Statistical Analysis of Second-Order Response of Marine Structures

1985 ◽  
Vol 29 (04) ◽  
pp. 270-284 ◽  
Author(s):  
Arvid Naess
Keyword(s):  
Volterra Series ◽  
Theoretical Method ◽  
Problem Formulation ◽  
Second Order ◽  
Quadratic Term ◽  
Closed Form Solutions ◽  
Marine Structure ◽  
Asymptotic Expressions ◽  
The Mean ◽  
Extreme Responses

A theoretical method is presented for estimating the response statistics of a marine structure that can be modeled as a second-order dynamic system subjected to a stationary, Gaussian sea. The method is particularly suitable for predicting extreme responses. The problem formulation expresses the response in terms of a second-order Volterra series, that is, including a linear and a quadratic term. For this response process the mean upcrossing frequency is found and asymptotic expressions are established that can be used to obtain closed-form solutions to the extreme-value problem.

Accurate Numerical Methods for Calculating the Response Statistics of Compliant Offshore Structures

2005 ◽  
Author(s):  
A. Naess ◽  
H. C. Karlsen ◽  
P. S. Teigen
Keyword(s):  
Numerical Methods ◽  
Volterra Series ◽  
State Of The Art ◽  
Offshore Structures ◽  
Second Order ◽  
Stochastic Response ◽  
Random Seas ◽  
The Mean ◽  
Extreme Responses ◽  
Key Parameter

The state-of-the-art representation of the horizontal motions of e.g. a TLP in random seas is in terms of a second order stochastic Volterra series. Until recently, there has been no method available for accurately calculating the mean level upcrossing rate of such response processes. Since the mean upcrossing rate is a key parameter for estimating the large and extreme responses it is clearly of importance to develop methods for its calculation. The paper describes numerical methods for calculating the mean level upcrossing rate of a stochastic response process represented as a second order stochastic Volterra series. Since no approximations are made, the only source of inaccuracy is in the numerical calculation, which can be controlled.

Nonlinear, Second-Order Response Statistics of Compliant Offshore Structures

2003 ◽  
Author(s):  
A. Naess ◽  
H. C. Karlsen
Keyword(s):  
Characteristic Function ◽  
Volterra Series ◽  
Offshore Structures ◽  
Second Order ◽  
Closed Form Expression ◽  
Level Crossing Rate ◽  
Three Stages ◽  
The Mean ◽  
Joint Characteristic ◽  
Method Of Steepest Descent

The paper continues previous work to develop a new method for calculating the mean level crossing rate of a stochastic process represented as a second order stochastic Volterra series. The derivation of this procedure consists of three stages. First the expression for the mean crossing rate is rewritten in terms of a joint characteristic function. Secondly, it is noted that a closed form expression for this joint characteristic function can be derived. Thirdly, it is then demonstrated how the method of steepest descent can be applied to the numerical calculation of the mean crossing rate. It is shown by an example that the numerical accuracy of this method is apparently very high.

Visualizing the Variance of a Random Variable

2011 ◽  
Vol 18 (01) ◽  
pp. 71-85
Author(s):  
Fabrizio Cacciafesta
Keyword(s):  
Stochastic Dominance ◽  
Mean Absolute Error ◽  
Random Variable ◽  
Absolute Error ◽  
Second Order ◽  
Taylor Formula ◽  
Order Stochastic Dominance ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Options Theory

We provide a simple way to visualize the variance and the mean absolute error of a random variable with finite mean. Some application to options theory and to second order stochastic dominance is given: we show, among other, that the "call-put parity" may be seen as a Taylor formula.

Drift Forces on a Floating Body of Simple Geometry Due to Second Order Interactions Between Pairs of Harmonics With Different Frequencies

2009 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Order Problem ◽  
Simple Geometry ◽  
The Mean ◽  
Order Quantities ◽  
Drift Forces

The paper presents an investigation of the slowly varying second order drift forces on a floating body of simple geometry. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom and a ratio of diameter to draft of 3.25. The hydrodynamic problem is solved with a second order boundary element method. The second order problem is due to interactions between pairs of incident harmonic waves with different frequencies, therefore the calculations are carried out for several difference frequencies with the mean frequency covering the whole frequency range of interest. Results include the surge drift force and pitch drift moment. The results are presented in several stages in order to assess the influence of different phenomena contributing to the global second order responses. Firstly the body is restrained and secondly it is free to move at the wave frequency. The second order results include the contribution associated with quadratic products of first order quantities, the total second order force, and the contribution associated to the free surface forcing.

scholarly journals Boundedness of solutions and stability of certain second-order difference equation with quadratic term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Emin Bešo ◽  
Senada Kalabušić ◽  
Naida Mujić ◽  
Esmir Pilav
Keyword(s):  
Difference Equation ◽  
Initial Conditions ◽  
Second Order ◽  
Quadratic Term ◽  
Real Numbers ◽  
Positive Real ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Rational Difference Equation

AbstractWe consider the second-order rational difference equation $$ {x_{n+1}=\gamma +\delta \frac{x_{n}}{x^{2}_{n-1}}}, $$xn+1=γ+δxnxn−12, where γ, δ are positive real numbers and the initial conditions $x_{-1}$x−1 and $x_{0}$x0 are positive real numbers. Boundedness along with global attractivity and Neimark–Sacker bifurcation results are established. Furthermore, we give an asymptotic approximation of the invariant curve near the equilibrium point.

scholarly journals Natural convection of Bingham fluids in rectangular cross-sectional cylindrical annuli with differentially heated vertical walls

2019 ◽  
Vol 29 (1) ◽  
pp. 43-77 ◽  
Author(s):  
Sahin Yigit ◽  
Nilanjan Chakraborty
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Natural Convection ◽  
Yield Stress ◽  
Thermal Transport ◽  
Second Order ◽  
Bingham Fluids ◽  
Cross Sectional ◽  
Content Type ◽  
The Mean

PurposeThis paper aims to numerically analyse natural convection of yield stress fluids in rectangular cross-sectional cylindrical annular enclosures. The laminar steady-state simulations have been conducted for a range of different values of normalised internal radius (ri/L1/8 to 16, whereLis the difference between outer and inner radii); aspect ratio (AR=H/Lfrom 1/8 to 8 whereHis the enclosure height); and nominal Rayleigh number (Rafrom 103to 106) for a single representative value of Prandtl number (Pris 500).Design/methodology/approachThe Bingham model has been used to mimic the yield stress fluid motion, and numerical simulations have been conducted for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for the vertical side walls. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.FindingsIt is found that the mean Nusselt number based on the inner peripheryNu¯iincreases (decreases) with an increase inRa(Bn) due to augmented buoyancy (viscous) forces irrespective of the boundary condition. The ratio of convective to diffusive thermal transport increases with increasingri/Lfor both Newtonian (i.e.Bn= 0) and Bingham fluids regardless of the boundary condition. Moreover, the mean Nusselt numberNu¯inormalised by the corresponding Nusselt number due to pure conductive transport (i.e.Nu¯i/(Nu¯i)cond) shows a non-monotonic trend with increasingARin the CWT configuration for a given set of values ofRa,Pr,Lifor both Newtonian (i.e.Bn= 0) and Bingham fluids, whereasNu¯i/(Nu¯i)condincreases monotonically with increasingARin the CWHF configuration. The influences of convective thermal transport strengthen while thermal diffusive transport weakens with increasingAR, and these competing effects are responsible for the non-monotonicNu¯i/(Nu¯i)condvariation withARin the CWT configuration.Originality/valueDetailed scaling analysis is utilised to explain the observed influences ofRa,BN,ri/LandAR, which along with the simulation data has been used to propose correlations forNu¯i.

scholarly journals Glacier Sliding Down an Inclined Wavy Bed

1976 ◽  
Vol 17 (77) ◽  
pp. 447-462 ◽  
Author(s):  
L. W. Morland
Keyword(s):  
Order Term ◽  
High Viscosity ◽  
Second Order ◽  
Temperature Fields ◽  
Surface Velocity ◽  
Flow Equations ◽  
Basal Sliding ◽  
Pressure Melting ◽  
The Mean ◽  
Bed Slope

The treatments by Nye and Kamb of glacier sliding over a wavy bed with small slope, which assume the ice to be approximated by a Newtonian fluid of high viscosity, are complemented by the inclusion of the glacier depth and the inclination of the bed to the horizontal. The driving force of the motion, gravity, is therefore present in the flow equations and defines immediately the mean drag on the bed. A geothermal heal flux is also included in order to estimate its possible effect on the flow. A complex variable method is used to determine the velocity and temperature fields to second order in the bed slope. These fields satisfy the zero shear traction and pressure-melting-regelation conditions to the same order on the actual bed profile. It is the balance of the second-order term which determines explicitly the (zero order) basal-sliding velocity and surface velocity in terms of the geometry and physical properties of both ice and bed. An explicit solution is illustrated for a sinusoidal bed. and a simple criterion for the onset of cavitation is obtained.

scholarly journals Students’Ability in Reading Comperhension of the Scond Grade at SMP 13 Berau 2018/2019

2018 ◽  
Vol 9 (1) ◽  
Author(s):  
Sarlina Sarlina ◽  
Nurbianta Nurbianta
Keyword(s):  
Reading Comprehension ◽  
Junior High School ◽  
Problem Formulation ◽  
Reading Skill ◽  
Reading Test ◽  
School Year ◽  
Quasi Experimental ◽  
The Subject ◽  
The Mean ◽  
Five Phases

The problem formulation of this research are: What is the students’ ability in reading comprehension . Design of this research was quasi experimental research, by conducted Pretest-treatments-posttest procedures. While the subject is 27 students of junior high school in the school year 2017/2018. The object the researchis the student’ ability in reading comprehension. To collect the data, the writer uses some tecniques suchas test and document. Data processing in this research is divided into five phases: validity, reability, Scoring the test, ranking  and mean,median and mode then all the data are analyzed quantitavely The result finding of this research was the mean score students' reading test is 77.41, the value of median is 65, and the value of mode is 80.The performance on posttest show that the students’ ability in reading comprehension is outgrowth, the students obtained positive progress in learning reading skill.

Stable Strontium Absorption as a Measure of Intestinal Calcium Absorption: Comparison with the Double-Radiotracer Calcium Absorption Test

1994 ◽  
Vol 87 (3) ◽  
pp. 363-368 ◽  
Author(s):  
Aubrey Blumsohn ◽  
Brian Morris ◽  
Richard Eastell
Keyword(s):  
Renal Failure ◽  
Chronic Renal Failure ◽  
Time Course ◽  
Calcium Absorption ◽  
Quadratic Term ◽  
The Mean ◽  
Stable Strontium ◽  
The Relationship ◽  
Dual Tracer ◽  
Fractional Absorption

1. Stable strontium (Sr) has been proposed as an alternative to calcium (Ca) isotopes for the measurement of intestinal Ca absorption. The aim of this study was to compare the time course and fractional absorption of Ca and Sr, when both are measured using dual-tracer techniques. 2. 45Ca and Sr absorption tests were carried out on consecutive days in patients with osteoporosis (n = 10) or chronic renal failure (n = 7). Both tests were repeated in four patients with chronic renal failure after treatment with calcitriol (1 μg daily for 10 days). 3. The time course of Ca absorption was determined using the 85Sr (intravenous)/45Ca (oral) dual-tracer technique, and the time course of Sr absorption using 85Sr (intravenous)/stable Sr (oral). Oral tracers were administered on consecutive days with a test meal containing 5.3 mmol of Ca and 2.5 mmol of either stable Sr or Ca carrier. The fractional absorption of 45Ca and Sr at 6 h (FA360) and the absorption rate as a function of time were calculated by deconvolution. 4. The mean FA360 for Sr (20.2%) was lower than the mean FA360 for 45Ca (37.8%, P < 0.001, paired t-test), but the time course of Sr absorption was similar to that of Ca. There was a significant correlation between the FA360 for 45Ca and Sr, although the relationship was improved by including a quadratic term (R2 = 0.89, P < 0.001, significance of quadratic term, P < 0.05). After 1,25-dihydroxyvitamin D treatment, the FA360 of stable Sr increased 4.29-fold, whereas the FA360 of 45Ca increased only 2.4-fold. 5. Although the fractional absorption of Sr determined by dual-tracer deconvolution was the best predictor of FA360 for 45Ca, little was lost by confining the analysis to a single serum Sr measurement taken 3 h or more after oral administration. 6. We conclude that Sr absorption is qualitatively similar to that of Ca, although absorption of Sr is much lower than that of Ca. Furthermore, the relationship does not appear to be linear. Stable Sr may be useful in place of Ca isotopes in the routine clinical evaluation of Ca absorption.

Mean-Square Response of a Second-Order System to Nonstationary, Random Excitation

1970 ◽  
Vol 37 (3) ◽  
pp. 612-616 ◽  
Author(s):  
L. L. Bucciarelli ◽  
C. Kuo
Keyword(s):  
Narrow Band ◽  
Random Excitation ◽  
Second Order ◽  
Envelope Function ◽  
Order System ◽  
Mean Square ◽  
Forcing Function ◽  
Mean Square Response ◽  
Noise Function ◽  
The Mean

The mean-square response of a lightly damped, second-order system to a type of non-stationary random excitation is determined. The forcing function on the system is taken in the form of a product of a well-defined, slowly varying envelope function and a noise function. The latter is assumed to be white or correlated as a narrow band process. Taking advantage of the slow variation of the envelope function and the small damping of the system, relatively simple integrals are obtained which approximate the mean-square response. Upper bounds on the mean-square response are also obtained.

Sign in / Sign up

Export Citation Format

Share Document