Estimating Design Levels for Strongly Nonlinear Response

2012 ◽  
Author(s):  
Thomas B. Johannessen ◽  
Øistein Hagen
Keyword(s):  
Nonlinear Response ◽  
Accurate Estimation ◽  
Response Type ◽  
Weakly Nonlinear ◽  
Norwegian Sea ◽  
Strongly Nonlinear ◽  
Peak Over Threshold ◽  
Interpolation Procedure ◽  
Wave Induced

The present paper is concerned with the accurate estimation of wave induced design responses in model test campaigns where only a relatively low number of seastates can be simulated. Three response types are considered, namely an essentially linear response type such as the linear elevation of wave crests, a weakly nonlinear response type such as the second order crest elevation, and finally a discontinuous badly behaved response type such as wave in deck loading. For each of these response types, the 100 year and 10 000 year response levels are calculated for a Norwegian Sea environment. The fractiles at which these response levels occur at the governing seastate along the 100 year and 10 000 year contours, are also calculated. Having established these quantities, the efficiency of three methods is evaluated. Firstly an extreme value approach with a Gumbel assumption is considered and it is evaluated how many three hour simulations are required to obtain a good estimate of the relevant fractile levels in the governing seastate. Similarly, a peak over threshold analysis of maxima is considered and the number of seastates required is compared with the Gumbel results. Finally, the 100 year and 10 000 year response levels are estimated directly by employing an iterative procedure on the probability integral of the long term distribution of the responses together with a simple interpolation procedure. It is found that the latter procedure is efficient, particularly for strongly nonlinear response types.

Nonlinear Dynamics and Internal Resonances of a Ship With a Rectangular Cross-Section in Head Seas

2008 ◽  
Author(s):  
A. Kleiman ◽  
O. Gottlieb
Keyword(s):  
Nonlinear Dynamics ◽  
Cross Section ◽  
Nonlinear Response ◽  
Rectangular Cross Section ◽  
Orbital Stability ◽  
Internal Resonances ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Evolution Dynamics ◽  
Ship Roll

We investigate the nonlinear dynamics and internal resonances of a ship with a rectangular cross-section in head seas. We employ an asymptotic averaging method to obtain the slowly varying system evolution dynamics for the weakly nonlinear response, complemented by numerical integration in the strongly nonlinear regime. This combined approach resolves both parametric instabilities and internal resonances induced for both weak and finite nonlinear interactions, and culminates with criteria for orbital stability thresholds describing the onset of quasiperiodic response and magnification of energy transfer between coupled pitch-heave and ship roll that can lead to capsize.

Influence of Whipping on Long-term Vertical Bending Moment

2004 ◽  
Vol 48 (04) ◽  
pp. 261-272
Author(s):  
Gro Sagli Baarholm ◽  
Jørgen Juncher Jensen
Keyword(s):  
Nonlinear Response ◽  
Extreme Values ◽  
Bending Moment ◽  
Sea Waves ◽  
Short Term ◽  
Strip Theory ◽  
Long Time ◽  
Wave Induced ◽  
Vertical Bending Moment

This paper is concerned with estimating the response value corresponding to a long return period, say 20 years. Time domain simulation is required to obtain the nonlinear response, and long time series are required to limit the statistical uncertainty in the simulations. It is crucial to introduce ways to improve the efficiency in the calculation. A method to determine the long-term extremes by considering only a few short-term sea states is applied. Long-term extreme values are estimated using a set of sea states that have a certain probability of occurrence, known as the contour line approach. Effect of whipping is included by assuming that the whipping and wave-induced responses are independent, but the effect of correlation of the long-term extreme value is also studied. Numerical calculations are performed using a nonlinear, hydroelastic strip theory as suggested by Xia et al (1998). Results are presented for the S-175 containership (ITTC 1983) in head sea waves. The analysis shows that whipping increases the vertical bending moment and that the correlation is significant.

scholarly journals Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel

2009 ◽  
Vol 16 (5) ◽  
pp. 587-598 ◽  
Author(s):  
J. C. Sánchez-Garrido ◽  
V. Vlasenko
Keyword(s):  
Solitary Waves ◽  
Nonlinear Effects ◽  
Kelvin Waves ◽  
Internal Solitary Waves ◽  
Kelvin Wave ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Petviashvili Equation ◽  
Rotating Channel

Abstract. The evolution of internal solitary waves (ISWs) propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evolve differently under the action of rotation. At the first stage of evolution an initially two-dimensional ISW transforms according to the scenario described by the rotation modified Kadomtsev-Petviashvili equation, namely, it starts to evolve into a Kelvin wave (with exponential decay of the wave amplitude across the channel) with front curved backwards. This transition is accompanied by a permanent radiation of secondary Poincaré waves attached to the leading wave. However, in a strongly-nonlinear limit not all the energy is transmitted to secondary radiated waves. Part of it returns to the leading wave as a result of nonlinear interactions with secondary Kelvin waves generated in the course of time. This leads to the formation of a slowly attenuating quasi-stationary system of leading Kelvin waves, capable of propagating for several hundreds hours as a localized wave packet.

scholarly journals Energy-Based Criterion for Testing the Nonlinear Response Strength of Strong Nonlinear Oscillators

2021 ◽  
Vol 25 (2) ◽  
pp. 225-231
Author(s):  
Akuro Big-Alabo
Keyword(s):  
Nonlinear Response ◽  
Approximate Analytical Solution ◽  
Periodic Oscillation ◽  
Nonlinear Oscillators ◽  
Response Strength ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Robust Testing ◽  
Nonlinear Regimes ◽  
Testing Criteria

This article proposes a simple energy-based criterion developed to characterize four commonly identified responses, namely: linear, weakly nonlinear, moderately nonlinear and strongly nonlinear regimes. The response of the nonlinear simple pendulum was used for benchmarking the boundary conditions for each of the four response regimes and the test criterion was demonstrated using relevant examples. The test presented in this article is important for clarifying the obscurity surrounding the accuracy and range of validity of recent approximate analytical schemes used to investigate strong nonlinear oscillators. Furthermore, it is meant to create awareness of the need to develop more robust testing criteria. Keywords: strong nonlinear oscillation; periodic oscillation; approximate analytical solution

scholarly journals Epidemic malaria and warmer temperatures in recent decades in an East African highland

2010 ◽  
Vol 278 (1712) ◽  
pp. 1661-1669 ◽  
Author(s):  
David Alonso ◽  
Menno J. Bouma ◽  
Mercedes Pascual
Keyword(s):  
Climate Change ◽  
East Africa ◽  
Nonlinear Response ◽  
Climate Change Impacts ◽  
Human Model ◽  
Recent Past ◽  
East African ◽  
Highly Nonlinear ◽  
The Impact

Climate change impacts on malaria are typically assessed with scenarios for the long-term future. Here we focus instead on the recent past (1970–2003) to address whether warmer temperatures have already increased the incidence of malaria in a highland region of East Africa. Our analyses rely on a new coupled mosquito–human model of malaria, which we use to compare projected disease levels with and without the observed temperature trend. Predicted malaria cases exhibit a highly nonlinear response to warming, with a significant increase from the 1970s to the 1990s, although typical epidemic sizes are below those observed. These findings suggest that climate change has already played an important role in the exacerbation of malaria in this region. As the observed changes in malaria are even larger than those predicted by our model, other factors previously suggested to explain all of the increase in malaria may be enhancing the impact of climate change.

Load Combination for Fatigue Analysis of Ship Structures

2004 ◽  
Author(s):  
Yung S. Shin ◽  
Booki Kim ◽  
Alexander J. Fyfe
Keyword(s):  
Bending Moment ◽  
Linear Summation ◽  
Load Combination ◽  
Longitudinal Stiffeners ◽  
Stress Components ◽  
Tank Pressure ◽  
Wave Induced ◽  
Vertical Bending Moment ◽  
Oil Tanker

A methodology for calculating the correlation factors to combine the long-term dynamic stress components of ship structure from various loads in seas is presented. The methodology is based on a theory of a stationary ergodic narrow-banded Gaussian process. The total combined stress in short-tem sea states is expressed by linear summation of the component stresses with the corresponding combination factors. This expression is proven to be mathematically exact when applied to a single random sea. The long-term total stress is similarly expressed by linear summation of component stresses with appropriate combination factors. The stress components considered here are due to wave-induced vertical bending moment, wave-induced horizontal bending moment, external wave pressure and internal tank pressure. For application, the stress combination factors are calculated for longitudinal stiffeners in cargo and ballast tanks of a crude oil tanker at midship section. It is found that the combination factors strongly depend on wave heading and period in the short-term sea states. It is also found that the combination factors are not sensitive to the selected probability of exceedance level of the stress in the long-term sense.

scholarly journals Models for strongly-nonlinear evolution of long internal waves in a two-layer stratification

2007 ◽  
Vol 14 (1) ◽  
pp. 31-47 ◽  
Author(s):  
T. Sakai ◽  
L. G. Redekopp
Keyword(s):  
Internal Waves ◽  
Nonlinear Evolution ◽  
Phase Speed ◽  
Environmental Parameters ◽  
Exact Expression ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Polynomial Fit ◽  
Nonlinear Relation ◽  
Nonlinear Extensions

Abstract. Models describing the evolution of long internal waves are proposed that are based on different polynomial approximations of the exact expression for the phase speed of uni-directional, fully-nonlinear, infinitely-long waves in the two-layer model of a density stratified environment. It is argued that a quartic KdV model, one that employs a cubic polynomial fit of the separately-derived, nonlinear relation for the phase speed, is capable of describing the evolution of strongly-nonlinear waves with a high degree of fidelity. The marginal gains obtained by generating higher-order, weakly-nonlinear extensions to describe strongly-nonlinear evolution are clearly demonstrated, and the limitations of the quite widely-used quadratic-cubic KdV evolution model obtained via a second-order, weakly-nonlinear analysis are assessed. Data are presented allowing a discriminating comparison of evolution characteristics as a function of wave amplitude and environmental parameters for several evolution models.

scholarly journals Ut vis sic tensio

2018 ◽  
Vol 45 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Elastic Strain ◽  
Strain Energy ◽  
Nonlinear Response ◽  
Solid Mechanics ◽  
Functional Form ◽  
Elastic Strain Energy ◽  
Strongly Nonlinear ◽  
Long Time

The mechanical properties of rubber-like materials have been offering an outstanding challenge to the solid mechanics community for a long time. The behaviour of such materials is quite difficult to predict because rubber self-organizes into mesoscopic physical structures that play a prominent role in determining their complex, history-dependent and strongly nonlinear response. In this framework one of the main problems is to find a functional form of the elastic strain-energy that best describes the experimental data in a mathematical feasible way. The aim of this paper is to give a survey of recent advances aimed at solving such a problem.

scholarly journals Macroeconomic Risk Factor in Fuzzy Present Value of Highway Development

2018 ◽  
Vol 7 (4.33) ◽  
pp. 71
Author(s):  
Siti Salihah Shaffie ◽  
Saiful Hafizah Jaaman ◽  
Daud Mohamad
Keyword(s):  
Economic Growth ◽  
Risk Assessment ◽  
Risk Factor ◽  
Cash Flow ◽  
Capital Investment ◽  
Accurate Estimation ◽  
Present Value ◽  
Macroeconomic Risk ◽  
Macroeconomic Factor

Highway developments are the backbone for the society and economic growth. It is part of the capital investment in infrastructure developments that require high spending, long term commitment and prognosticated with numbers of risks. This is because the investment is associated with uncertainty and vagueness due to long term duration of construction and operation of the project. Hence, the valuation of the investment requires accommodated model to present more accurate estimation of the project. This study proposed to evaluate fuzzy present value of a highway project with anticipated risk assessment in its valuation using fuzzy present value. The risk assessment is part of the estimation of fuzzy cash flow to represent better present value of the project. The results show an estimated value comprise with risk assessment of macroeconomic factor to portray better estimation that can assist decision maker to make decision towards the project.   

Analysis of Ship Structural Loading in a Seaway

1972 ◽  
Vol 9 (02) ◽  
pp. 173-194
Author(s):  
Dan Hoffman
Keyword(s):  
Pressure Distribution ◽  
Phase Relationship ◽  
Bending Moment ◽  
Green Water ◽  
Detailed Structural Analysis ◽  
Transverse Pressure ◽  
Structural Loading ◽  
Wave Induced

The recent advent of the large tanker and bulk carrier has promoted the requirements for more detailed structural analysis of a ship and the reevaluation of theories for calculating the static, quasistatic and dynamic loads. The paper begins with discussion of the methods available to determine the various types of loads expected, their phase relationship, and ways of superimposing them. It then proceeds to the treatment of sea loads based on theoretical and experimental data, and techniques of determining the ship response in a seaway are discussed. The response to regular waves is reviewed with special reference to the determination of pressure distribution on the hull. Statistical ship response, immediate and cumulative over the life of the ship, is demonstrated in relation to the prediction of long-term bending moment trends, and the distribution of the extremes is discussed. Special loading conditions are described with special emphasis on the transverse pressure distribution, dynamic effects due to motion of liquid cargo in tanks, shipping of green water, wave-induced vibrations, slamming pressures and whipping stresses due to various causes. The paper treats the above subjects in a broad manner and no attempt to illustrate the theory in detail is made.

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