An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a...An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide.展开更多
Ocean boundaries present a significant effect on the vibroacoustic characteristics and sound propagation of an elastic structure in practice.In this study,an efficient finite element/wave superposition method(FE/WSM)f...Ocean boundaries present a significant effect on the vibroacoustic characteristics and sound propagation of an elastic structure in practice.In this study,an efficient finite element/wave superposition method(FE/WSM)for predicting the three-dimen-sional acoustic radiation from an arbitrary-shaped radiator in Pekeris waveguides with a lossy seabed is proposed.The method is based on the FE method(FEM),WSM,and sound propagation models.First,a near-field vibroacoustic model is established by the FEM to obtain vibration information on a radiator surface.Then,the WSM based on the Helmholtz boundary integral is used to pre-dict the far-field acoustic radiation and propagation.Furthermore,the rigorous image source method and complex normal mode are employed to obtain the near-and far-field Green’s function(GF),respectively.The former,which is based on the spherical wave decomposition,is adopted to accurately solve the near-field source strength,and the far-field acoustic radiation is calculated by the latter and perturbation theory.The simulations of both models are compared to theoretical wavenumber integration solutions.Finally,numerical experiments on elastic spherical and cylindrical shells in Pekeris waveguides are presented to validate the accuracy and efficiency of the proposed method.The results show that the FE/WSM is adaptable to complex radiators and ocean-acoustic envi-ronments,and are easy to implement and computationally efficient in calculating the structural vibration,acoustic radiation,and sound propagation of arbitrarily shaped radiators in practical ocean environments.展开更多
In this paper, for the fast computation of the coordinates under the basis of the eigenfunctions of Helmholtz operator, we derive the conjugate operator with the radiation boundary condition. Further, we prove the cro...In this paper, for the fast computation of the coordinates under the basis of the eigenfunctions of Helmholtz operator, we derive the conjugate operator with the radiation boundary condition. Further, we prove the cross orthogonality between the linearly-independent eigenfunctions of the Helmholtz operator and the linearly-independent eigenfunctions of the conjugate operator. The numerical simulations demonstrate the effectiveness of our treatment.展开更多
Focus on sound intensity, particle velocity, complex sound intensity and waveguide impedance, the formation mechanism of interference structures in range-frequency domain for the above four kinds of physical quantitie...Focus on sound intensity, particle velocity, complex sound intensity and waveguide impedance, the formation mechanism of interference structures in range-frequency domain for the above four kinds of physical quantities in Pekeris waveguides is analyzed based on Nor- mal Mode Theory. Also, a sea-trial with broadband radiated source is conducted to verify the analysis results. Both the simulation results and the analysis of sea-trial data indicate that, in range-frequency domain, the four kinds of physical quantities will exhibit a stable interfer- ence structure which can be expressed with waveguide invariant /3. Among these quantities, the coherent components of complex sound intensity can better reflect the interference char- acteristics of the waveguide. Finally, a multi-scale linear filter is introduced to deal with the sea-trial LOFAR （Low Frequency Analysis Recording） spectrum, the processing results show that the proposed filter can effectively enhance the interference characteristics in images, and conductively detect and extract striations＇ information from interference structures in LOFAR spectrum.展开更多
A self-normalized statistic the modified modal scintillation index MMSI is proposed and defined as the variance of the modulus of modal excitation normalized by the square of its expected value over some observation i...A self-normalized statistic the modified modal scintillation index MMSI is proposed and defined as the variance of the modulus of modal excitation normalized by the square of its expected value over some observation intervals.It is proved in an analytical form that the MMSI is a depth dependent signature and independent of the source level and the source range under the condition of the ideal waveguide while the classical modal scintillation index MSI depends on both the source level and the source range.The MSI and the MMSI in the Pekeris waveguide at 70 Hz are simulated with different source levels and source ranges by the Kraken normal mode model.The simulation results are consistent with the theoretical deduction.The MMSI probability density functions PDFs of different normal modes for surface and submerged sources are calculated using the mode filtering methods with the same variations of vertical motions.It is indicated that the PDFs can be used to separate the submerged and the surface sources except for the fourth mode.展开更多
In order to solve the problem of depth classification of the underwater target in a very low frequency acoustic field, the active component of cross spectra of particle pressure and horizontal velocity （ACCSPPHV） is...In order to solve the problem of depth classification of the underwater target in a very low frequency acoustic field, the active component of cross spectra of particle pressure and horizontal velocity （ACCSPPHV） is adopted to distinguish the surface vessel and the underwater target. According to the effective depth of a Pekeris waveguide, the placing depth forecasting equations of passive vertical double vector hydrophones are proposed. Numerical examples show that when the sum of depths of two hydro- phones is the effective depth, the sign distribution of ACCSPPHV has nothing to do with horizontal distance; in addition, the sum of the first critical surface and the second critical surface is equal to the effective depth. By setting the first critical surface less than the difference between the effective water depth and the actual water depth, that is, the second critical surface is greater than the actual depth, the three positive and negative regions of the whole ocean volume are equivalent to two positive and negative regions and therefore the depth classification of the underwater target is obtained. Besides, when the 20 m water depth is taken as the first critical surface in the simulation of underwater targets （40 Hz, 50 Hz, and 60 Hz respectively）, the effectiveness of the algorithm and the cor- reemess of relevant conclusions are verified, and the analysis of the corresponding forecasting performance is conducted.展开更多
We study Duffin-Kemmer-Petiau(DKP) equation in the presence of the Woods-Saxon potential and obtain eigenvalues and corresponding eigenfunctions for any J state by using of the Nikiforov-Uvarov(NU) method.The Pekeris ...We study Duffin-Kemmer-Petiau(DKP) equation in the presence of the Woods-Saxon potential and obtain eigenvalues and corresponding eigenfunctions for any J state by using of the Nikiforov-Uvarov(NU) method.The Pekeris approximation is used to deal with centrifugal term.展开更多
We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris ...We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.展开更多
In this paper,a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode(BDRM)theory is presented.According to the BDRM theory,the contribution of the beam displacement and the t...In this paper,a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode(BDRM)theory is presented.According to the BDRM theory,the contribution of the beam displacement and the time delay to the group velocity can be easily considered in a shallow water waveguide.A more accurate dispersion formula is derived by using the cycle distance formula to calculate the group velocity of normal modes.The derived dispersion formula can be applied to the homogeneous shallow water waveguide.Theoretically,the formula is related to the phase of the reflection coefficient and suitable for various bottom models.Furthermore,based on the derived dispersion relation,the modified warping operator is developed to obtain linear modal structures.For the Pekeris model,the formulae for the phase of the reflection coefficient are derived in this work.By taking account of the effect of the bottom attenuation on the reflection coefficient,the formula for the phase of the reflection coefficient including the bottom attenuation is obtained for the Pekeris model with a lossy bottom.Performance and accuracy of different formulae are evaluated and compared.The numerical simulations indicate that the derived dispersion formulae and the modified warping operator are more accurate.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11125420)the Knowledge Innovation Program of the Chinese Academy of Sciences+2 种基金the China Postdoctoral Science Foundation(Grant No.2014M561882)the Doctoral Fund of Shandong ProvinceChina(Grant No.BS2012HZ015)
文摘An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide.
基金financially supported by the National Key Research and Development Plan of China (No. 2016YFC1401203)the National Natural Science Foundation of China (Nos. 42006168 and 11404079)
文摘Ocean boundaries present a significant effect on the vibroacoustic characteristics and sound propagation of an elastic structure in practice.In this study,an efficient finite element/wave superposition method(FE/WSM)for predicting the three-dimen-sional acoustic radiation from an arbitrary-shaped radiator in Pekeris waveguides with a lossy seabed is proposed.The method is based on the FE method(FEM),WSM,and sound propagation models.First,a near-field vibroacoustic model is established by the FEM to obtain vibration information on a radiator surface.Then,the WSM based on the Helmholtz boundary integral is used to pre-dict the far-field acoustic radiation and propagation.Furthermore,the rigorous image source method and complex normal mode are employed to obtain the near-and far-field Green’s function(GF),respectively.The former,which is based on the spherical wave decomposition,is adopted to accurately solve the near-field source strength,and the far-field acoustic radiation is calculated by the latter and perturbation theory.The simulations of both models are compared to theoretical wavenumber integration solutions.Finally,numerical experiments on elastic spherical and cylindrical shells in Pekeris waveguides are presented to validate the accuracy and efficiency of the proposed method.The results show that the FE/WSM is adaptable to complex radiators and ocean-acoustic envi-ronments,and are easy to implement and computationally efficient in calculating the structural vibration,acoustic radiation,and sound propagation of arbitrarily shaped radiators in practical ocean environments.
文摘In this paper, for the fast computation of the coordinates under the basis of the eigenfunctions of Helmholtz operator, we derive the conjugate operator with the radiation boundary condition. Further, we prove the cross orthogonality between the linearly-independent eigenfunctions of the Helmholtz operator and the linearly-independent eigenfunctions of the conjugate operator. The numerical simulations demonstrate the effectiveness of our treatment.
基金supported by the National Natural Science Foundation of China(11234002)the Scientific Research Foundation of Zhejiang Ocean University(21105013415)the Open Foundation from Marine Sciences in the Most Important Subjects of Zhejiang(20160103)
文摘Focus on sound intensity, particle velocity, complex sound intensity and waveguide impedance, the formation mechanism of interference structures in range-frequency domain for the above four kinds of physical quantities in Pekeris waveguides is analyzed based on Nor- mal Mode Theory. Also, a sea-trial with broadband radiated source is conducted to verify the analysis results. Both the simulation results and the analysis of sea-trial data indicate that, in range-frequency domain, the four kinds of physical quantities will exhibit a stable interfer- ence structure which can be expressed with waveguide invariant /3. Among these quantities, the coherent components of complex sound intensity can better reflect the interference char- acteristics of the waveguide. Finally, a multi-scale linear filter is introduced to deal with the sea-trial LOFAR （Low Frequency Analysis Recording） spectrum, the processing results show that the proposed filter can effectively enhance the interference characteristics in images, and conductively detect and extract striations＇ information from interference structures in LOFAR spectrum.
基金The National Natural Science Foundation of China(No.11104029)
文摘A self-normalized statistic the modified modal scintillation index MMSI is proposed and defined as the variance of the modulus of modal excitation normalized by the square of its expected value over some observation intervals.It is proved in an analytical form that the MMSI is a depth dependent signature and independent of the source level and the source range under the condition of the ideal waveguide while the classical modal scintillation index MSI depends on both the source level and the source range.The MSI and the MMSI in the Pekeris waveguide at 70 Hz are simulated with different source levels and source ranges by the Kraken normal mode model.The simulation results are consistent with the theoretical deduction.The MMSI probability density functions PDFs of different normal modes for surface and submerged sources are calculated using the mode filtering methods with the same variations of vertical motions.It is indicated that the PDFs can be used to separate the submerged and the surface sources except for the fourth mode.
基金supported by Public Science and Technology Research Funds Projects of Ocean(201405036-4)the National Natural Science Foundation of China(Grant Nos.11404406,51179034,41072176 and 11204109)+1 种基金Defense Technology Research(JSJC2013604C012)Postdoctoral Science Foundation of China(Grant No.2013 M531015)
文摘In order to solve the problem of depth classification of the underwater target in a very low frequency acoustic field, the active component of cross spectra of particle pressure and horizontal velocity （ACCSPPHV） is adopted to distinguish the surface vessel and the underwater target. According to the effective depth of a Pekeris waveguide, the placing depth forecasting equations of passive vertical double vector hydrophones are proposed. Numerical examples show that when the sum of depths of two hydro- phones is the effective depth, the sign distribution of ACCSPPHV has nothing to do with horizontal distance; in addition, the sum of the first critical surface and the second critical surface is equal to the effective depth. By setting the first critical surface less than the difference between the effective water depth and the actual water depth, that is, the second critical surface is greater than the actual depth, the three positive and negative regions of the whole ocean volume are equivalent to two positive and negative regions and therefore the depth classification of the underwater target is obtained. Besides, when the 20 m water depth is taken as the first critical surface in the simulation of underwater targets （40 Hz, 50 Hz, and 60 Hz respectively）, the effectiveness of the algorithm and the cor- reemess of relevant conclusions are verified, and the analysis of the corresponding forecasting performance is conducted.
文摘We study Duffin-Kemmer-Petiau(DKP) equation in the presence of the Woods-Saxon potential and obtain eigenvalues and corresponding eigenfunctions for any J state by using of the Nikiforov-Uvarov(NU) method.The Pekeris approximation is used to deal with centrifugal term.
基金Project supported by the Fund from the Science and Technology Committee of Shanghai Municipality,China (Grant No. 11ZR1412300)the National Natural Science Foundation of China (Grant No. 61108010)
文摘We study the eigenvalues of the rotating Morse potential by using the quantization condition from the analytical transfer matrix（ATM） method.A hierarchy of supersymmetric partner potentials is obtained with Pekeris approximation,which can be used to calculate the energies of higher rotational states from the energies of lower states.The energies of rotational states of the hydrogen molecule are calculated by the ATM condition,and comparison of the results with those from the hypervirial perturbation method reveals that the accuracy of the approximate expression of Pekeris for the eigenvalues of the rotating Morse potential can be improved substantially in the framework of supersymmetric quantum mechanics.
基金supported by the National Natural Science Foundation of China(Grant Nos.11174312 and 11074269)
文摘In this paper,a modified warping operator for homogeneous shallow water based on the Beam-Displacement Ray-Mode(BDRM)theory is presented.According to the BDRM theory,the contribution of the beam displacement and the time delay to the group velocity can be easily considered in a shallow water waveguide.A more accurate dispersion formula is derived by using the cycle distance formula to calculate the group velocity of normal modes.The derived dispersion formula can be applied to the homogeneous shallow water waveguide.Theoretically,the formula is related to the phase of the reflection coefficient and suitable for various bottom models.Furthermore,based on the derived dispersion relation,the modified warping operator is developed to obtain linear modal structures.For the Pekeris model,the formulae for the phase of the reflection coefficient are derived in this work.By taking account of the effect of the bottom attenuation on the reflection coefficient,the formula for the phase of the reflection coefficient including the bottom attenuation is obtained for the Pekeris model with a lossy bottom.Performance and accuracy of different formulae are evaluated and compared.The numerical simulations indicate that the derived dispersion formulae and the modified warping operator are more accurate.
