The Investigation On Predicting And Measuring The Sound Radiation Of Underwater Shell Structure In Low Frequency

A shell structure with large length-to-radius ratio is the typical structure of a hull. Studyon its low-frequency radiation characteristics has practical significance in quantitativelyforecasting and through appropriate measures reducing the vibration and sound radiation ofthe submarine. There are two purposes in this work, the first one is based on the soundradiation characteristics and the existing forecasting methods, an efficient forecasting methodis explored to predict the vibration and the sound radiation of the shell structure with largelength-to-radius ratio in low frequency; the second one is to achieve the accuratemeasurement of the submarine radiated noise and the noise sources identification, thelow-frequency applications are to be expanded by use of the reverberant measurement resultsin a non-anechoic water tank.The investigations on predicting and measuring the sound radiation of underwater shellstructure in low frequency are carried out in this work.In forecasting research, firstly, the modal expansion method is used in the analyticanalysis of vibration and radiation of an underwater ring-stiffened cylindrical shell withacoustic coating, which is simply supported on semi-infinite cylindrical baffles, is derived.The analytical model can be used to verify the correctness of the numerical calculation andthe equivalent algorithm, subsequently. Secondly, a simplified FEM+BEM numerical methodis established to predict the radiation characteristics of the underwater complex shell structurewith a large length-to-radius ratio, and which is carried out by use of ANSYS and SYSNOISE.The coupling effect of the fluid on the low-frequency vibration can be approximated to anadded density loading to the structure. For calculating the response of the low-frequencyvibration in water by using ANSYS, a limited fluid domain of not less than five times theradius of the shell structure is chosen instead of the huge spherical fluid domain determinedby the sound absorbing boundary radius, thus the efficiency of the numerical calculation isgreatly improved. Then, in order to improve the computational efficiency of the vibration andthe sound radiation of underwater cylindrical shells with the large length-to-radius ratio(L/a>20) in low frequency, a method using the equivalent beams is proposed. The equivalentbeam theoretical model is based on Euler-Bernoulli beam theory, in which the interactionbetween the structures and water is approximated as added mass. Different equivalentYoung’s modulus coefficients for the beam models are obtained, through which the modalfrequencies of the beams are made identical to the beam-type modal frequencies of the cylindrical shell. The equivalent Young’s modulus coefficients curves for the first five orderbeam-type natural frequencies of cylindrical shells with different length-to-radius ratio arecalculated, through which the radiated sound power and the beam-type modes of theunderwater simply cylindrical shells in the first five beam-type bending frequency range canbe precisely predicted by using a simple beam theoretical model. Finally, the equivalentalgorithm is expanded into the prediction of the radiated sound power of a complex variablecross-section shell structure in low frequency, which is shown as an universal and efficientmethod by analyzing the effect of different boundary, structural parameters and other factors.In experimental research, a fine calibration method is proposed by measuring thedifference between the mean square sound pressure in the non-anechoic water tank and that inthe free-field, and the radiated sound power of a complex structure is accurately measured.Using this fine calibration method, the reverberant measurement is expanded to be valid innon-anechoic water tank below the lower limit frequency range, and the measurement ofreverberation time in the non-anechoic water tank is avoided. In order to find the theoreticalbasis of the fine calibration method on reverberant measurement, the sound field and theradiation resistance of a point source in a rectangle reverberant pool with absolutely softboundary are derived, both the reverberant field to free field ratio of the mean square soundpressure and the ratio of the radiation resistance are further analyzed by numericalcomputation, and effect of the radiation resistance on the radiated sound power is analyzed. Inthe end of this work, both the radiated sound power of the typical sound source and thecomplex structure are measured in the anechoic water tank and the non-anechoic water tank,respectively, and the accuracy and the validity of the fine calibration method on reverberantmeasurement are verified. The test results show that, for a spherical sound source above2000Hz, the radiated sound power is accurately measured in the glass pool with lower limit infrequency being8000Hz, and the intense undulation effect caused by the normal waveresonance is eliminated. Compared to the radiated sound power tested in the anechoic watertank, the narrowband spectrum deviation tested in non-anechoic water tank is less than3dB,and the sound power level of1/3octave spectrum deviation is less than1dB. For a cylindricalshell model in the range2000Hz above, by using different known sound source for calibration,a good consistency of the radiated sound power is measured in the non-anechoic water tank,and the deviation compared to the results tested in anechoic water tank is less than1.5dB.