Study on the impulsive pressure of tank oscillating by force towards multiple degrees of freedom

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1 EPJ Web of Conferences 80, 0034 (08) EFM 07 Stdy on the implsive pressre of tank oscillating by force towards mltiple degrees of freedom Shigeyki Hibi,* The ational Defense Academy, Department of Mechanical Systems Engineering, -0-0 Hashirimiz, Yokoska, Kanagawa , Japan Abstract. Implsive loads shold be excited nder nonlinear phenomena with free srface flctating severely sch as sloshing and slamming. Estimating implsive loads properly are important to recent nmerical simlations. Bt it is still difficlt to rely on the reslts of simlations perfectly becase of the nonlinearity of the phenomena. In order to develop the algorithm of nmerical simlations experimental reslts of nonlinear phenomena are needed. In this stdy an apparats which can oscillate a tank by force was introdced in order to investigate implsive pressre on the wall of the tank. This apparats can oscillate it simltaneosly towards 3 degrees of freedom with each phase differences. The implsive pressre nder the varios combinations of oscillation direction was examined and the specific phase differences to appear the largest peak vales of pressre were identified. Experimental reslts were verified throgh FFT analysis and statistical methods. Introdction Implsive loads[,] shold be excited nder nonlinear phenomena with free srface flctating severely sch as sloshing and slamming in the field of naval architectre. Many stdies abot not only the estimation of the implsive loads bt also elastic behavior of strctres have been carried ot along with the recent developments of the nmerical simlation methods. However the nmber of experiments to verify those nmerical techniqes is not enogh becase of the nonlinearity of the phenomena. In this stdy an apparats which can oscillate a tank by force was introdced in order to investigate implsive pressre on the wall of the tank. This apparats can oscillate it simltaneosly towards 3 degrees of freedom (p-down, left-right and rotation) with each phase differences. It cold happen that larger implsive pressre is excited nder oscillating the tank simltaneosly towards mltiple degrees of freedom than nder single direction oscilation. The athor examined the implsive pressre nder the varios combinations of oscillation direction and identified the specific phase differences to appear the largest peak vales of pressre. Therefor the athor showed larger implsive pressre cold appear nder the oscillation towards mltiple directions in comparison with the oscillation towards a single direction. In the meantime the ncertainty of the reslt of experiments has been settled by the GUM[3] (Gide to the Expression of Uncertainty in Measrement) since 993. Based on this a FFT analysis abot measred pressre vales was carried ot and the confidence interval of them based on t-distribtion was also determined. At last ncertainty analysis based on the GUM was exected and the reliability of the experiment was assred. Experimental apparats and measring instrments. Specification of oscillation apparats The apparats sed in this stdy can oscillate a tank attached on the bracket harmonically and simltaneosly towards 3 degrees of freedom with each phase differences (See Fig. and Table ). * Corresponding athor: hibiter@nda.ac.jp The Athors, pblished by EDP Sciences. This is an open access article distribted nder the terms of the Creative Commons Attribtion License 4.0 (

2 EPJ Web of Conferences 80, 0034 (08) EFM 07 The size of tank is (mm) (Height WidthDepth). We define the symbols for the oscillation directions of 3 degrees of freedom as follows in Fig.. Heave oscillation (Up down) stands for Z and Sway oscillation (Left right) stands for X and Roll oscillation (Rotation) stands for. Table. Specification of the apparats abot oscillation. Direction of oscillation Heave (Z) (Up-down) Sway (X) (Left-right) Maximm amplitde Minimm period 50 mm.0 sec. 50 mm.0 sec. Roll ( ) (rotation) 45 deg..0 sec.. Measring instrments Fig.. Oscillation apparats with 3 degrees of freedom. () Potentiometer In order to confirm the acclacy of the roll oscillation control of a servo motor a potentiometer is attached to measre a rotation angle at every moment. () Laser displacement gage In order to confirm the acclacy of both heave and sway oscillation control of servo motors laser displacement gages are placed to measre displacements at every moment. (3) Pressre sensor A pressre sensor is attached on the right side of the tank monted on the apparats. The position of the sensor is 40mm from the bottom. The pressre receiver is a rond with a diameter of 8mm. 3 Analytical methods for measred data 3.. FFT (Fast Forier Transform) analysis A FFT analysis are applied to the measred pressre data of time history in this stdy. Freqency components inclding in each data wave profile are discssed. 3. Determining the confidence intervals based on the t-distribtion Fig.. Oscillation direction and pressre sensor position. Independent randam variables sbject to the normal distribtion X, X,... X are assmed that mean vales are and variances are (sally nkonwn). Then sample mean X and nbiased variance are defined by eq. (). X i X i, i ( X i X ) ()

3 EPJ Web of Conferences 80, 0034 (08) EFM 07 Then randam variable T defined by eq. () is sbject to Stdent s t distribtion of degree of freedom. X / T / () Probability density fnction of the t distribtion f t is given by eq. (3). f t t / (3) Here is the gamma fnction. Therefore in case of a sample of size the confidence interval at a confidence level z % is given by eq. (4). x t ( z%) x t ( z%) (4) 3.3 Uncertainty analysis Uncertainty abot measring according to the GUM gidance is evalated as follows. First of all we determine factors of dispersion in the measring procedre. There are types of methods for the estimation of ncertainty in the GUM gidance. One is called A type of ncertainty. Its type is based on a statistical method. We estimate ncertainty of each factor sing mean vales and standard deviations in this type of ncertainty. The other is called B type of ncertainty. Its type is based on another method (e.g. technical information or some experience) withot a statistical approach. After we select the dispersion factors into types of ncertainty, we combine the reslt to estimate the total ncertainty. the expanded ncertainty U is obtained by mltiplying the combined standard ncertainty c(y) by a coverage factor k (k =. This means the 95% confidence level ). 4 Experiment and discssion 4. Investigating phase differences dring simltaneos oscillation towards degrees of freedom The reliability of oscillation amplitde towards each degree of freedom is assred even with a period close to the natral period of the tank by previos stdy. In this stdy we chose 3 pairs of degrees of freedom from 3 one. Those will be sbscribed as follows ( X, Z, X Z ). The oscillation period is niformly.08 (sec.) which is close to the natral period of the tank in case of the water depth is 60 mm (fixed). The oscillation amplitdes are 5 mm for X and Z and 0 degrees for. We measred time historys of pressre on the wall of the tank repeatedly while changing the phase difference from 0 degree to 360 degrees. We identified the phase difference which case the largest peak vale of pressre for each oscillation pair ( X, Z, X Z ). The reslts are shown in Table. Table. Phase difference which case the largest peak vale. Oscillation pair X Z X Z Phase difference 5 degrees 335 degrees 0 degrees Example reslts of time history of pressre for each oscillation pair are shown in Figs. 3(a), (b) and (c). In any cases it can be dedced that there is periodicity in the pressre flctation, bt it is fond that the peak vales have variations. 4. FFT analysis for measred time history of pressre FFT analysis was carried ot with, and 9 period intervals from the measred data of time history of pressre for each oscillation pair. The reslts are shown in Figs. 4(a), (b) and (c). The waveform of the spectrm for period 3

4 EPJ Web of Conferences 80, 0034 (08) EFM 07 interval contains the ones for and 9 period intervals. We can also dedce that althogh the obtained peak vales varies, the waveform itself seems periodic. S(f) p (Pa) f(hz) Fig. 4(a). FFT analysis abot X oscillation. S(f) Fig. 3(a). Time history of pressre abot X oscillation. p (Pa) f(hz) Fig. 3(b). Time history of pressre abot Z oscillation. Fig. 4(b). FFT analysis abot Z oscillation. S(f) p (Pa) Fig. 3(c). Time history of pressre abot X Z oscillation. Fig. 4(c). FFT analysis abot X Z oscillation. f(hz) 4

5 EPJ Web of Conferences 80, 0034 (08) EFM Estimation of confidence intervals for the confidence level 95% Experiments were repeated as one measrement for 0 seconds. Peak vales were extracted from the time history of pressre for each oscillation pair. ext confidence intervals for the confidence level 95 % were determined. The reslts are shown in the Fig. 4. Althogh the width of the confidence interval tends to decrease when the nmber of samples increases, it is considered that there is a significant width, which may indicate the nonlinearity of the present experimental data. Sampling nmbers Fig. 5(c). Estimation of peak vales at confidence level 95% abot X Z oscillation. 4.4 Determining the expanded ncertainty Sampling nmbers Fig. 5(a). Estimation of peak vales at confidence level 95% abot X oscillation. Expanded ncertainty was determined according to the bdget table shown in Table 3. The fnction f sed to estimate the ncertainty when measring pressre vales is in eq. (5). f g a V ( d) V (0) (5) Where is the density of water and g is the gravitational acceleration. a is the coefficient for conversion from voltage to pressre. V(d) is the voltage vale of an amplifier at the d mm water depth and V(0) is the voltage vale of an amplifier at the 0 mm water depth. The expanded ncertainty calclated from Table 3 is 0.9 (Pa). The nmber of iterations sed here is times. In most cases it can be seen that the peak vale varies arond a mean vale at this interval. 5 Conclsion In this stdy implsive pressre on the tank wall were measred and some information were fond abot it as below. Sampling nmbers Fig. 5(b). Estimation of peak vales at confidence level 95% abot Z oscillation. The flctation measred had some periodism bt the peak vales had variation. From the estimation of confidence intervals for the measred vales at the confidence level 95% significant intervals were fond to exist. Since characteristics of implsive pressre for the oscillation directions of degrees of freedom is known, confirmation of that for the oscillation directions of 3 degrees of freedom is a ftre task. 5

6 pdt / 0 c EPJ Web of Conferences 80, 0034 (08) EFM 07 References. Hakan Akyildiza, Erdem U nal, Ocean Engineering 3, 503 (005). P. Temarel, W. Bai, A. Brns, Q. Derbanne, D. Dessi,S. Dhavalikar,. Fonseca, T. Fkasawa, X. G, A. estegård,a. Papanikolao, J. Parnov, K.H. Song m, S. Wang, Ocean Engineering 9, 74 (06) 3. JCGM008, Evalation of measrement data - Gide to the expression of ncertainty in measrement, (008) Table 3. Bdget table for the estimation of ncertainty V Factors of ncertainty : x i Coefficient for conversion a from voltage to pressre Voltage vale at the 0 0mm water depth Calibration of Vp the pressre sensor Vamp Calibration of the amplifier Combined c standart ncertainty Expanded ncertainty Case of ncertainty Type of ncertainty Shapes of probabilistic distribtion Mean Sensitivity vale factor Standard ncertainty Repeated experiment A ormal Repeated experiment A ormal Calibration error of the pressre sensor Calibration error of the amplifier B Uniform B Uniform f x i (Pa) 0.9 (Pa) 6