Issue 12

A. Namdar et alii, Frattura ed Integrità Strutturale, 12 (2010) 57-62 ; DOI: 10.3221/IGF-ESIS.12.06 58 The winds, waves, currents, ice, earthquake, soil movement and ship collision could be analysis and modeled by mathematical method. The Morison equation could be used in estimating of wave force acting on offshore structure, it may be written as [6]. F=0.5ρC d A p |U|U+ρ C m ׊ (dU/dt) ρ = Density C d = 0.6 – 1.2 A p = Projected frontal area U = velocity of the ambient flow C m = Inertia coefficient = 2 ׊ = Displaced of volume of structure (dU/dt) = assumed ∂u/∂t And also the Isaacson (1979) equation is complete expression for the inertial force in the X direction of wave [6]. It is assumed that the wave is bi-dimensional, X and Y being the 2D coordinates, all the formulae can be used in the two directions, and this maintains permanent form and also incompressible, inviscid and the flow is irrotational. L =Wave length = T√(gd) H =Wave height T =Wave period Z =H/2 C =Wave speed = (L/T) Range of validity; Kd< (π/10) (d/L) < (1/20) (d/gT 2 ) < 0.0025 P = Pressure = ρgz + 0.5ρgH cosθ E = Average Energy Density = 0.125 ρgH 2 S xx = Radiation Stress = 1.5 E S yy = Radiation Stress = 0.5 E S xy =S yx = Radiation Stress =0 R ESULTS AND D ISCUSSION he mathematical modeling and numerical simulation of wave can be performed to understand wave characteristics. The result of Tab. 1 -3 and Fig. 1- 3 indicate that the wave length has a direct correlation with dangerous wave effects. Sl. No Wave length (m) Wave Speed (m/s) Pressure (kg/m 2 ) Average Energy Density (kg/m 3 ) Radiation Stress in X Direction (kg/m 2 ) Radiation Stress in Y Direction (kg/m 2 ) 1 10 2.21 26.39 10.20 15.31 5.10 2 20 3.13 52.79 40.83 61.25 20.41 3 30 3.83 79.18 91.88 137.82 45.94 4 40 4.42 105.58 163.34 245.01 81.67 5 50 4.95 131.97 255.22 382.835 127.61 6 60 5.42 158.37 367.52 551.28 183.76 7 70 5.85 184.76 500.23 750.35 250.11 8 80 6.26 211.16 653.37 980.05 326.68 9 90 6.64 237.55 826.92 1240.38 413.46 10 100 7 263.95 1020.89 1531.34 510.44 Table 1 : Mathematical Characteristics of Wave in Shallow Water. T