In order to build a rapid ocean ambient noise model adapted for a stratified shallow water, a hybrid model of normal mode method (for far field) and ray method (for near field) is suggested which combines the advantag...In order to build a rapid ocean ambient noise model adapted for a stratified shallow water, a hybrid model of normal mode method (for far field) and ray method (for near field) is suggested which combines the advantages of both methods. Since the near field of wind-generated noise is not sensitive to the sound speed pro- file, the sound speed profile is regarded as a constant; which makes the model rapid and accurate. The simulation results are in agreement with those of the wave model.展开更多
Cross-ice acoustic information transmission is an effective means of communication in polar sea areas covered by ice.However,the channel is extremely complicated because of the combined influence of water,ice,and air....Cross-ice acoustic information transmission is an effective means of communication in polar sea areas covered by ice.However,the channel is extremely complicated because of the combined influence of water,ice,and air.Based on the normalmode theory,this paper establishes a cascade acoustic channel(CAC)model for the transmission of underwater acoustic waves across ice layer.The model can calculate the displacement response of the ice layer’s upper surface by separating the upward waves from normal modes in the water and multiplying it by a transmission coefficient matrix.The relationship between the displacement response of the upper surface of ice layer and the acoustic frequency is calculated by the finite-element method,and the calculation result was consistent with that of the CAC model.To verify the applicability of the model,a cross-ice acoustic communication experiment was conducted in Songhua River in January 2019.Experimental results show the energy of the acoustic signals received by geophones is closely related to sound frequency and crossice acoustic communication is feasible.The result of present research is important for understanding crossice acoustic channel characteristics and developing future cross-ice acoustic communication in polar sea areas.展开更多
Atmospheric disturbances at 300 hPa are decomposed into normal modes, referred as discrete—spectrum disturbances which can propagate freely in the observed zonal mean flow, and non—modal transient disturbances, refe...Atmospheric disturbances at 300 hPa are decomposed into normal modes, referred as discrete—spectrum disturbances which can propagate freely in the observed zonal mean flow, and non—modal transient disturbances, referred as continuous—spectrum disturbances which are continuously sheared and eventually absorbed by the zonal flow. It is shown that normal modes represent only a small fraction of the observed atmospheric disturbances, while continuous—spectrum disturbances represent the majority of observed disturbances, even when the basic flow is unstable. Daily variabilities of the observed continuous—spectrum disturbances are presented. They are shown to follow the results of wave—packet theory. Calculations suggest that there are abundant sources to excite continuous—spectrum disturbances in the atmosphere.展开更多
A technique to extract real modes from the identified complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtain...A technique to extract real modes from the identified complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtained. The theoretical derivation of the method is provided in detail. An 11-DOF vibration system is used to validate the algorithm, and to analyze the effects of the number of modes utilized and measurement DOFs on the extraction results. Finally, the method is used to extract real modes from both experimental modal analysis and operational modal analysis.展开更多
The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonanc...The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.展开更多
Normal mode analysis in dihedral angle space was carried out on two X ray crystal structures and one model structure responded to the same sequence of duplex DNA: d(CGCGAATTCGCG). Comparing these results indicates th...Normal mode analysis in dihedral angle space was carried out on two X ray crystal structures and one model structure responded to the same sequence of duplex DNA: d(CGCGAATTCGCG). Comparing these results indicates that it is reliable and meaningful to carry out normal mode analysis on model structures. The reliability is greater except for the ends of helix.展开更多
Data-derived normal mode extraction is an effective method for extracting normal mode depth functions in the absence of marine environmental data.However,when the corresponding singular vectors become nonunique when t...Data-derived normal mode extraction is an effective method for extracting normal mode depth functions in the absence of marine environmental data.However,when the corresponding singular vectors become nonunique when two or more singular values obtained from the cross-spectral density matrix diagonalization are nearly equal,this results in unsatisfactory extraction outcomes for the normal mode depth functions.To address this issue,we introduced in this paper a range-difference singular value decomposition method for the extraction of normal mode depth functions.We performed the mode extraction by conducting singular value decomposition on the individual frequency components of the signal's cross-spectral density matrix.This was achieved by using pressure and its range-difference matrices constructed from vertical line array data.The proposed method was validated using simulated data.In addition,modes were successfully extracted from ambient noise.展开更多
A continuum based model is presented which identifies a favorable set of operational conditions whereby an effective and efficient electromagnetically induced vibratory motion can proceed within an induction system.Sp...A continuum based model is presented which identifies a favorable set of operational conditions whereby an effective and efficient electromagnetically induced vibratory motion can proceed within an induction system.Specifically, an analytical assessment is presented for the electromagnetic field and the electromagnetically induced acoustic field, with parametric factors incorporated into the model to permit a normal modes solution for the acoustic field which here is sensitive to the compliance of both the molten metal and the wall,as well as electromagnetic properties of the metal.A parametric analysis is presented which identifies the importance of matching the mechanical impedances of the melt-wall configuration so that the generation of acoustic energy within the melt system can be more effectively utilized.Relatively straight-forward calculations,presented for the acoustic field,may provide a more computationally efficient means for implementing process simulation studies for these systems.展开更多
A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynami...A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystemmodeling framework. It is clearly elucidated for the first time that,dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beamand the transverse vibration deformation of the beam. The modeling approach in this paper successfully avoids problems which are caused by other popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can＇t be provided. First,the continuous dynamic models of the flexible beamand the central rigid body are established via structural dynamics and angular momentumtheory respectively. Then,based on the conclusions of orthogonalization about the normal constrained modes,the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations showthat： dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper,which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately,and has a clear modeling mechanism,concise expressions and a good convergence.展开更多
We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forwa...We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.展开更多
The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and deca...The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and decay in the Southern Hemisphere atmosphere duringApril, November, and December 1989. The statistics of 100 evolved errors are studied for six-dayperiods and compared with the growth and structures of fast growing normal modes and finite-timenormal modes (FTNMs). The amplification factors of most initially random errors are slightly lessthan those of the fastest growing FTNM for the same time interval. During their evolution, thestandard deviations of the error fields become concentrated in the regions of rapid dynamicaldevelopment, particularly associated with developing and decaying blocks. We have calculatedprobability distributions and the mean and standard deviations of pattern correlations between eachof the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. Themean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases withincreasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but notalways, gives the largest mean pattern correlation with error fields. Corresponding patterncorrelations with the fast growing normal modes of the instantaneous basic state flow aresignificant' but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increasefurther when the time interval is increased beyond six days.展开更多
Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation t...Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation technique. Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerated. For nonresonances, it is analytically presented that a single-mode motion and localization of vibrations occur in the system, and the degree of localization relates not only to the coupling stiffness between oscillators, but also to the asymmetric parameter. The parametric threshold value of localization is analytically given. For 1 : 1 resonance, there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying. The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.展开更多
A general model of the equations of the Lord-Sulman theory including one relaxation time and the Green-Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory, are applied to the st...A general model of the equations of the Lord-Sulman theory including one relaxation time and the Green-Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory, are applied to the study of the influence of reinforcement on the total deformation for an infinite space weakened by a finite linear opening mode- I crack. We study the influence of reinforcement on the total deformation of rotating thermoelastic half-space and their interaction with each other. The material is homogeneous isotropic elastic half space. The crack is subjected to prescribed temperature and stress distributions. The normal mode analysis is used to obtain the exact expressions for displacement components, force stresses, and temperature. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results obtained in the three theories with and without rotation. A comparison is also made between the two theories for different depths.展开更多
Optomechanical dynamics in two systems which are a transmission line resonator and Fabrya-Perot optical cavity via radiation-pressure are investigated by linearized quantum Langevin equation. We work in the resolved s...Optomechanical dynamics in two systems which are a transmission line resonator and Fabrya-Perot optical cavity via radiation-pressure are investigated by linearized quantum Langevin equation. We work in the resolved sideband regime where the oscillator resonance frequency exceeds the cavity linewidth. Normal mode splittings of the mechanical resonator as a pure result of the coupling interaction in the two optomechanical systems is studied, and we make a comparison of normal mode splitting of mechanical resonator between the two systems. In the optical cavity, the normal mode splitting of the movable mirror approaches the latest experiment very well. In addition, an approximation scheme is introduced to demonstrate the ground state cooling, and we make a comparison of cooling between the two systems dominated by two key factors, which are the initial bath temperature and the mechanical quality factor. Since both the normal mode splitting and cooling require working in the resolved sideband regime, whether the normal mode splitting influences the cooling of the mirror is considered. Considering the size of the mechanical resonator and precooling the system, the mechanical resonator in the transmission line resonator system is easier to achieve the ground state cooling than in optical cavity.展开更多
The physical size of an antenna becomes an important characteristic when receiving signals in bands with long wavelengths. Size determines two important aspects of antenna performance;impedance and efficiency. For exa...The physical size of an antenna becomes an important characteristic when receiving signals in bands with long wavelengths. Size determines two important aspects of antenna performance;impedance and efficiency. For example, the VHF antennas installed on radio sets that intended to receive FM or the latest technology Digital Audio Broadcasting (DAB) radio signals in Bands II, III respectively. Antennas that are installed on mobile platforms (i.e. portable receivers) require a receiver that utilizes a whip telescopic antenna with adjustable length which can operate as a λ/4 monopole antenna. Whereas, non-portable applications like a deck commercial receiver has no built in antenna due to the large size of the radiator needed and so must be connected with an external antenna. This paper presents a new design of a very small size Normal Mode Multiloop Helical Antenna (NMMHA) with superior performance developed for commercial receivers operate in band II, III. The major drawback which has been overcome with this design is the very narrow bandwidth of the Normal Mode Helical Antenna, which originally was optimized to provide the minimum Voltage Standing Wave Ratio VSWR response across Band II (87.5 - 108 MHz). The NMMHA’s size allows it to be a build in block of a deck commercial receiver.展开更多
Three point-like massive particles/atoms are connected with three springs forming an equilateral triangle replicating a prototype triatomic molecule. The triangle is inscribed within a stationary frame via three addit...Three point-like massive particles/atoms are connected with three springs forming an equilateral triangle replicating a prototype triatomic molecule. The triangle is inscribed within a stationary frame via three additional springs confining the vibrations of the molecule to a 2D space. It is the objective of this research flavored investigation to seek the normal vibrational modes for this three-body six-spring structure. The entire analysis including symbolic, numeric, and graphics is carried out by adapting a suitable Computer Algebra System (CAS), Mathematica. For a comprehensive understanding, the frequency of the normal mode is used for a visual animation;an actual mechanical replica of the “molecule” for the scenario on hand is fabricated.展开更多
A Wentzel-Kramers-Brillouin(WKB)method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean.The method utilizes a mode sum and employs the re...A Wentzel-Kramers-Brillouin(WKB)method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean.The method utilizes a mode sum and employs the reference functions method to describe the solution to the depth-separated wave equation approximately using parabolic cylinder functions.The conditions for the validity of this approximation are also discussed.Furthermore,a formula that incorporates waveguide effects for the modal group velocity is derived,revealing that boundary effects at very low frequencies can have a significant impact on the propagation characteristics of even low-order normal modes.The present method not only offers improved accuracy compared to the classical WKB approximation and the uniform asymptotic approximation based on Airy functions,but also provides a wider range of depth applicability.Additionally,this method exhibits strong agreement with numerical methods and offers valuable physical insights.Finally,the method is applied to the study of very-low-frequency sound propagation in the South China Sea,leading to sound transmission loss predictions that closely align with experimental observations.展开更多
Normal mode extraction has attracted extensive attention over the past few decades due to its practical value in enhancing the performance of underwater acoustic signal processing.Singular value decomposition(SVD)is a...Normal mode extraction has attracted extensive attention over the past few decades due to its practical value in enhancing the performance of underwater acoustic signal processing.Singular value decomposition(SVD)is an effective method to extract modal depth functions using vertical line arrays(VLA),particularly in scenarios when no prior environment information is available.However,the SVD method requires rigorous orthogonality conditions,and its performance severely degenerates in the presence of mode degeneracy.Consequently,the SVD approach is often not feasible in practical scenarios.This paper proposes a full rank decomposition(FRD)method to address these issues.Compared to the SVD method,the FRD method has three distinct advantages:1)the conditions that the FRD method requires are much easier to be fulfilled in practical scenarios;2)both modal depth functions and wavenumbers can be simultaneously extracted via the FRD method;3)the FRD method is not affected by the phenomenon of mode degeneracy.Numerical simulations are conducted in two types of waveguides to verify the FRD method.The impacts of environment configurations and noise levels on the precision of the extracted modal depth functions and wavenumbers are also investigated through simulation.展开更多
The spatial correlations of acoustic field have important implications for underwater target detection and other ap- plications in deep water. In this paper, the spatial correlations of the high intensity zone in the ...The spatial correlations of acoustic field have important implications for underwater target detection and other ap- plications in deep water. In this paper, the spatial correlations of the high intensity zone in the deep-water acoustic field are investigated by using the experimental data obtained in the South China Sea. The experimental results show that the structures of the spatial correlation coefficient at different ranges and depths are similar to the transmission loss structure in deep water. The main reason for this phenomenon is analyzed by combining the normal mode theory with the ray theory. It is shown that the received signals in the high intensity zone mainly include one or two main pulses which are contributed by the interference of a group of waterbome modes with similar phases. The horizontal-longitudinal correlations at the same receiver depth but in different high intensity zones are analyzed. At some positions, more pulses are received in the arrival structure of the signal due to bottom reflection and the horizontal-longitudinal correlation coefficient decreases accordingly. The multi-path arrival structure of receiving signal becomes more complex with increasing receiver depth.展开更多
Understanding the effect of source-receiver geometry on sound propagation in surface ducts can improve the performance of near-surface sonar in deep water. The Lloyd-mirror and normal mode theories are used to analyze...Understanding the effect of source-receiver geometry on sound propagation in surface ducts can improve the performance of near-surface sonar in deep water. The Lloyd-mirror and normal mode theories are used to analyze the features of surface-duct propagation in this paper. Firstly, according to the Lloyd-mirror theory, a shallow point source generates directional lobes, whose grazing angles are determined by the source depth and frequency. By assuming a part of the first lobe to be just trapped in the surface duct, a method to calculate the minimum cutoff frequency （MCF） is obtained. The presented method is source depth dependent and thus is helpful for determining the working depth for sonar. Secondly, it is found that under certain environments there exists a layer of low transmission loss （TL） in the surface duct, whose thickness is related to the source geometry and can be calculated by the Lloyd-mirror method. The receiver should be placed in this layer to minimize the TL. Finally, the arrival angle on a vertical linear array （VLA） in the surface duct is analyzed based on normal mode theory, which provides a priori knowledge of the beam direction of passive sonar.展开更多
基金This work was supported by Naval Weapon Department under contract No. 41303090207, and by Science and Technology Ministry under con-tract No. 2001AA631080 and No. 2003AA604010.
文摘In order to build a rapid ocean ambient noise model adapted for a stratified shallow water, a hybrid model of normal mode method (for far field) and ray method (for near field) is suggested which combines the advantages of both methods. Since the near field of wind-generated noise is not sensitive to the sound speed pro- file, the sound speed profile is regarded as a constant; which makes the model rapid and accurate. The simulation results are in agreement with those of the wave model.
基金This research was funded by the National Key R&D Program of China(2018YFC1405900)The National Natural Science Foundation of China(Grant No.61631008 and No.51779061)+2 种基金the Fok Ying-Tong Education Foundation,China(Grant,No.151007)The Heilongjiang Province Outstanding Youth Science Fund(JC2017017)and the Innovation Special Zone of National Defense Science and Technology.
文摘Cross-ice acoustic information transmission is an effective means of communication in polar sea areas covered by ice.However,the channel is extremely complicated because of the combined influence of water,ice,and air.Based on the normalmode theory,this paper establishes a cascade acoustic channel(CAC)model for the transmission of underwater acoustic waves across ice layer.The model can calculate the displacement response of the ice layer’s upper surface by separating the upward waves from normal modes in the water and multiplying it by a transmission coefficient matrix.The relationship between the displacement response of the upper surface of ice layer and the acoustic frequency is calculated by the finite-element method,and the calculation result was consistent with that of the CAC model.To verify the applicability of the model,a cross-ice acoustic communication experiment was conducted in Songhua River in January 2019.Experimental results show the energy of the acoustic signals received by geophones is closely related to sound frequency and crossice acoustic communication is feasible.The result of present research is important for understanding crossice acoustic channel characteristics and developing future cross-ice acoustic communication in polar sea areas.
文摘Atmospheric disturbances at 300 hPa are decomposed into normal modes, referred as discrete—spectrum disturbances which can propagate freely in the observed zonal mean flow, and non—modal transient disturbances, referred as continuous—spectrum disturbances which are continuously sheared and eventually absorbed by the zonal flow. It is shown that normal modes represent only a small fraction of the observed atmospheric disturbances, while continuous—spectrum disturbances represent the majority of observed disturbances, even when the basic flow is unstable. Daily variabilities of the observed continuous—spectrum disturbances are presented. They are shown to follow the results of wave—packet theory. Calculations suggest that there are abundant sources to excite continuous—spectrum disturbances in the atmosphere.
文摘A technique to extract real modes from the identified complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtained. The theoretical derivation of the method is provided in detail. An 11-DOF vibration system is used to validate the algorithm, and to analyze the effects of the number of modes utilized and measurement DOFs on the extraction results. Finally, the method is used to extract real modes from both experimental modal analysis and operational modal analysis.
文摘The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled. The bifurcation problem of the coupled NNM of system with 1 : 2 : 5 dual internal resonance is in two variables. The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found. Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom. At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.
文摘Normal mode analysis in dihedral angle space was carried out on two X ray crystal structures and one model structure responded to the same sequence of duplex DNA: d(CGCGAATTCGCG). Comparing these results indicates that it is reliable and meaningful to carry out normal mode analysis on model structures. The reliability is greater except for the ends of helix.
基金supported in part by the Young Scientists Fund of National Natural Science Foundation of China (No.42206226)the National Key Research and Development Program of China (No.2021YFC3101603)。
文摘Data-derived normal mode extraction is an effective method for extracting normal mode depth functions in the absence of marine environmental data.However,when the corresponding singular vectors become nonunique when two or more singular values obtained from the cross-spectral density matrix diagonalization are nearly equal,this results in unsatisfactory extraction outcomes for the normal mode depth functions.To address this issue,we introduced in this paper a range-difference singular value decomposition method for the extraction of normal mode depth functions.We performed the mode extraction by conducting singular value decomposition on the individual frequency components of the signal's cross-spectral density matrix.This was achieved by using pressure and its range-difference matrices constructed from vertical line array data.The proposed method was validated using simulated data.In addition,modes were successfully extracted from ambient noise.
文摘A continuum based model is presented which identifies a favorable set of operational conditions whereby an effective and efficient electromagnetically induced vibratory motion can proceed within an induction system.Specifically, an analytical assessment is presented for the electromagnetic field and the electromagnetically induced acoustic field, with parametric factors incorporated into the model to permit a normal modes solution for the acoustic field which here is sensitive to the compliance of both the molten metal and the wall,as well as electromagnetic properties of the metal.A parametric analysis is presented which identifies the importance of matching the mechanical impedances of the melt-wall configuration so that the generation of acoustic energy within the melt system can be more effectively utilized.Relatively straight-forward calculations,presented for the acoustic field,may provide a more computationally efficient means for implementing process simulation studies for these systems.
文摘A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystemmodeling framework. It is clearly elucidated for the first time that,dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beamand the transverse vibration deformation of the beam. The modeling approach in this paper successfully avoids problems which are caused by other popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can＇t be provided. First,the continuous dynamic models of the flexible beamand the central rigid body are established via structural dynamics and angular momentumtheory respectively. Then,based on the conclusions of orthogonalization about the normal constrained modes,the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations showthat： dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper,which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately,and has a clear modeling mechanism,concise expressions and a good convergence.
基金Supported by the National Natural Science Foundation of China under Grant No 11774374the Natural Science Foundation of Shandong Province of China under Grant No ZR2016AL10
文摘We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.
文摘The structural organization of initially random errors evolving in abarotropic tangent linear model, with time-dependent basic states taken from analyses, is examinedfor cases of block development, maturation and decay in the Southern Hemisphere atmosphere duringApril, November, and December 1989. The statistics of 100 evolved errors are studied for six-dayperiods and compared with the growth and structures of fast growing normal modes and finite-timenormal modes (FTNMs). The amplification factors of most initially random errors are slightly lessthan those of the fastest growing FTNM for the same time interval. During their evolution, thestandard deviations of the error fields become concentrated in the regions of rapid dynamicaldevelopment, particularly associated with developing and decaying blocks. We have calculatedprobability distributions and the mean and standard deviations of pattern correlations between eachof the 100 evolved error fields and the five fastest growing FTNMs for the same time interval. Themean of the largest pattern correlation, taken over the five fastest growing FTNMs, increases withincreasing time interval to a value close to 0.6 or larger after six days. FTNM 1 generally, but notalways, gives the largest mean pattern correlation with error fields. Corresponding patterncorrelations with the fast growing normal modes of the instantaneous basic state flow aresignificant' but lower than with FTNMs. Mean pattern correlations with fast growing FTNMs increasefurther when the time interval is increased beyond six days.
文摘Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation technique. Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerated. For nonresonances, it is analytically presented that a single-mode motion and localization of vibrations occur in the system, and the degree of localization relates not only to the coupling stiffness between oscillators, but also to the asymmetric parameter. The parametric threshold value of localization is analytically given. For 1 : 1 resonance, there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying. The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.
文摘A general model of the equations of the Lord-Sulman theory including one relaxation time and the Green-Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory, are applied to the study of the influence of reinforcement on the total deformation for an infinite space weakened by a finite linear opening mode- I crack. We study the influence of reinforcement on the total deformation of rotating thermoelastic half-space and their interaction with each other. The material is homogeneous isotropic elastic half space. The crack is subjected to prescribed temperature and stress distributions. The normal mode analysis is used to obtain the exact expressions for displacement components, force stresses, and temperature. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results obtained in the three theories with and without rotation. A comparison is also made between the two theories for different depths.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10647132 and 11104113)the Scientific Research Fund of Hunan Provincial Education Department of China (Grant No. 10A100)
文摘Optomechanical dynamics in two systems which are a transmission line resonator and Fabrya-Perot optical cavity via radiation-pressure are investigated by linearized quantum Langevin equation. We work in the resolved sideband regime where the oscillator resonance frequency exceeds the cavity linewidth. Normal mode splittings of the mechanical resonator as a pure result of the coupling interaction in the two optomechanical systems is studied, and we make a comparison of normal mode splitting of mechanical resonator between the two systems. In the optical cavity, the normal mode splitting of the movable mirror approaches the latest experiment very well. In addition, an approximation scheme is introduced to demonstrate the ground state cooling, and we make a comparison of cooling between the two systems dominated by two key factors, which are the initial bath temperature and the mechanical quality factor. Since both the normal mode splitting and cooling require working in the resolved sideband regime, whether the normal mode splitting influences the cooling of the mirror is considered. Considering the size of the mechanical resonator and precooling the system, the mechanical resonator in the transmission line resonator system is easier to achieve the ground state cooling than in optical cavity.
文摘The physical size of an antenna becomes an important characteristic when receiving signals in bands with long wavelengths. Size determines two important aspects of antenna performance;impedance and efficiency. For example, the VHF antennas installed on radio sets that intended to receive FM or the latest technology Digital Audio Broadcasting (DAB) radio signals in Bands II, III respectively. Antennas that are installed on mobile platforms (i.e. portable receivers) require a receiver that utilizes a whip telescopic antenna with adjustable length which can operate as a λ/4 monopole antenna. Whereas, non-portable applications like a deck commercial receiver has no built in antenna due to the large size of the radiator needed and so must be connected with an external antenna. This paper presents a new design of a very small size Normal Mode Multiloop Helical Antenna (NMMHA) with superior performance developed for commercial receivers operate in band II, III. The major drawback which has been overcome with this design is the very narrow bandwidth of the Normal Mode Helical Antenna, which originally was optimized to provide the minimum Voltage Standing Wave Ratio VSWR response across Band II (87.5 - 108 MHz). The NMMHA’s size allows it to be a build in block of a deck commercial receiver.
文摘Three point-like massive particles/atoms are connected with three springs forming an equilateral triangle replicating a prototype triatomic molecule. The triangle is inscribed within a stationary frame via three additional springs confining the vibrations of the molecule to a 2D space. It is the objective of this research flavored investigation to seek the normal vibrational modes for this three-body six-spring structure. The entire analysis including symbolic, numeric, and graphics is carried out by adapting a suitable Computer Algebra System (CAS), Mathematica. For a comprehensive understanding, the frequency of the normal mode is used for a visual animation;an actual mechanical replica of the “molecule” for the scenario on hand is fabricated.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12174048 and 12204128)。
文摘A Wentzel-Kramers-Brillouin(WKB)method is introduced for obtaining a uniform asymptotic solution for underwater sound propagation at very low frequencies in deep ocean.The method utilizes a mode sum and employs the reference functions method to describe the solution to the depth-separated wave equation approximately using parabolic cylinder functions.The conditions for the validity of this approximation are also discussed.Furthermore,a formula that incorporates waveguide effects for the modal group velocity is derived,revealing that boundary effects at very low frequencies can have a significant impact on the propagation characteristics of even low-order normal modes.The present method not only offers improved accuracy compared to the classical WKB approximation and the uniform asymptotic approximation based on Airy functions,but also provides a wider range of depth applicability.Additionally,this method exhibits strong agreement with numerical methods and offers valuable physical insights.Finally,the method is applied to the study of very-low-frequency sound propagation in the South China Sea,leading to sound transmission loss predictions that closely align with experimental observations.
基金supported by the National Natural Science Foundation of China(Nos.12304504,12304506 and U22 A2012)the Youth Innovation Promotion Association,Chinese Academy of Sciences(No.2021023)+1 种基金the Strategy Priority Research Program(Category B)of Chinese Academy of Sciences(Nos.XDB0700100 and XDB0700000)the Natural Science Foundation of Tianjin(No.22JCYBJC00070).
文摘Normal mode extraction has attracted extensive attention over the past few decades due to its practical value in enhancing the performance of underwater acoustic signal processing.Singular value decomposition(SVD)is an effective method to extract modal depth functions using vertical line arrays(VLA),particularly in scenarios when no prior environment information is available.However,the SVD method requires rigorous orthogonality conditions,and its performance severely degenerates in the presence of mode degeneracy.Consequently,the SVD approach is often not feasible in practical scenarios.This paper proposes a full rank decomposition(FRD)method to address these issues.Compared to the SVD method,the FRD method has three distinct advantages:1)the conditions that the FRD method requires are much easier to be fulfilled in practical scenarios;2)both modal depth functions and wavenumbers can be simultaneously extracted via the FRD method;3)the FRD method is not affected by the phenomenon of mode degeneracy.Numerical simulations are conducted in two types of waveguides to verify the FRD method.The impacts of environment configurations and noise levels on the precision of the extracted modal depth functions and wavenumbers are also investigated through simulation.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11434012 and 41561144006)
文摘The spatial correlations of acoustic field have important implications for underwater target detection and other ap- plications in deep water. In this paper, the spatial correlations of the high intensity zone in the deep-water acoustic field are investigated by using the experimental data obtained in the South China Sea. The experimental results show that the structures of the spatial correlation coefficient at different ranges and depths are similar to the transmission loss structure in deep water. The main reason for this phenomenon is analyzed by combining the normal mode theory with the ray theory. It is shown that the received signals in the high intensity zone mainly include one or two main pulses which are contributed by the interference of a group of waterbome modes with similar phases. The horizontal-longitudinal correlations at the same receiver depth but in different high intensity zones are analyzed. At some positions, more pulses are received in the arrival structure of the signal due to bottom reflection and the horizontal-longitudinal correlation coefficient decreases accordingly. The multi-path arrival structure of receiving signal becomes more complex with increasing receiver depth.
基金Project supported by the National Natural Science Foundation of China(Grant No.11174235)the Science and Technology Development Project of Shaanxi Province,China(Grant No.2010KJXX-02)+1 种基金the Science and Technology Innovation Foundation of Northwestern Polytechnical University of Chinathe Doctorate Foundation of Northwestern Polytechnical University,China(Grant No.CX201226)
文摘Understanding the effect of source-receiver geometry on sound propagation in surface ducts can improve the performance of near-surface sonar in deep water. The Lloyd-mirror and normal mode theories are used to analyze the features of surface-duct propagation in this paper. Firstly, according to the Lloyd-mirror theory, a shallow point source generates directional lobes, whose grazing angles are determined by the source depth and frequency. By assuming a part of the first lobe to be just trapped in the surface duct, a method to calculate the minimum cutoff frequency （MCF） is obtained. The presented method is source depth dependent and thus is helpful for determining the working depth for sonar. Secondly, it is found that under certain environments there exists a layer of low transmission loss （TL） in the surface duct, whose thickness is related to the source geometry and can be calculated by the Lloyd-mirror method. The receiver should be placed in this layer to minimize the TL. Finally, the arrival angle on a vertical linear array （VLA） in the surface duct is analyzed based on normal mode theory, which provides a priori knowledge of the beam direction of passive sonar.
