Spectral Analysis of Nonlinear Random Wave Loadings

2005 ◽  
Author(s):  
Rujian Ma ◽  
Guixi Li ◽  
Dong Zhao
Keyword(s):  
Spectral Analysis ◽  
Finite Amplitude ◽  
Wave Profile ◽  
Circular Cylinders ◽  
Random Wave ◽  
Wave Spectra ◽  
Random Waves ◽  
First Order ◽  
Nonlinear Random Wave ◽  
Nonlinear Spectral Analysis

The spectral analysis of nonlinear random wave loadings on circular cylinders is performed in this paper by means of nonlinear spectral analysis. The study is carried out by expressing the wave profile and velocities of water particles as a nonlinear composition of the first order wave profile. Under the assumption of the first order wave profile being a zero-mean Gaussian process, the random wave spectra of finite amplitude waves are given. In order to solve the loading spectra of the finite amplitude random waves, the drag force is extended into power series of velocity. The loadings of the finite amplitude random waves are then expressed as nonlinear compositions of the first order wave profile and its derivatives. These techniques made it easier to compute the spectral densities of the finite amplitude random wave loadings.

Experimental Study of Slow-Drift Ship Motions in Shallow Water Random Waves

2011 ◽  
Author(s):  
Carl Trygve Stansberg ◽  
Trygve Kristiansen
Keyword(s):  
Spectral Analysis ◽  
Shallow Water ◽  
Transfer Functions ◽  
Second Order ◽  
Ship Motions ◽  
Random Wave ◽  
Random Waves ◽  
Low Frequencies ◽  
Wave Basin ◽  
Drift Forces

Slowly varying motions and drift forces of a large moored ship in random waves at 35m water depth are investigated by an experimental wave basin study in scale 1:50. A simple horizontal mooring set-up is used. A second-order wave correction is applied to minimize “parasitic” long waves. The effect on the ship motion from the correction is clearly seen, although less in random wave spectra than in pure bi-chromatic waves. Empirical quadratic transfer functions (QTFs) of the surge drift force are found by use of cross-bi-spectral analysis, in two different spectra have been obtained. The QTF levels increase significantly with lower wave frequencies (except at the diagonal), which is special for finite and shallow water. Furthermore, the QTF levels frequencies at low frequencies increase significantly out from the QTF diagonal. Thus Newman’s approximation should preferrably not be used in these cases. Using the LF waves as a direct excitation in a “linear” ship force analysis gives random records that compare reasonably well with those from the cross-bi-spectral analysis. This confirms the idea that the drift forces in shallow water are closely correlated to the second-order potential, and thereby by the second-order LF waves.

scholarly journals Comparison of Extreme Surface Elevation for Linear and Nonlinear Random Wave Theory for Offshore Structures

2018 ◽  
Vol 203 ◽  
pp. 01021
Author(s):  
Nurul 'Azizah Mukhlas ◽  
Noor Irza Mohd Zaki ◽  
Mohd Khairi Abu Husain ◽  
Gholamhossein Najafian
Keyword(s):  
Probabilistic Approach ◽  
Wave Theory ◽  
Offshore Structures ◽  
Random Wave ◽  
Linear Wave ◽  
Random Waves ◽  
Sea State ◽  
Higher Order Terms ◽  
Structural Responses ◽  
Nonlinear Random Wave

For offshore structural design, the load due to wind-generated random waves is usually the most important source of loading. While these structures can be designed by exposing them to extreme regular waves (100-year design wave), it is much more satisfactory to use a probabilistic approach to account for the inherent randomness of the wave loading. This method allows the statistical properties of the loads and structural responses to be determined, which is essential for the risk-based assessment of these structures. It has been recognized that the simplest wave generation is by using linear random wave theory. However, there is some limitation on its application as some of the nonlinearities cannot be explained when higher order terms are excluded and lead to underestimating of 100-year wave height. In this paper, the contribution of nonlinearities based on the second order wave theory was considered and being tested at a variety of sea state condition from low, moderate to high. Hence, it was proven that the contribution of nonlinearities gives significant impact the prediction of 100-year wave's design as it provides a higher prediction compared to linear wave theory.

An Analytical Approach for the Calculation of Random Wave Forces on Submerged Tunnels

2008 ◽  
Author(s):  
Alessandra Romolo ◽  
Giovanni Malara ◽  
Giuseppe Barbaro ◽  
Felice Arena
Keyword(s):  
Wave Field ◽  
Wave Force ◽  
Ocean Waves ◽  
Circular Cylinders ◽  
Random Wave ◽  
Vertical Force ◽  
Random Waves ◽  
Gaussian Random Process ◽  
Large Wave ◽  
Diffraction Coefficient

This paper deals with the random forces produced by high ocean waves on submerged horizontal circular cylinders. Arena [1] obtained the analytical solution of the random wave field for two dimensional waves by extending the classical Ogilvie solution [2,3] to the case of random waves. In this paper, the wave force acting on the cylinder is investigated and the Froude Krylov force [4], on the ideal water cylinder, is calculated from the random incident wave field. Both forces represent a Gaussian random process of time. The diffraction coefficient of the wave force is obtained as quotient between the standard deviations of the force on the solid cylinder and of the Froude Krylov force. It is found that the diffraction coefficient of the horizontal force Cdo is equal to the Cdv of the vertical force. Finally, it is shown that, given that a very large wave force occurs on the cylinder, it may be calculated, in time domain, starting from the Froude Krylov force. It is then shown that this result is due to the fact that the frequency spectrum of the force acting on the cylinder is nearly identical to that of the Froude-Krylov force.

scholarly journals Time Scale for Scour Beneath Pipelines Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Current

2021 ◽  
Vol 9 (2) ◽  
pp. 114
Author(s):  
Dag Myrhaug ◽  
Muk Chen Ong
Keyword(s):  
Time Scale ◽  
Current Flow ◽  
Irregular Waves ◽  
Wave Crest ◽  
Random Wave ◽  
Random Waves ◽  
Flow Conditions ◽  
Regular Waves ◽  
Nonlinear Random Waves ◽  
2D And 3D

This article derives the time scale of pipeline scour caused by 2D (long-crested) and 3D (short-crested) nonlinear irregular waves and current for wave-dominant flow. The motivation is to provide a simple engineering tool suitable to use when assessing the time scale of equilibrium pipeline scour for these flow conditions. The method assumes the random wave process to be stationary and narrow banded adopting a distribution of the wave crest height representing 2D and 3D nonlinear irregular waves and a time scale formula for regular waves plus current. The presented results cover a range of random waves plus current flow conditions for which the method is valid. Results for typical field conditions are also presented. A possible application of the outcome of this study is that, e.g., consulting engineers can use it as part of assessing the on-bottom stability of seabed pipelines.

Steep gravity waves in water of arbitrary uniform depth

1977 ◽  
Vol 286 (1335) ◽  
pp. 183-230 ◽  
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Perturbation Parameter ◽  
Intermediate Energy ◽  
Finite Amplitude ◽  
Wave Profile ◽  
Accurate Calculation ◽  
Theoretical Developments ◽  
Deep Water Waves

Modern applications of water-wave studies, as well as some recent theoretical developments, have shown the need for a systematic and accurate calculation of the characteristics of steady, progressive gravity waves of finite amplitude in water of arbitrary uniform depth. In this paper the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible. The series are extended to high order and summed with Padé approximants. For any given wavelength and depth it is found that the highest wave is not the fastest. Moreover the energy, momentum and their fluxes are found to be greatest for waves lower than the highest. This confirms and extends the results found previously for solitary and deep-water waves. By calculating the profile of deep-water waves we show that the profile of the almost-steepest wave, which has a sharp curvature at the crest, intersects that of a slightly less-steep wave near the crest and hence is lower over most of the wavelength. An integration along the wave profile cross-checks the Padé-approximant results and confirms the intermediate energy maximum. Values of the speed, energy and other integral properties are tabulated in the appendix for the complete range of wave steepnesses and for various ratios of depth to wavelength, from deep to very shallow water.

Elasticity Solution for a Radially Nonhomogeneous Hollow Circular Cylinder

1999 ◽  
Vol 66 (3) ◽  
pp. 598-606 ◽  
Author(s):  
Xiangzhou Zhang ◽  
Norio Hasebe
Keyword(s):  
Circular Cylinder ◽  
Continuous Functions ◽  
Variable Coefficients ◽  
Circular Cylinders ◽  
Explicit Solutions ◽  
Elasticity Solution ◽  
First Order ◽  
Hollow Circular Cylinder ◽  
Homogeneous Elasticity ◽  
Ordinary Differential Equation Systems

An exact elasticity solution is developed for a radially nonhomogeneous hollow circular cylinder of exponential Young’s modulus and constant Poisson’s ratio. In the solution, the cylinder is first approximated by a piecewise homogeneous one, of the same overall dimension and composed of perfectly bonded constituent homogeneous hollow circular cylinders. For each of the constituent cylinders, the solution can be obtained from the theory of homogeneous elasticity in terms of several constants. In the limit case when the number of the constituent cylinders becomes unboundedly large and their thickness tends to infinitesimally small, the piecewise homogeneous hollow circular cylinder reverts to the original nonhomogeneous one, and the constants contained in the solutions for the constituent cylinders turn into continuous functions. These functions, governed by some systems of first-order ordinary differential equations with variable coefficients, stand for the exact elasticity solution of the nonhomogeneous cylinder. Rigorous and explicit solutions are worked out for the ordinary differential equation systems, and used to generate a number of numerical results. It is indicated in the discussion that the developed method can also be applied to hollow circular cylinders with arbitrary, continuous radial nonhomogeneity.

scholarly journals Crystal flex bases and the RUM spectrum

2021 ◽  
pp. 1-27
Author(s):  
G. Badri ◽  
D. Kitson ◽  
S. C. Power
Keyword(s):  
Spectral Analysis ◽  
Space Group ◽  
First Order ◽  
2D And 3D

A theory of infinite spanning sets and bases is developed for the first-order flex space of an infinite bar-joint framework, together with space group symmetric versions for a crystallographic bar-joint framework ${{\mathcal {C}}}$ . The existence of a crystal flex basis for ${{\mathcal {C}}}$ is shown to be closely related to the spectral analysis of the rigid unit mode (RUM) spectrum of ${{\mathcal {C}}}$ and an associated geometric flex spectrum. Additionally, infinite spanning sets and bases are computed for a range of fundamental crystallographic bar-joint frameworks, including the honeycomb (graphene) framework, the octahedron (perovskite) framework and the 2D and 3D kagome frameworks.

Nonlinear Superposition Methods Applied to Continuous Ocean Wave Spectra

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Thomas B. Johannessen
Keyword(s):  
Model Comparison ◽  
Harmonic Wave ◽  
Vertical Cylinder ◽  
Wave Profile ◽  
Ocean Wave ◽  
Irregular Waves ◽  
Linear Wave ◽  
Beam Model ◽  
Wave Spectra ◽  
Linear Solution

The present paper addresses the challenges associated with applying weakly nonlinear mode-coupled solutions for wave interaction problems to irregular waves with continuous spectra. Unlike the linear solution, the nonlinear solutions will be strongly dependent on cut-off frequency for problems such as the wave elevation itself or loads on a slender cylinder used together with typical ocean wave spectra. It is found that the divergence of the solutions with respect to the cut-off frequency is related to the nonlinear interaction between waves with very different frequencies. This is, in turn, linked to a long standing discussion about the ability of mode-coupled methods to describe the modulation of a short wave due to the presence of a long wave. In cases where nonlinear properties associated with a measured or assumed history of the surface elevation is sought, it is not necessary to calculate accurately the nonlinear evolution of the wave field in space and time. For such cases it is shown that results which are independent of frequency cut-off may be obtained by introducing a maximum bandwidth in frequency between waves which are allowed to interact. It is shown that a suitable bandwidth can be found by applying this method to the problem of back-calculating a linear wave profile from a measured wave profile. In order to verify that this choice of bandwidth is suitable for second and third order terms, nonlinear loads on a slender vertical cylinder are calculated using the FNV method of Faltinsen, Newman, and Vinje (1995, “Nonlinear Wave Loads on a Slender, Vertical Cylinder,” J. Fluid Mech., 289, pp. 179–198). The method is used to compare loads calculated based on measured surface elevations with measurements of loads on two cylinders with different diameters. This comparison indicates that the bandwidth formulation is suitable and that the FNV solution gives a reasonable estimate of loading on slender cylinders. There are, however, loading mechanisms that the FNV solution does not describe, notably the secondary loading cycle first observed by Grue et al. (1993, Higher Harmonic Wave Exciting Forces on a Vertical Cylinder, Institute of Mathematics, University of Oslo, Preprint No. 2). Finally, the method is employed to calculate the ringing response on a large concrete gravity base platform. The base moment response is calculated using the FNV loading on the shafts and linear loads from a standard diffraction code, together with a structural finite element beam model. Comparison with results from a recent model testing campaign shows a remarkable agreement between the present method and the measured response.

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