives, a standard well‐known technique that has been commonly used in the seismological literature for solving the elastic equation of motion, can also be used to obtain a stable time‐domain, finite‐difference scheme for solving the anelastic equation of motion. We compare the results of the scheme for a heterogeneous medium with those of the time‐domain finite‐difference scheme previously developed by Emmerich and Korn and find that they agree very closely. We show, analytically, that in the case of a homogeneous medium, the two schemes give identical numerical results for certain zero initial conditions. The scheme based on the standard technique uses more computer time and memory than the scheme of Emmerich and Korn. However, from a theoretical viewpoint, it is easier to analyze, as it is developed solely with a familiar standard method.

Computing Large Amplitude Motions of a Floating Offshore Structure in the Time Domain

2008 ◽  
Author(s):  
Wei Qiu ◽  
Hongxuan Peng
Keyword(s):  
Time Domain ◽  
Large Amplitude ◽  
Offshore Structures ◽  
The Body ◽  
Surface Boundary ◽  
Offshore Structure ◽  
Floating Structure ◽  
Time Step ◽  
Large Amplitude Motions ◽  
The Time Domain

Based on the panel-free method, large-amplitude motions of floating offshore structures have been computed by solving the body-exact problem in the time domain using the exact geometry. The body boundary condition is imposed on the instantaneous wetted surface exactly at each time step. The free surface boundary is assumed linear so that the time-domain Green function can be applied. The instantaneous wetted surface is obtained by trimming the entire NURBS surfaces of a floating structure. At each time step, Gaussian points are automatically distributed on the instantaneous wetted surface. The velocity potentials and velocities are computed accurately on the body surface by solving the desingularized integral equations. Nonlinear Froude-Krylov forces are computed on the instantaneous wetted surface under the incident wave profile. Validation studies have been carried out for a Floating Production Storage and Offloading (FPSO) vessel. Computed results were compared with experimental results and solutions by the panel method.

A Numerical Method for Representing Retardation Functions With Complex Exponentials

2017 ◽  
Author(s):  
Fushun Liu ◽  
Lei Jin ◽  
Jiefeng Chen ◽  
Wei Li
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Added Mass ◽  
Memory Effects ◽  
Floating Structure ◽  
Frequency Dependent ◽  
Laplace Domain ◽  
The Time Domain ◽  
Frequency Domain Techniques

Numerical time- or frequency-domain techniques can be used to analyze motion responses of a floating structure in waves. Time-domain simulations of a linear transient or nonlinear system usually involve a convolution terms and are computationally demanding, and frequency-domain models are usually limited to steady-state responses. Recent research efforts have focused on improving model efficiency by approximating and replacing the convolution term in the time domain simulation. Contrary to existed techniques, this paper will utilize and extend a more novel method to the frequency response estimation of floating structures. This approach represents the convolution terms, which are associated with fluid memory effects, with a series of poles and corresponding residues in Laplace domain, based on the estimated frequency-dependent added mass and damping of the structure. The advantage of this approach is that the frequency-dependent motion equations in the time domain can then be transformed into Laplace domain without requiring Laplace-domain expressions of the added mass and damping. Two examples are employed to investigate the approach: The first is an analytical added mass and damping, which satisfies all the properties of convolution terms in time and frequency domains simultaneously. This demonstrates the accuracy of the new form of the retardation functions; secondly, a numerical six degrees of freedom model is employed to study its application to estimate the response of a floating structure. The key conclusions are: (1) the proposed pole-residue form can be used to consider the fluid memory effects; and (2) responses are in good agreement with traditional frequency-domain techniques.

A note on the calibration of the electromagnetic seismograph

1973 ◽  
Vol 63 (3) ◽  
pp. 1145-1155
Author(s):  
Hans Jarosch ◽  
A. R. Curtis
Keyword(s):  
Time Domain ◽  
Initial Conditions ◽  
System Parameters ◽  
Electromagnetic Seismograph ◽  
The Time Domain ◽  
Explicit Expressions

abstract Explicit expressions are given for the response in the time domain of a zerocoupled seismometer-galvanometer combination for a step of acceleration as initial conditions. The results may be directly applied for computing the system parameters.

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