PRELIMINARY ANALYSIS OF WAVE SLAMMING FORCE RESPONSE DATA FROM TESTS ON A TRUSS STRUCTURE IN LARGE WAVE FLUME, HANNOVER, GERMANY

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1 NTNU Norwegian University of Science and Technology Department of Civil and Transport Engineering Report No.: IBAT/MB R1-213 Authors Christy Ushanth Navaratnam Alf Tørum Øivind A. Arntsen PRELIMINARY ANALYSIS OF WAVE SLAMMING FORCE RESPONSE DATA FROM TESTS ON A TRUSS STRUCTURE IN LARGE WAVE FLUME, HANNOVER, GERMANY 29 th August 213, Trondheim, Norway

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3 Norwegian University of Science and Technology NTNU Department of Civil and Transport Engineering REPORT Title PRELIMINARY ANALYSIS OF WAVE SLAMMING FORCE RESPONSE DATA FROM TESTS ON A TRUSS STRUCTURE IN LARGE WAVE FLUME, HANNOVER, GERMANY Authors Christy Ushanth Navaratnam Alf Tørum Øivind A. Arntsen ISBN No. ISBN (Paper Version) ISBN (Electronic Version) Client Division of Marine Civil Engineering Report no. BAT/MB-R1/213. Date 213 Sign. Knut V. Høyland Head of division Number of pages 59 Availability Open Abstract The foundation of offshore wind turbines are sometimes steel truss structures. In shallow water these structures may be subjected to wave slamming forces due to plunging breakers. Previous researches show that the impulsive forces from the plunging wave may be the governing factors in the design response of the truss structure and the foundations. Large scale (1:8) tests were carried out at the Large Wave Flume in Hannover Germany in order to investigate the wave slamming forces on the truss structures and to improve the method to calculate forces from the plunging breakers. This report presents some of the analysis of the data obtained from the test. The obtained data were analysed based on total force response as well as the local force response. Total force data have been analysed using Frequency Response Function (FRF) method whereas the local force measurements have been analysed using Duhamel integral method as well as the Frequency Response Function method. The results showed that the measured slamming forces on the truss is very much less compared to the calculated slamming forces based on Wienke & Oumeraci (25). This could be due to the size effects and wave form when the wave hits the structure. The slamming factor C s was found to be smaller compared to the value that was suggested by Wienke & Oumeraci (25). The pattern of the slamming force distribution was found to be triangular as found by Sawaragi and Nochino (1984) and Ros (211). It was found that both FRF and Duhamel integral methods give almost similar results. It was found that there is a time phase shift in between the wave profile and the local force measurement which needs to be investigated and further detailed analyse is recommended in order to come up with better results. Stikkord (Norwegian) Keywords (English) Wave slamming Response force Breaking waves Mail address Ph Location Høgskoleringen 7A Fax Høgskoleringen 7A NO-7491 Trondheim Org. no. NO NORWAY

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5 PREFACE This report presents some analyses of the data that have been obtained from the experiments on a truss structure, which was carried out at the Large Wave Channel, Hannover, Germany in May and June, 213. The objective of this study to investigate and improve the method to calculate the wave slamming forces from plunging breaking waves on truss structures through model on a large scale. The work described in this publication was supported by the European Community's 7th Framework Programme through the grant to the budget of the Integrating Activity HYDRALAB IV, Contract no This document reflects only the authors views and not those of the European Community. This work may rely on data from sources external to the HYDRALAB IV project Consortium. Members of the Consortium do not accept liability for loss or damage suffered by any third party as a result of errors or inaccuracies in such data. The information in this document is provided "as is" and no guarantee or warranty is given that the information is fit for any particular purpose. The user thereof uses the information at its sole risk and neither the European Community nor any member of the HYDRALAB IV Consortium is liable for any use that may be made of the information. Christy Ushanth Navaratnam Alf Tørum Øivind A. Arntsen NTNU, August 213 i

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7 TABLE OF CONTENTS 1 INTRODUCTION LITERARURE REVIEW Morison s Equation Wave Slamming Force Slamming Coefficients Curling Factor Breaking Waves METHODOLGY Experimental set-up Data Analysing Methods Frequency Response Function (FRF) Duhamel Integral Method ANALYSIS OF DATA Total Force Analysis Wave Test with hammer test and Large-hammer-test- 213_6_24_18_42_ Local Force Transducers Duhamel integral approach: FRF Approach CONCLUSION AND RECOMMENDATIONS REFERENCES APPENDICES ii

8 LIST OF FIGURES Figure 2.1: Definition sketch of von Karman s model (Ros Collados, 211)... 2 Figure 2.2: Definition sketch of impact force on vertical cylinder (Wienke & Oumeraci, 25)... 3 Figure 2.3: Definition sketch of 2D impact distribution (Wienke & Oumeraci, 25)... 3 Figure 2.4: Instrumented cylinder [cm]. (Tørum, 213)... 4 Figure 2.5: Time histories of line forces according to different theories (Wienke & Oumeraci, 25)... 5 Figure 2.6: Curling factor for different inclination of the pile (Wienke & Oumeraci, 25)... 6 Figure 2.7: Breaker types based on Iribarren parameter (Judith & Marcel, 212)... 7 Figure 3.1: Experimental set-up in the Large Wave Flume (Arntsen, 213)... 7 Figure 3.2: Instrumented Structure... 8 Figure 3.3: Local force transducers... 9 Figure 3.4: West side (front). Approximate location of points, marked with big yellow stars, for application of the 1.5 kg impulse hammer for the whole structure. Approximate location of points, marked with small yellow stars for application of the.1 kg impulse hammer on the local force cells. (Arntsen, 213)... 1 Figure 3.5: The derivation of the Duhamel integral (Ros Collados, 211) Figure 3.6: Main steps involving in the Duhamel integral approach (Ros Collados, 211) Figure 4.1: Hammer Impulse Figure 4.2: The total response of hammer impulse Figure 4.3: Spectrum of hammer and response forces Figure 4.4: Series of measured total responses Figure 4.5: Deep water wave and wave at structure [wave period 5.55s] Figure 4.6: Decomposition of total response Figure 4.7: Dynamic Response Figure 4.8: Spectrum of dynamic response Figure 4.9: Low-pass filtered slamming force variation (with the cut-off frequency of 2Hz).. 19 Figure 4.1: Hammer impact at point Figure 4.11: Total hammer response... 2 Figure 4.12: Chosen hammer impulse... 2 Figure 4.13: Spectrum of the hammer force Figure 4.14: Spectrum of both hammer force and total force Figure 4.15: Un-filtered slamming force Figure 4.16: Low-pass filtered slamming force (with the cut-off frequency of 2Hz) Figure 4.17: Low-pass filtered slamming force (with the cut-off frequency of 4Hz) Figure 4.18: Hammer impulse and Response on FTLF Figure 4.19: Time expanded view of above figure Figure 4.2: Spectrum of both hammer impulse and the response Figure 4.21: Spectrum of the response forces Figure 4.22: The maximum response to a suddenly applied triangular force time history (Naess, Figure 4.23: Duhamel integral approach with impact duration.1s and rising time.8s Figure 4.24: Duhamel integral approach with impact duration.5s and rising time.8s. 28 Figure 4.25: Duhamel integral approach with impact duration.5s and rising time.1s Figure 4.26: Duhamel integral approach with impact duration.5s and rising time.5s Figure 4.27: Duhamel integral approach with impact duration.5s and rising time.8s... 3 Figure 4.28: Un-filtered force variation on FTLF iii

9 Figure 4.29: Filtered force variation on FTLF2 [Cut-off frequency- 2Hz] Figure 4.3: Filtered force variation on FTLF2 [Cut-off frequency- 4Hz] Figure 4.31: Filtered force variation on FTLF2 [Cut-off frequency- 6Hz] Figure 4.32: Time series of measures response of local force transducers [FTLF1-FTLF5] Figure 4.33: Time series of measures response of local force transducers [FTLF6-FTLF1] Figure 4.34: Time expanded view of local force transducer responses Figure 4.35: The dynamic part of the total response on FTLF Figure 4.36: Power spectrum of the total response forces Figure 4.37: Force variation on FTLF1 [Cut-off frequency 2Hz] Figure 4.38: Force variation on FTLF2 [Cut-off frequency 2Hz] Figure 4.39: Force variation on FTLF3 [Cut-off frequency 2Hz] Figure 4.4: Force variation on FTLF4 [Cut-off frequency 2Hz] Figure 4.41: Force variation on FTLF5 [Cut-off frequency 2Hz] Figure 4.42: Force variation on FTLF6 [Cut-off frequency 2Hz] Figure 4.43: Force variation on FTLF7 [Cut-off frequency 2Hz] Figure 4.44: Force variation on FTLF8 [Cut-off frequency 2Hz]... 4 Figure 4.45: Force variation on FTLF9 [Cut-off frequency 2Hz]... 4 Figure 4.46: Force variation on FTLF1 [Cut-off frequency 2Hz] Figure 4.47: The variation of the force intensity with the depth [based on FRF method] at the time of maximum total response, t=128.3s Figure 4.48: Duhamel integral approach for FTLF3 (response at about 128.3s) Figure 4.49: Duhamel integral approach for FTLF4 (response at about 128.3s) Figure 4.5: Duhamel integral approach for FTLF7 (response at about 128.3s) Figure 4.51: Duhamel integral approach for FTLF8 (response at about 128.3s) Figure 4.52: The variation of the force intensity with the depth [based on Duhamel integral approach] at the time of maximum total response, t=128.3s Figure 4.53: The response of FTLF2 (blue) and the wave at the structure (red) iv

10 LIST OF TABLES Table 4.1: Characteristics of test Table 4.2: Measured forces on each local force transducers [based on FRF method] Table 4.3: Measured forces on each local force transducers [based on Duhamel integral approach] v

11 1 INTRODUCTION The foundation of offshore wind turbines are sometimes steel truss structures. In shallow water these structures may be subjected to wave slamming forces due to plunging breakers. Previous researches show that the impulsive forces from the plunging wave may be the governing factors in the design response of the truss structure and the foundations. Large scale (1:8) tests were carried out at the Large Wave Flume in Hannover Germany in order to investigate the wave slamming forces on the truss structures and to improve the method to calculate forces from the plunging breakers. This report presents some of the analysis of the data obtained from the test. 2 LITERARURE REVIEW [The following literature review has been directly extracted from the master s thesis; Navaratnam (213)] Many researches about wave slamming forces or breaking wave forces have been carried out and still being carried out all over the world. In this chapter, findings from previous researches have been described. 2.1 Morison s Equation The non-breaking wave forces acting on a vertical pile can be calculated using Morison s equation (Morison, et al., 195) which is the summation of the quasi static inertia and drag forces. df = df D + df M = 1 2 ρ πd 2 wc D D u u dz + ρ w 4 C du M dt dz (2.1) Where ρ w is the water density, C D is the drag coefficient, C M is the inertia coefficient, D is the diameter of the pile, u is the water particle velocity, z is the water depth and t is the time. The values of the drag and coefficients are depending on the Reynolds number, Keulagen Carpenter number, roughness parameters and interaction parameters (Morison, et al., 195). The total force can be obtained by integrating the equation (2.1) along the height of the pile. η F = F D + F M = 1 2 ρ πd 2 wc D D u u dz + ρ w 4 C du M dt dz d Where, η is the water surface elevation and the d is the total water depth. The force coefficients C D and C M have been obtained with laboratory experiments. Different range of values were found for a non-breaking wave for various flow conditions. Generally the Morison equation is valid for small diameter members that don t significantly modify the incident waves, and it depends on the ratio of the wavelength to the member diameter. If this ratio is more than 5, the Morison equation is applicable (Chella, et. al., 212). When it comes to breaking wave attack, an additional force of short duration because of the impact of the vertical breaker front and the breaker tongue has to be considered (Irschik, et. al., 22). So, an additional force term which is called slamming force (F S ) has to be added to the Morison equation as given in the equation (2.3). 1 η d (2.2)

12 2.2 Wave Slamming Force F = F D + F M + F S (2.3) The first wave impact model and theoretical formulation of water impact force on rigid body was derived by von Karman (von Karman, 1929). In his research, he considered a horizontal cylindrical body with a wedged-shaped under surface as it strikes the horizontal surface of water and calculated the force acting between the cylindrical body and the water. As it s shown in the Figure 2.1, a cylinder is approximated by a flat plate of width c(t) which is equal to the immersed portion of the cylinder at each instant of the impact. The force on this plate could be calculated by considering the potential flow under the plate and integrating the pressures which can be found by the Bernoulli s equation and for this, the time history of the width of the plate should be known as well. Figure 2.1: Definition sketch of von Karman s model (Ros Collados, 211) According to von Karman theory, the line force f(t) is given by the following equation, f(t) =.5 C s ρ w D C b 2 (2.4) C s = π (1 C b R t) (2.5) Where, C s is the slamming factor, C b is the wave celerity and D is the diameter of the cylinder and R is the radius of the cylinder. The maximum line force occurs when the time t is zero (t=, i.e. beginning of the impact), and the slamming factor becomes π. As this line force is two dimensional and was derived for an infinite length of cylinder based on von Karman s model, it should be integrated over the length of the impact area (Figure 2.2) of cylinder assuming the same line force acting everywhere in the cylinder. 2

13 Figure 2.2: Definition sketch of impact force on vertical cylinder (Wienke & Oumeraci, 25) As Figure 2.2 shows, the height of the impact area was found to be the multiplication of the curling factor λ and the maximum breaking wave crest height η b (Goda, et. al.,1966). So, the slamming force F s on the cylinder, F s (t) =.5 ρ w D C b 2 π (1 C b R t) λ η b (2.6) F s (t) = π ρ w R C b 2 (1 C b R t) λ η b (2.7) At the beginning of the impact with t= the equation (2.7) follows, 2 F s = π ρ w R λ η b C b (2.8) From equation (2.4), the line force based on von Karman (1929), 2 f(t) = π ρ w R C b (2.9) Figure 2.3: Definition sketch of 2D impact distribution (Wienke & Oumeraci, 25) 3

14 The line force given in equation (2.9) was obtained by considering the momentum conservation during the impact. By taking into consideration not only the momentum conservation, but also the flow beside the flat plate would result in the so-called pile-up effect, that is the deformation of the water free surface (Figure 2.3). Because of this pile-up effect, the immersion of the cylinder occurs earlier. As a result, the duration of impact decreases and the maximum line force increases (Wienke & Oumeraci, 25). According to Wagner (1932), the maximum line force is given as follows, f(t) = 2π ρ w R C b 2 (2.1) The maximum line force calculated by Wagner s theory is twice the maximum line force calculated by von Karman s theory. Generally this maximum line force is described as a function Slamming Coefficient C s. 2.3 Slamming Coefficients f(t) = C S ρ w R C b 2 (2.11) So, the general form of wave slamming force is given in the following equation. F s = C S ρ w R λ η b C b 2 (2.12) According to von Karman (1929) and Goda et. al. (1966), Cs is π and Wagner s theory suggests a C s value of 2π. Wienke & Oumeraci (25) suggest a C s value of 2π as they show that the formulation of Wagner s theory is more accurate even though Goda et. al (1966) s description of the impact is based on von Karman (1929). Ros Collados (211) investigated the slamming coefficient on a vertical cylinder in his master s thesis and estimated a C s value of 4.3 for a triangular load case, and this value is between π and 2π. This experiment was done with a vertical cylinder with a series of force transducers placed on it in different elevations as shown in Figure 2.4. Figure 2.4: Instrumented cylinder [cm]. (Tørum, 213) 4

15 The C s values were found by considering the maximum impact force at the third transducer. It should be noted that the impact duration time was set as.8s for all the cases, which was defined at the same time as the triangular load. Another experiment was carried out by Aune (211) as part of his master s thesis and he calculated a C s value of But, this experiment was performed on a truss structure. Wienke and Oumeraci (25) obtained a time history of the impact line force. This is shown in Figure 2.5. This shows that the value of the line force at the beginning of the impact (t=), i.e. the maximum line force that is calculated by their proposed model is equal to the value obtained from the Wagner s model. Figure 2.5: Time histories of line forces according to different theories (Wienke & Oumeraci, 25) 2.4 Curling Factor Wienke and Oumeraci (25) investigated about the curling factor for the vertical and inclined cylinders. The ratio of the impact force F s to the line force f(t) provides the height area of the impact η b, where η b is the maximum surface elevation of the breaking wave and the λ is the curling factor. Figure 2.6 shows the variation of the cylinder factor with the different inclination of the cylinder, i.e. yaw angle α. For a vertical cylinder, the maximum curling factor is λ=.46 and this is in agreement with the values of curling factors cited in literature, for example, Goda, et. al. (1966) proposed a range of curling factors λ=.4-.5 for plunging wave breakers. 5

16 Figure 2.6: Curling factor for different inclination of the pile (Wienke & Oumeraci, 25) 2.5 Breaking Waves Waves breaking process is taken place in various different ways depending on the wave properties and angle of bed slope (Judith & Marcel, 212). Battjes (1974) showed that the Iribarren parameter influences in the wave breaking process. The Iribarren parameter is difined as follows, tan α ξ = (2.13) H /L where, tan α is the steepness of the bed, H is the deep water wave height and L is the wave length in deep water. The Iribarren number ξ represents the ratio of the slope of the bed and the deep water wave steepness. A distinction is made between spilling, plunging, collapsing and surging breakers based on the value of ξ (Figure 2.7). The values of Iribarren number are indicative and the transition between the various breaker types is gradual. Spilling breakers are generally found along the flat bed. Plunging breaking occurs on a mild slope bed and the curling top is characteristic of such a wave. When the curling top breaks over the lower part of the wave, a lot of energy is dissipated into turbulence. 6

17 Figure 2.7: Breaker types based on Iribarren parameter (Judith & Marcel, 212) 3 METHODOLGY 3.1 Experimental set-up The experimental set-up at the Large Wave Flume, Hannover, Germany is shown in the Figure 3.1. Figure 3.1: Experimental set-up in the Large Wave Flume (Arntsen, 213) The Figure 3.2 shows an isometric view of the instrumented structure. The structure is instrumented as follows, - 4 total force transducers, two at the top and the two at the bottom to measure the total force on the structure - 1 local force transducers at the front vertical legs of the structure - 12 XY force transducers to measure the total force on six bracings 7

18 Figure 3.2: Instrumented Structure Since there were only forces from total force transducers and the local force transducers were analysed, the hammer points are shown only for these cases. 8

19 Figure 3.3: Local force transducers 9

20 Figure 3.4: West side (front). Approximate location of points, marked with big yellow stars, for application of the 1.5 kg impulse hammer for the whole structure. Approximate location of points, marked with small yellow stars for application of the.1 kg impulse hammer on the local force cells. (Arntsen, 213) 3.2 Data Analysing Methods [This section is directly extracted from the master s thesis; Navaratnam (213)] A procedure used by Määtänen (1979) to resolve ice forces from measured response forces on structures subjected to moving ice is applicable for wave slamming loads as well (Tørum, 213). The analysis method that Wienke and Oumeraci (25) used was deconvolution method which is similar to Duhamel integral method that was used by Ros Collados (211). These deconvolution 1

21 and Duhamel integral approaches are more complex for truss structures and have not been used so far for truss structure. So, the method used by Määtänen (1979), Frequency Response Function method was used for both individual cylinders and truss structures. But, Duhamel integral method also used for only individual cylinders in order to compare and check the influence of the analysis methods. The measured response force f(t) could be expanded into Fourier integral and in case of forced vibration will be, f(t) = 1 2π H(ω)S F(ω)e iωt dω (3.1) Where, H(ω) is the frequency response function (FRF) and S(ω) is the linear spectrum of the forcing function. The frequency response function H(ω) or the transfer function is a calibration factor which is obtained by the pluck test by impulse hammer at several ponts. The Fourier transform of equation (3.1) gives, H(ω)S F (ω) = f(t) e iωt dω = S f (ω) (3.2) S f (ω) is the linear spectrum of the measured signal f(t). So, S f (ω) can be solved from this above equation as, S F (ω) = S f(ω) H(ω) (3.3) Finally, the Inverse Fourier Transform (IFFT) of the above equation gives the requested wave slamming force. F(t) = 1 2π S f(ω) H(ω) eiωt dω (3.4) The above equations can easily be solved by computer programs such as Matlab, although they look complicated. In this case Matlab has been used for the calculations and analyses. Frequency Response Function (FRF) As previously described, the frequency response function or transfer function was obtained by the pluck test using impulse hammer. Plucking points are shown in The total response force due to an impact by the impulse hammer can be sum of all the force transducers connected to the structure assuming structure responding based on single degree of freedom (SDOF. The impact force is directly measured by the impulse hammer. So, the ratio of the power spectrum of impulse force to the response forces gives the transfer function or the frequency response function. So, frequency response function is now, 11

22 H(ω) = S Total,hammer(ω) S Hammer (ω) (3.5) Where, S Total,hammer (ω) is the fast Fourier transform of the total response forces (power spectrum) obtained by summing up all the transducer forces due to the impact by the hammer and S Hammer (ω) is the fast Fourier transform of the impact measurement obtained directly from hammer. And, S Total,hammer (ω) = f Total,hammer (t) e iωt dt (3.6) S Hammer (ω) = f Hammer (t) e iωt dt (3.7) The frequency response function H(ω) is counter checked by multiplying it bys Hammer (ω), this should be equal tos Total,hammer (ω). So both the spectrum were checked in order to make sure it has been done correctly. Duhamel Integral Method Duhamel integral approach has been used only for cylinder structures to compare with the results with the FRF method. The theoretical description of the Duhamel integral method is briefly described in this chapter. This method was used by Ros Collados (211) in his master s thesis. Figure 3.5: The derivation of the Duhamel integral (Ros Collados, 211) 12

23 The above figure (Figure 3.5) shows the differential response for a given impact p(τ). The total calculated response can be obtained by integrating all the differential responses developed during the loading history (Ros Collados, 211). R c (t) = t k p(τ)sinω mω d (t τ)e ξω(t τ) dτ d Where, m is the oscillating mass, ω d is the damped frequency of oscillation, p(τ) is the impact load applied for very short time τ and ξ is the damping coefficient and t is the time. It should be noticed that for small values of damping ω ω d. Equation (3.8) is called as Duhamel integral equation and this is being used to estimate the response of an undamped single degree of freedom (SDOF) system subject to any form of dynamic loading p(τ). This equation can be simplified and written as follows (Clough & Penzien, 1975) (3.8) where, R c (t) = A(t) sin ω d t B(t) cos ω d t (3.9) A(t) = B(t) = t k p(τ) eξωτ mω d e ξωt cos ω dτ dτ k p(τ) eξωτ mω d e ξωt sin ω dτ dτ t (3.1) (3.11) The incremental summation procedure can be used to evaluate the above given integral equations. The equation (3.1) can be written as below in order to describe the exponential decay behaviour caused by damping. This is an approximate recursive form using simple summation. A N A N 1 e ξω τ + τ k mω d y N 1 e ξω τ, N = 1,2,3, (3.12) where, y 1 = p 1 cos ω d t 1, y 2 = p 2 cos ω d t 2, etc. The same expressions will be applicable for B N but, now y N is in terms of sin ω d t N, i.e. y 1 = p 1 sin ω d t 1, y 2 = p 2 sin ω d t 2 and so on. Finally, knowing all the calculated values of A N and B N for successive values of N, the corresponding ordinates of the response will be obtained by using equation (3.9). R cn = A N sin ω d t N B N cos ω d t N (3.13) Although these expressions and procedure look more complex, it can be easy evaluated by the Matlab program. A Matlab code written by Ros Collados (21) was modified according to the requirement. The main steps involving in this Duhamel integral method is shown in Figure 3.6. This method was only used for individual local force meters and was not used for truss structure sections. 13

24 Figure 3.6: Main steps involving in the Duhamel integral approach (Ros Collados, 211) This is an iterative process as the assumed impact force and the measured responses should be in good agreement with each other. It means that the measures responses and calculated responses should be coincided with each other or almost geometrically fit on to another for a particular triangular impact force. Once these two responses are in agreement the impact force corresponds to that response will be the wave slamming force. 4 ANALYSIS OF DATA 4.1 Total Force Analysis Wave Test with hammer test and Large-hammertest-213_6_24_18_42_58. Wave test has been chosen for all the analyses. The characteristics of the wave test is given in Table 4.1. Table 4.1: Characteristics of test Wave Period 5.55s Deep water wave height 1.7m Wave height at structure 2.8m Water depth at structure 4.3m Wave type Regular The hammer test was done using large hammer and that was plucked at point 2 as shown in Figure 3.4. The following figure shows the hammer impulse of this test. There are two subsequent impacts and the first impact has been chosen for this analysis. The hammer impulse data before and after 14

25 the impact has been adjusted to zero in order to get the clean spectrum. Figure 4.2 shows the total response due to the hammer impact. 12 Test: Hammer at Point 5 Hammer Force 1 8 Force [kn] Figure 4.1: Hammer Impulse 2 Test: Hammer at Point 2 Total Hammer Response Force [kn] Figure 4.2: The total response of hammer impulse It should be noted that the total response is the sum of forces from four total force transducers, two at the top and two at the bottom. The spectrum of both hammer impulse and the total response are shown in Figure 4.3, 15

26 Test: Hammer at Point 2 Data Points: Power Spectrum 9 Hammer Force Total Force Relative Values Frequency [Hz] Figure 4.3: Spectrum of hammer and response forces Figure 4.4 shows a series of measured total responses while Figure 4.5 shows the deep-water wave and the waves measured at the structure, i.e. at the front section of the structure Test: Hammer at Point 5 Total Measured Response Total Response Wave at Structure 25 2 Force [kn] Figure 4.4: Series of measured total responses As it can be seen in Figure 4.4, the total response varies considerably from wave to wave. The response at a time approximately 128s has been chosen for the analyses. 16

27 2 Test: Data Points: Waves Deep water wave Wave at structure Wave Height [m] Figure 4.5: Deep water wave and wave at structure [wave period 5.55s] As it was described in the previous chapter, the total force response is sum of all four transducers and this total response consists of quasi-static forces and dynamic forces. Basically, the slamming force comes from the dynamic forces. So, it s important to decompose of the total responses. Low-pass filtering does this decomposition, as it s shown in Figure 4.6 filtered total force will be the quasi-static force and the dynamic force will be obtained by subtracting quasi-static force from the total response. Test: Data Points: Forces 3 Filtered Total Force Total Force-Filtered Total Force Force [kn] Time [sec] Figure 4.6: Decomposition of total response 17

28 Force [kn]. Relative Values Test: Data Points: Forces Time [sec] Figure 4.7: Dynamic Response Test: , Hammer at Point 2 14 Data Points: Power Spectrum of Response Forces Frequency [Hz] Figure 4.8: Spectrum of dynamic response 18

29 Figure 4.9: Low-pass filtered slamming force variation (with the cut-off frequency of 2Hz) According to the above figure, the measured slamming force for this test will be about 14kN. Although the above figure shows many high forces for a cut-off frequency of 2Hz, it can be eliminated if we use lower cut-off frequency for filtering. This will be illustrated in the following section. The same test with different hammer point (Hammer point 5 test ) The same wave test has been analysed using different hammer point that is point 5 shown in Figure Force [kn]. Test: , Hammer at Point 2 Data Points: Filtered IFFT(S(w)/H(w))=SS(w) Data Points Test: Hammer at Point 5 Hammer Force 1 8 Force [kn] Figure 4.1: Hammer impact at point 5. 19

30 Test: Hammer at Point 5 Total Hammer Response Force [kn] Figure 4.11: Total hammer response 8 Test: Hammer at Point 5 Hammer Impulse Force [kn] x 1-3 Figure 4.12: Chosen hammer impulse 2

31 Test: Hammer at Point 5 Data Points: Power Spectrum-Hammer Forces Relative Values Frequency [Hz] Figure 4.13: Spectrum of the hammer force Test: Hammer at Point 5 Data Points: Power Spectrum 12 Hammer Force Total Force 1 8 Relative Values Frequency [Hz] Figure 4.14: Spectrum of both hammer force and total force 21

32 Force [kn]. Force [kn]. Test: , Hammer at Point 5 15 Data Points: IFFT(S(w)/H(w))=SS(w) Figure 4.15: Un-filtered slamming force Test: , Hammer at Point 5 Data Points: Filtered IFFT(S(w)/H(w))=SS(w) Figure 4.16: Low-pass filtered slamming force (with the cut-off frequency of 2Hz) 22

33 Force [kn]. Test: , Hammer at Point 5 Data Points: Filtered IFFT(S(w)/H(w))=SS(w) Figure 4.17: Low-pass filtered slamming force (with the cut-off frequency of 4Hz) According to Figure 4.16 & Figure 4.17, the measured slamming force is approximately 8-13 kn. Calculated Slamming Force based on Wienke & Oumeraci (25), Slamming forces on two front vertical legs = 2 [.5 2π ρ w D λ η b C 2 b ] Wave celerity can be calculated by using the formula, Cb = g(h + η) = 9.81( ) = 5.77 m/s So, the slamming forces on two front vertical legs = 2 [.5*2π*1*.14*.5*1.4* ] = kn Length of bracing within the wave impact area = 2 [λ η b /Sinθ] where, θ is the inclination of the bracing. = 2*[.5*1.4/Sin27.8] = 3m Slamming forces on front bracing =.5*2π*1*.14*3* = kn So, total slamming force = 63.9 kn 23

34 As we see from the above calculation, the calculated slamming force based on Wienke & Oumeraci (25) is about 64 kn. It should be noted that the calculated slamming force on the bracing is much more larger than that on two front legs as the length of the bracing that exposed to the breaking wave is larger. So, according to the above calculations, the measured slamming force is very less than that we obtained based on Wienke & Oumeraci (25). 4.2 Local Force Transducers The hammer test on local force transducer FTLF2 (Figure 3.3) was chosen for analysis. Test: FTLF2-2 Forces 6 Hammer Impulse Response Force 5 4 Force [N] Figure 4.18: Hammer impulse and Response on FTLF2 24

35 6 5 4 Force [N] Relative Values Test: FTLF2-2 Forces Hammer Impulse Response Force Figure 4.19: Time expanded view of above figure If we look into Figure 4.19 response occurs ahead of the impact, apparently this is impossible. It was found that the reason for such time lag is related to the hardware system during analogue/digital conversion. This time lag will not affect the results although it makes confusion to the reader. The spectrum of the hammer impulse and the total response is shown in the following figures x 1 4 Test: FTLF2-2 Data Points: Power Spectrum-Hammer Forces Hammer Impulse Response Force Frequency [Hz] Figure 4.2: Spectrum of both hammer impulse and the response 25

36 Relative Values 3 x 1 4 Test: FTLF2-2 Data Points: Power Spectrum-Response Forces Frequency [Hz] Figure 4.21: Spectrum of the response forces Comments on the spectrum shown in Figure 4.21, - Decreasing high force until 6Hz due to the clean response signal (similar to the spectrum for the hammer impulse signal) - As we see on Figure 4.21, there are two clean peaks at 628 Hz and 122Hz, this could be due to the small oscillation in between two peaks in Figure According to Figure 4.19, The impact duration (t d ) The natural period of oscillation (t n ) =.29 s Ratio t d /t n = =.16s (based on 628Hz) 26

37 Figure 4.22: The maximum response to a suddenly applied triangular force time history (Naess, 211) If the hammer impact shown in Figure 4.19 can be approximated to a symmetric triangular impact, the response ratio has to be about 1.2 for a time ratio of 1.8., but if we look in to the Figure 4.19, the measured response ratio (measured response/impact force) is about 1.8 (65N/6N). This difference could be due to the difference in theoretical impact duration [~.1s = (.5*.14/6)] and the measured impact duration of hammer impact (about.3s) from Figure Duhamel integral approach: Test for Local Force Transducer FTLF2 The Duhamel integral approach has been used to the local force transducer FTLF2 shown in Figure 3.3, in this case the maximum response of this local force transducer has been chosen for the analysis and the results are shown in the following figures. An impact duration of.1s has been considered for this analysis as the theoretical impact duration is.13s. It should be noted that the rising time of the impact is denoted as T p although T p is used fir peak period. 27

38 6 5 F= 33 N Tp=.8s Triangular Impulse Calculated Response Measured Response Relative response [N] Figure 4.23: Duhamel integral approach with impact duration.1s and rising time.8s When impact duration is.5s, the following figure shows the result, 6 5 F=315 N Tp=.8s Triangular Impulse Calculated Response Measured Response Relative response [N] Figure 4.24: Duhamel integral approach with impact duration.5s and rising time.8s 28

39 When the rising time increases, 6 5 F= 38 N Tp=.1s Triangular Impulse Calculated Response Measured Response Relative response [N] Figure 4.25: Duhamel integral approach with impact duration.5s and rising time.1s 6 5 F=365 N Tp=.5s Triangular Impulse Calculated Response Measured Response Relative response [N] Figure 4.26: Duhamel integral approach with impact duration.5s and rising time.5s 29

40 6 5 Tp=.8s Triangular Impulse Calculated Response Measured Response Relative response [N] Figure 4.27: Duhamel integral approach with impact duration.5s and rising time.8s Measured Slamming Factor As we see in the above figures, when the rising time increases, the impact force also increases and finally it becomes very hard to fit the measured response curve as it lags behind it. According to Figure 4.23, the measured Cs value will be, Measured slamming factor [Cs] = Fs/[.5 ρ w D h C b 2 ] = 33/ [.5*1*.14*.4* ] = 3.33 As we see from the above calculation, the slamming factor is very small compared to the slamming factor 2π that Wienke & Oumeraci (25) used. Since the maximum total response occurred at the FTLF2 and the measured slamming force also found to be highest compared to the slamming force that has been obtained from the other local force transducers (Figure 4.32 & Figure 4.33 ), the above slamming factor will be larger than the slamming factor that can be obtained from other local forces FRF Approach Now we consider the Frequency Response Function method for the same local force transducer FTLF2. Hammer tests that were done on FTLF2 has been used in all the analysis in order to compare the results of both the analysing methods, Duhamel integral approach and frequency response function method. 3

41 8 Test: FTLF2, FTLF2-2 Data Points: IFFT(S(w)/H(w))=SS(w) 6 4 Force [N] Figure 4.28: Un-filtered force variation on FTLF2 Test: FTLF2, FTLF2-2 2 Data Points: Filtered IFFT(S(w)/H(w))=SS(w) 15 1 Force [N] Figure 4.29: Filtered force variation on FTLF2 [Cut-off frequency- 2Hz] 31

42 Test: FTLF2, FTLF2-2 3 Data Points: Filtered IFFT(S(w)/H(w))=SS(w) Force [N] Figure 4.3: Filtered force variation on FTLF2 [Cut-off frequency- 4Hz] Test: FTLF2, FTLF Data Points: Filtered IFFT(S(w)/H(w))=SS(w) Force [N] Figure 4.31: Filtered force variation on FTLF2 [Cut-off frequency- 6Hz] As it can be seen in above figures, if we expect the slamming force to be very clean as theoretical then the Figure 4.29 is the most suitable situation where the slamming force is about 18N that is less than that we obtained from the Duhamel integral approach (33N). Although it can always be expected to get force variation shown in Figure 4.29, still the slamming force shown in Figure 4.31 is acceptable and in this case the slamming force is about 315N which is almost similar to what we obtained from the Duhamel integral approach. 32

43 Force [kn] Force [kn] Force [kn] Force [kn] Force [kn].5 FTLF FTLF FTLF FTLF FTLF Figure 4.32: Time series of measures response of local force transducers [FTLF1-FTLF5] Force [kn] Force [kn] Force [kn] Force [kn] Force [kn].5 FTLF FTLF FTLF FTLF FTLF Figure 4.33: Time series of measures response of local force transducers [FTLF6-FTLF1] 33

44 Force [kn] Force [kn] Force [kn] Force [kn] Force [kn] Force [kn] Force [kn] Force [kn] Force [kn] Force [kn].2 FTLF FTLF FTLF FTLF FTLF FTLF FTLF FTLF FTLF FTLF Figure 4.34: Time expanded view of local force transducer responses 34

45 Figure 4.32 and Figure 4.33 show the time series of the measured response from each local force transducer for test As we see in these figures, the measured response is different in each local force transducer at a particular time. Figure 4.34 clearly shows that the maximum response occurs at different time points in each local force transducers. For example, consider FTLF3 and FTLF7, both are located at the same height from the still water line but on different legs, FTLF3 gives the maximum response at s whereas FTLF7 gives the maximum response at about s. This confirms that the wave is not so uniform across the channel. Although this time difference is small, this will be significant when it s compared to the impact duration. FTLF1 and FTLF5 are located at about 1.45m above the still water line, the crest height of this wave is about 1.4m, but we still get some response on FTLF1 and FTLF5, this could be due to the wave run-up also another reason might be the wave recorded close to channel wall and at some distance from the structure. It s interesting to note that Figure 4.34 shows that the forces on FTLF1, FTLF2 and to some extent FTLF3, FTLF5 and FTLF6 are somewhat ahead of the forces on the other local force transducers, except FTLF9 and FTLF1. This may be due to curling over of the wave crest, as indicated in Figure 2.4. As we can see in Figure 4.34, there are two peaks in some local force transducers, this might be due to the wave run-up, but it should be investigated further. The maximum response on the total force analysis was occurred at about sec of the test (Figure 4.4). So, the responses at this time in each local force transducers will be considered for the analysis in order to compare the total forces from the total force transducer with the total force from the local force transducers. Please note that the hammer test on the FTLF2 is only considered for all the analysis assuming the hammer response behaviour is the same for all local transducers. Test: FTLF2 Data Points: Dynamic Response Forces Force [N] Time [sec] Figure 4.35: The dynamic part of the total response on FTLF2 35

46 Test: 2.5 x FTLF1, FTLF2-2 Data Points: Power Spectrum of Response Forces 2 Relative Values Frequency [Hz] Figure 4.36: Power spectrum of the total response forces Test: FTLF1, FTLF2-2 1 Data Points: Filtered IFFT(S(w)/H(w))=SS(w) 8 X: Y: Force [N] Figure 4.37: Force variation on FTLF1 [Cut-off frequency 2Hz] It should be noted that the values (x-values) shown in the boxes in each figures are round off to first decimal. 36

47 Similarly the force variation from the other local force transducers are given below. Test: FTLF2, FTLF Data Points: Filtered IFFT(S(w)/H(w))=SS(w) X: Y: Force [N] Figure 4.38: Force variation on FTLF2 [Cut-off frequency 2Hz] Test: FTLF3, FTLF Data Points: Filtered IFFT(S(w)/H(w))=SS(w) X: Y: Force [N] Figure 4.39: Force variation on FTLF3 [Cut-off frequency 2Hz] 37

48 Test: FTLF4, FTLF Data Points: Filtered IFFT(S(w)/H(w))=SS(w) X: Y: Force [N] Figure 4.4: Force variation on FTLF4 [Cut-off frequency 2Hz] Test: FTLF5, FTLF2-2 6 Data Points: Filtered IFFT(S(w)/H(w))=SS(w) 5 4 X: Y: Force [N] Figure 4.41: Force variation on FTLF5 [Cut-off frequency 2Hz] 38

49 Test: FTLF6, FTLF Data Points: Filtered IFFT(S(w)/H(w))=SS(w) X: Y: X: Y: Force [N] Figure 4.42: Force variation on FTLF6 [Cut-off frequency 2Hz] Test: FTLF7, FTLF2-2 2 Data Points: Filtered IFFT(S(w)/H(w))=SS(w) 15 X: Y: Force [N] Figure 4.43: Force variation on FTLF7 [Cut-off frequency 2Hz] 39

50 Test: FTLF8, FTLF Data Points: Filtered IFFT(S(w)/H(w))=SS(w) X: Y: Force [N] Figure 4.44: Force variation on FTLF8 [Cut-off frequency 2Hz] Test: FTLF9, FTLF Data Points: Filtered IFFT(S(w)/H(w))=SS(w) 2 15 X: Y: Force [N] Figure 4.45: Force variation on FTLF9 [Cut-off frequency 2Hz] 4

51 Test: FTLF1, FTLF Data Points: Filtered IFFT(S(w)/H(w))=SS(w) 2 X: Y: Force [N] Figure 4.46: Force variation on FTLF1 [Cut-off frequency 2Hz] As it can be seen in all the above figures, the maximum force occurred at around s and the local force transducers FTLF9 and FTLF1 give very less or almost no force at this time as its located away from the slamming point. The following table shows the summary of the forces of each transducers. Please note that the z is the height above the still water line, which means that z is zero at the still water line. Table 4.2: Measured forces on each local force transducers [based on FRF method] FTLF Z (mm) Meas. Force (N) Front Leg Front Leg

52 Z [mm] Based on the above table, the force intensity has been plotted against the location each transducers which is shown in the following figure Front Leg 1 Front Leg f s [N/mm] Figure 4.47: The variation of the force intensity with the depth [based on FRF method] at the time of maximum total response, t=128.3s The response from all individual local force transducers at 128.3s has been analysed using Duhamel integral approach. Few of them (those give maximum forces) shown in the following figures F=99 N Triangular Impulse Calculated Response Measured Response Relative response [N] Figure 4.48: Duhamel integral approach for FTLF3 (response at about 128.3s) 42

53 35 3 F= 186N Triangular Impulse Calculated Response Measured Response 25 Relative response [N] Figure 4.49: Duhamel integral approach for FTLF4 (response at about 128.3s) 35 3 F=182N Triangular Impulse Calculated Response Measured Response 25 Relative response [N] Figure 4.5: Duhamel integral approach for FTLF7 (response at about 128.3s) 43

54 5 4 F= 265N Triangular Impulse Calculated Response Measured Response Relative response [N] Figure 4.51: Duhamel integral approach for FTLF8 (response at about 128.3s) Table 4.3: Measured forces on each local force transducers [based on Duhamel integral approach] FTLF Z (mm) Meas. Force (N) Front Leg Front Leg

55 Z [mm] Front Leg 1 Front Leg f s [N/mm] Figure 4.52: The variation of the force intensity with the depth [based on Duhamel integral approach] at the time of maximum total response, t=128.3s According to both the analysing methods, the maximum slamming force seems to have occurred at about 1.5m above the still water line or at the local force transducers FTLF4 and FTLF8. The slamming force distribution is triangular as found by Sawaragi and Nochino (1984) and Ros (211) and not uniform as used by Goda et al. (1966) and Wienke and Oumeraci (25). Figure 4.53: The response of FTLF2 (blue) and the wave at the structure (red) 45

56 As we see in Figure 4.53, the maximum wave crest occurs at about 122.9s and the maximum response occurs at s, this indicates that there is a time phase shift which is still unclear and needs to be investigated further. 5 CONCLUSION AND RECOMMENDATIONS There were few data analysed and presented in this report. Initially the total force on the structure was analysed using Frequency Response Function (FRF) method. The wave test was chosen for all the analysis. In the total force analysis it was observed that the measured slamming force is very less compared to the calculated slamming force based on Wienke & Oumeraci (25). In the analysis of the local force measurement, there were two methods used such as Duhamel integral approach and the frequency response function method. Both of the analysing methods seem to be promising as they both give almost similar result for a particular test. The slamming factor, C s is small (3.3) according to the measured slamming force whereas the slamming factor used in the Wienke & Oumeraci (25) method was 2π, which is much larger than the obtained slamming factor. The forces acting on different level of each front vertical legs have been found and plotted against the depth. This shows almost the similar pattern that Ross (211) obtained in his tests. It was also observed from the local forces that the same wave hits the structure at different times but the time difference is very small. Apelt and Piorewicz (1987) who point out that there is a size effect (varying D/H). Their results indicate that we should have smaller forces than obtained by Wienke and Oumeraci (25). Wienke and Oumeraci (25) had a diameter of.7 m, while we had diameters D =.14 m. According to Apelt and Piorewicz (1987), we should have relatively smaller forces than Wienke and Oumeraci (25). There was a time lag observed between wave recording and the response data, still it s unclear and has to be investigated. Also, there were two peak points observed on the local force transducer recording, this could be due to the wave run-up on the structure, but still it needs to be further investigated. Further detailed analysis with different analysis methods would be recommended to overcome such problems and to come up with better conclusions. 46

57 6 REFERENCES Aashamar, M. (212). Wave slamming forces on truss support structures for wind turbines. NTNU, Department of Civil and Transport Engineering. Trondheim: Norwegian University of Science and Technology. Apelt, C., & Piorewicz, J. (1987). Laboratory Studies of Breaking Wave Forces Acting on Vertical Cylinders in Shallow Water. Coastal Engineering, 11, Arntsen, Ø. (213). WAVE SLAMMING FORCES ON TRUSS STRUCTURES IN SHALLOW WATER. Trondheim. Aune, L. (211). Bølgjeslag mot jacket på grunt vatn (Wave slamming forces on jacket in shallow water). Trondheim: Department of Structural Engineering. Battjes, J. (1974). Surf similarity. Proceedings of 14th International Conference on Coastal Engineering, 1, pp Copenhagen. Chella, M., Tørum, A., & Myrhaug, D. (212). An Overview of Wave Impact Forces on Offshore Wind. Energy Procedia, 2, Clough, R., & Penzien, J. (1975). Dyanamics of structure (2nd ed.). International Editions. Retrieved 1993 Endresen, H., & Tørum, A. (1992). Wave forces on a pipeline through the surf zone. Coastal Engineering, 18, Goda, Y., Haranka, S., & Kitahata, M. (1966). Study of impulsive breaking wave forces on piles. Port and Harbour Research Institute, 5(6), 1-3. Irschik, K., Sparboom, U., & Oumeraci, H. (22). Breaking wave characteristics for the loading of a slender pile. Cardiff: ASCE. Judith, B., & Marcel, S. J. (212). Coastal Dynamics I. Delft: VSSD, Delft University of Technology. Morison, J., O'brien, M., Johnson, J., & Schaaf, S. (195). The forces exerted by surface waves on piles. Jounal of Petroleum Technology, Petroleum transactions, AMIE, 189, Naess, A. (211). An introduction to random vibrations. Trondheim: Centre for Ships and Ocean Structures, NTNU. Navaratnam, C. (213). Wave slamming forces on truss structure for wind turbine structures. Trondheim: Norwegian University of Science and Technology. Ros Collados, X. (211). Impact forces on a vertical pile from plunging breaking waves. Trondheim: Norwegian University of Science and Technology. 47

58 Sawaragi, T., & Nochino, M. (1984). Impact forces of nearly breaking waves on a vertical circular cylinder. Coastal Engineering, 27, Tanimoto, K., Takahashi, S., Kaneko, T., & Shiota, K. (1986). Impulsive breaking wave forces on an inclined pile exerted by random waves. Proceedings of 2th International Conference on Coastal Engineering, (pp ). Tørum, A. (213). Analysis of force response data from tests on a model of a truss structure subjected to plunging breaking waves. Department of Civil and Transport Engineering. Trondheim, Norway: Norwegian University of Science and Technology. von Karman, T. (1929). The impact on seaplane floats during landing. Washington: National Advisory Committee for Aeronautics. Wagner, H. (1932). Über stoss-und gleitvorgänge an der oberfläche von flüssigkeiten. Zeitshrift für Angewandte Mathmatik und Mechanik, 12(4), Wienke, J., & Oumeraci, H. (25). Breaking wave impact force on a vertical and inclined slender pile theoretical and large-scale model investigations. Coastal Engineering, 52,

59 APPENDICES 49

60 Attachment I - Dimensions of the local force transducer sections (Pole 1,2,3)

61 Pole 1 Pole 1 Pole Pole 3 Truss structure z = 195mm Joint steel z = 177mm z = 145mm z = 13mm 4 42 z = 115mm z = 163mm Joint steel z = 95mm z = 77 mm Z= mm at MWL Drawing not in scale Torque on connection rods: 81 Nm each

62 Pole 2 Pole 1 Pole Pole 3 Truss structure z = 195mm Joint steel z = 177mm z = 145mm z = 13mm 4 42 z = 115mm z = 163mm Joint steel z = 95mm z = 77 mm Z= mm at MWL Drawing not in scale Torque on connection rods: 81 Nm each

63 Pole 3 Pole 1 Pole Pole 3 Truss structure z = 67mm Joint steel z = 49 mm z = 398 mm z = 377mm z = 25mm Joint steel z = -238 mm z = -33 mm z = -51 mm Z= mm at MWL Drawing not in scale Torque on connection rods: 81 Nm each