In order to forecast the distribution of crest amplitudes and the occurrence of freak waves in a short crested coastal sea,a novel transformed linear simulation method is initially proposed in this paper.A Hermite tra...In order to forecast the distribution of crest amplitudes and the occurrence of freak waves in a short crested coastal sea,a novel transformed linear simulation method is initially proposed in this paper.A Hermite transformation model expressed as a monotonic cubic polynomial serves as the foundation for the novel simulation technique.The wave crest amplitude exceedance probabilities of two sea states-one with a directional wave spectrum based on the measured wave elevation data at the Yura coast and the other with a typical directional JONSWAP wave spectrum-have been predicted using the novel simulation method that has been proposed.The likelihood that a particular critical wave crest amplitude will be exceeded is directly correlated with the probability that freak waves will occur.It is shown that the novel simulation approach suggested can provide predictions that are more precise than those obtained from the Rayleigh crest amplitude distribution model,the Jahns and Wheeler crest amplitude distribution model,or the conventional linear simulation method.This study also demonstrated that the nonlinear simulation method is less effective than the novel simulation method in terms of efficiency.展开更多
In this paper,layered periodic foundations(LPFs)are numerically examined for their responses to longitudinal and transverse modes in the time and frequency domains.Three different unit-cells,i.e.,2-layer,4-layer,and 6...In this paper,layered periodic foundations(LPFs)are numerically examined for their responses to longitudinal and transverse modes in the time and frequency domains.Three different unit-cells,i.e.,2-layer,4-layer,and 6-layer unit-cells,comprising concrete/rubber,concrete/rubber/steel/rubber,and concrete/rubber/steel/rubber/lead/rubber materials,respectively,are taken into account.Also,the viscoelasticity behavior of the rubber is modeled with two factors,i.e.,a frequency-independent(FI)loss factor and a linear frequency-dependent(FD)loss factor.Following the extraction of the complex dispersion curves and the identification of the band gaps(BGs),the simulations of wave transmission in the time and frequency domains are performed using the COMSOL software.Subsequent parametric studies evaluate the effects of the rubber viscoelasticity models on the dispersion curves and the wave transmission for the longitudinal and transverse modes.The results show that considering the rubber viscoelasticity enhances the wave attenuation performance.Moreover,the transverse-mode damping is more sensitive to the viscoelasticity model than its longitudinal counterpart.The 6-layer unit-cell LPF exhibits the lowest BG,ranging from 4.8 Hz to 6.5 Hz.展开更多
In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed.We assume that the free surface is almost periodic in the horizontal dir...In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed.We assume that the free surface is almost periodic in the horizontal direction.Using conformal mappings,one can change the free boundary problem into a fixed boundary problem for some unknown functions with the boundary condition.By virtue of the Hilbert transform,the problem is equivalent to a quasilinear pseudodifferential equation for an almost periodic function of one variable.The bifurcation theory ensures that we can obtain an existence result.Our existence result generalizes and covers the recent result in[15].Moreover,our result implies a non-uniqueness result at the same bifurcation point.展开更多
The chaotic oscillator has already been considered as a powerful method to detect weak signals, even weak signals accompanied with noises. However, many examples, analyses and simulations indicate that chaotic oscilla...The chaotic oscillator has already been considered as a powerful method to detect weak signals, even weak signals accompanied with noises. However, many examples, analyses and simulations indicate that chaotic oscillator detection system cannot guarantee the immunity to noises (even white noise). In fact the randomness of noises has a serious or even a destructive effect on the detection results in many cases. To solve this problem, we present a new detecting method based on wavelet threshold processing that can detect the chaotic weak signal accompanied with noise. All theoretical analyses and simulation experiments indicate that the new method reduces the noise interferences to detection significantly, thereby making the corresponding chaotic oscillator that detects the weak signals accompanied with noises more stable and reliable.展开更多
A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics ...A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β.展开更多
A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element...A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.展开更多
With the launch of altimeter,much effort has been made to develop algorithms on the wind speed and the wave period.By using a large data set of collocated altimeter and buoy measurements,the typical wind speed and wav...With the launch of altimeter,much effort has been made to develop algorithms on the wind speed and the wave period.By using a large data set of collocated altimeter and buoy measurements,the typical wind speed and wave period algorithms are validated.Based on theoretical argument and the concept of wave age,a semi-empirical algorithm for the wave period is also proposed,which has the wave-period dimension,and explicitly demonstrates the relationships between the wave period and the other variables.It is found that Ku and C band data should be applied simultaneously in order to improve either wind speed or wave period algorithms.The dual-band algorithms proposed by Chen et al.(2002) for the wind speed and Quilfen et al.(2004) for the wave period perform best in terms of a root mean square error in the practical applications.展开更多
An oblique detonation wave for a Mach 7 inlet flow over a long enough wedge of 30 turning angle is simulated numerically using Euler equation and one-step rection model.The fifth-order WENO scheme is adopted to captur...An oblique detonation wave for a Mach 7 inlet flow over a long enough wedge of 30 turning angle is simulated numerically using Euler equation and one-step rection model.The fifth-order WENO scheme is adopted to capture the shock wave.The numerical results show that with the compression of the wedge wall the detonation wave front structure is divided into three sections:the ZND model-like strcuture,single-sided triple point structure and dual-headed triple point strucuture.The first structure is the smooth straight,and the second has the characteristic of the triple points propagating dowanstream only with the same velocity,while the dual-headed triple point structure is very complicated.The detonation waves facing upstream and downstream propagate with different velocities,in which the periodic collisions of the triple points cause the oscillation of the detonation wave front.This oscillation process has temporal and spatial periodicity.In addition,the triple point trace are recorded to obtain different cell structures in three sections.展开更多
The joint distribution of wave heights and periods of individual waves is usually approximated by the joint distribution of apparent wave heights and periods. However there is difference between them. This difference ...The joint distribution of wave heights and periods of individual waves is usually approximated by the joint distribution of apparent wave heights and periods. However there is difference between them. This difference is addressed and the theoretical joint distributions of apparent wave heights and periods due to Longuet-Higgins and Sun are modified to give more reasonable representations of the joint distribution of wave heights and periods of individual waves. The modification has overcome an inherent drawback of these joint PDFs that the mean wave period is infinite. A comparison is made between the modified formulae and the field data of Goda, which shows that the new formulae consist with the measurement better than their original counterparts.展开更多
This paper is concerned with the dynamic behaviors of wave propagation in layered periodic composites consisting of piezoelectric and piezomagnetic phases. The dispersion relations of Lamb waves axe derived. Dispersio...This paper is concerned with the dynamic behaviors of wave propagation in layered periodic composites consisting of piezoelectric and piezomagnetic phases. The dispersion relations of Lamb waves axe derived. Dispersion curves and displacement fields are calculated with different piezoelectric volume fractions. Numerical results for BaTiO3/CoFe2O4 composites show that the dispersion curves resemble the symmetric Lamb waves in a plate. Exchange between the longitudinal (i.e. thickness) mode and coupled mode takes place at the crossover point between dispersion curves of the first two branches. With the increase of BaTiO3 volume fraction, the crossover point appears at a lower wave number and wave velocity is higher. These findings are useful for magnetoelectric transducer applications.展开更多
This paper investigates shear horizontal (SH) waves propagating in a periodically layered structure that consists of piezoelectric (PE) layers perfectly bonded with piezomagnetic (PM) layers alternately. The exp...This paper investigates shear horizontal (SH) waves propagating in a periodically layered structure that consists of piezoelectric (PE) layers perfectly bonded with piezomagnetic (PM) layers alternately. The explicit dispersion relations are derived for the two cases when the propagation directions of SH waves are normal to the interface and parallel to the interface, respectively. The asymptotic expressions for dispersion relations are also given when the wave number is extremely small. Numerical results for stop band effect and phase velocity are presented for a periodic system of alternating BaTiO3 and Terfenol-D layers. The influence of volume fraction on stop band effect and dispersion behaviors is discussed and revealed.展开更多
The South China Sea (SCS), in particular the northern SCS, is one of ocean areas where energetic internal solitary waves (ISWs)occur most frequently (Cai et al., 2012; Zheng, 2017). Based on the re-appearance pe...The South China Sea (SCS), in particular the northern SCS, is one of ocean areas where energetic internal solitary waves (ISWs)occur most frequently (Cai et al., 2012; Zheng, 2017). Based on the re-appearance period (RP) at an observation station, Ramp et al.(2004) divided the ISWs into two types:Type-a and Type-b. Type-a ISWs arrive regularly at the same time every day, i.e., the RP is about 24 h, and Type-b ISWs arrive about one hour late every day, i.e., the RP is about 25 h.展开更多
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are...In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.展开更多
This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu +uxx = uv + |u|^2u, vtt-vxx=(|u|^2)xx.First, we prove the existence of a smooth c...This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu +uxx = uv + |u|^2u, vtt-vxx=(|u|^2)xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].展开更多
A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element...A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.展开更多
In this study we have for the first time proposed a novel transformed linear simulation method for the estimation of wave crest amplitudes distribution and freak wave occurrence in a short crested mixed sea with a bim...In this study we have for the first time proposed a novel transformed linear simulation method for the estimation of wave crest amplitudes distribution and freak wave occurrence in a short crested mixed sea with a bimodal 3D spectrum. For implementing the proposed transformed linear simulation method, a Hermite transformation model expressed in a monotonic cubic polynomial has been constructed so that the first four moments of the original true process match the corresponding moments of the transformed model. The proposed novel simulation method has been applied to forecast the freak wave occurrence in two short crested mixed sea states, one with a directional wave spectrum based on the measured surface elevation data at the coast of Yura, and the other one with a typical directional bimodal Torsethaugen wave spectrum. It is shown in the two cases that the proposed novel simulation method can offer more accurate forecasting results than those obtained from the traditional linear simulation method or by using Rayleigh distribution model. It is also demonstrated in this article that the proposed novel simulation method is more efficient than the nonlinear simulation method.展开更多
The elastic wave propagation phenomena in two-dimensional periodic beam lattices are studied by using the Bloch wave transform. The numerical modeling is applied to the hexagonal and the rectangular beam lattices, in ...The elastic wave propagation phenomena in two-dimensional periodic beam lattices are studied by using the Bloch wave transform. The numerical modeling is applied to the hexagonal and the rectangular beam lattices, in which, both the in-plane (with respect to the lattice plane) and out-of-plane waves are considered. The dispersion relations are obtained by calculating the Bloch eigenfrequencies and eigenmodes. The frequency bandgaps are observed and the influence of the elastic and geometric properties of the primitive cell on the bandgaps is studied. By analyzing the phase and the group velocities of the Bloch wave modes, the anisotropic behaviors and the dispersive characteristics of the hexagonal beam lattice with respect to the wave prop- agation are highlighted in high frequency domains. One im- portant result presented herein is the comparison between the first Bloch wave modes to the membrane and bend- ing/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the hexagonal beam lattice. It is shown that, in low frequency ranges, the homog- enized plate model can correctly represent both the in-plane and out-of-plane dynamic behaviors of the beam lattice, its frequency validity domain can be precisely evaluated thanks to the Bloch modal analysis. As another important and original result, we have highlighted the existence of the retro- propagating Bloch wave modes with a negative group veloc- ity, and of the corresponding "retro-propagating" frequency bands.展开更多
A general solution, including three arbitrary functions, is obtained for a (2~l)-dimensional modified dispersive water-wave (MDWW) equation by means of the WTC truncation method. Introducing proper multiple valued...A general solution, including three arbitrary functions, is obtained for a (2~l)-dimensional modified dispersive water-wave (MDWW) equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.展开更多
We extend the multiple-scattering theory (MST) for elastic wave scattering and propagating in two-dimensional composite. The formalism for the band structure calculation is presented by taking into account the full ve...We extend the multiple-scattering theory (MST) for elastic wave scattering and propagating in two-dimensional composite. The formalism for the band structure calculation is presented by taking into account the full vector character of the elastic wave. As a demonstration of application of the formalism we calculate the band structure of elastic wave propagating in a two-dimensional periodic arrangement of cylinders. The results manifest that the MST shows great promise in complementing the plane-wave (PW) approach for the study of elastic wave.展开更多
The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear d...The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.展开更多
基金financially supported by the Chinese State Key Laboratory of Ocean Engineering(Grant No.GKZD010068/084).
文摘In order to forecast the distribution of crest amplitudes and the occurrence of freak waves in a short crested coastal sea,a novel transformed linear simulation method is initially proposed in this paper.A Hermite transformation model expressed as a monotonic cubic polynomial serves as the foundation for the novel simulation technique.The wave crest amplitude exceedance probabilities of two sea states-one with a directional wave spectrum based on the measured wave elevation data at the Yura coast and the other with a typical directional JONSWAP wave spectrum-have been predicted using the novel simulation method that has been proposed.The likelihood that a particular critical wave crest amplitude will be exceeded is directly correlated with the probability that freak waves will occur.It is shown that the novel simulation approach suggested can provide predictions that are more precise than those obtained from the Rayleigh crest amplitude distribution model,the Jahns and Wheeler crest amplitude distribution model,or the conventional linear simulation method.This study also demonstrated that the nonlinear simulation method is less effective than the novel simulation method in terms of efficiency.
文摘In this paper,layered periodic foundations(LPFs)are numerically examined for their responses to longitudinal and transverse modes in the time and frequency domains.Three different unit-cells,i.e.,2-layer,4-layer,and 6-layer unit-cells,comprising concrete/rubber,concrete/rubber/steel/rubber,and concrete/rubber/steel/rubber/lead/rubber materials,respectively,are taken into account.Also,the viscoelasticity behavior of the rubber is modeled with two factors,i.e.,a frequency-independent(FI)loss factor and a linear frequency-dependent(FD)loss factor.Following the extraction of the complex dispersion curves and the identification of the band gaps(BGs),the simulations of wave transmission in the time and frequency domains are performed using the COMSOL software.Subsequent parametric studies evaluate the effects of the rubber viscoelasticity models on the dispersion curves and the wave transmission for the longitudinal and transverse modes.The results show that considering the rubber viscoelasticity enhances the wave attenuation performance.Moreover,the transverse-mode damping is more sensitive to the viscoelasticity model than its longitudinal counterpart.The 6-layer unit-cell LPF exhibits the lowest BG,ranging from 4.8 Hz to 6.5 Hz.
基金partially the National Key R&D Program of China(2021YFA1002100)the NSFC(12171493,11701586)+2 种基金the FDCT(0091/2018/A3)the Guangdong Special Support Program(8-2015)the Key Project of NSF of Guangdong Province(2021A1515010296)。
文摘In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed.We assume that the free surface is almost periodic in the horizontal direction.Using conformal mappings,one can change the free boundary problem into a fixed boundary problem for some unknown functions with the boundary condition.By virtue of the Hilbert transform,the problem is equivalent to a quasilinear pseudodifferential equation for an almost periodic function of one variable.The bifurcation theory ensures that we can obtain an existence result.Our existence result generalizes and covers the recent result in[15].Moreover,our result implies a non-uniqueness result at the same bifurcation point.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10731050)the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (Grant No. IRTO0742)
文摘The chaotic oscillator has already been considered as a powerful method to detect weak signals, even weak signals accompanied with noises. However, many examples, analyses and simulations indicate that chaotic oscillator detection system cannot guarantee the immunity to noises (even white noise). In fact the randomness of noises has a serious or even a destructive effect on the detection results in many cases. To solve this problem, we present a new detecting method based on wavelet threshold processing that can detect the chaotic weak signal accompanied with noise. All theoretical analyses and simulation experiments indicate that the new method reduces the noise interferences to detection significantly, thereby making the corresponding chaotic oscillator that detects the weak signals accompanied with noises more stable and reliable.
文摘A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β.
基金Project supported by the National Basic Research Program of China (973Project) (No.2002CB412709) and the National Natural Science Foundation of China (Nos.50278012,10272027,19832010)
文摘A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.
基金The National Natural Science Foundation of China under contract Nos 41076007 and 40676014the National Basic Research Program of China under contract No. 2009CB421201the Program of Introducing Talents of Discipline to Universities of China under contract No. B07036
文摘With the launch of altimeter,much effort has been made to develop algorithms on the wind speed and the wave period.By using a large data set of collocated altimeter and buoy measurements,the typical wind speed and wave period algorithms are validated.Based on theoretical argument and the concept of wave age,a semi-empirical algorithm for the wave period is also proposed,which has the wave-period dimension,and explicitly demonstrates the relationships between the wave period and the other variables.It is found that Ku and C band data should be applied simultaneously in order to improve either wind speed or wave period algorithms.The dual-band algorithms proposed by Chen et al.(2002) for the wind speed and Quilfen et al.(2004) for the wave period perform best in terms of a root mean square error in the practical applications.
基金supported by the National Natural Science Foundation of China (10872096)the Open Fund of State Key Laboratory of Explosion Science and Technology,Beijing Institute of Technology (KFJJ09-13)
文摘An oblique detonation wave for a Mach 7 inlet flow over a long enough wedge of 30 turning angle is simulated numerically using Euler equation and one-step rection model.The fifth-order WENO scheme is adopted to capture the shock wave.The numerical results show that with the compression of the wedge wall the detonation wave front structure is divided into three sections:the ZND model-like strcuture,single-sided triple point structure and dual-headed triple point strucuture.The first structure is the smooth straight,and the second has the characteristic of the triple points propagating dowanstream only with the same velocity,while the dual-headed triple point structure is very complicated.The detonation waves facing upstream and downstream propagate with different velocities,in which the periodic collisions of the triple points cause the oscillation of the detonation wave front.This oscillation process has temporal and spatial periodicity.In addition,the triple point trace are recorded to obtain different cell structures in three sections.
文摘The joint distribution of wave heights and periods of individual waves is usually approximated by the joint distribution of apparent wave heights and periods. However there is difference between them. This difference is addressed and the theoretical joint distributions of apparent wave heights and periods due to Longuet-Higgins and Sun are modified to give more reasonable representations of the joint distribution of wave heights and periods of individual waves. The modification has overcome an inherent drawback of these joint PDFs that the mean wave period is infinite. A comparison is made between the modified formulae and the field data of Goda, which shows that the new formulae consist with the measurement better than their original counterparts.
基金supported by the National Natural Science Foundation of China(Nos.10672108 and 10632020)the key project of the Ministry of Education of China(No.206014).
文摘This paper is concerned with the dynamic behaviors of wave propagation in layered periodic composites consisting of piezoelectric and piezomagnetic phases. The dispersion relations of Lamb waves axe derived. Dispersion curves and displacement fields are calculated with different piezoelectric volume fractions. Numerical results for BaTiO3/CoFe2O4 composites show that the dispersion curves resemble the symmetric Lamb waves in a plate. Exchange between the longitudinal (i.e. thickness) mode and coupled mode takes place at the crossover point between dispersion curves of the first two branches. With the increase of BaTiO3 volume fraction, the crossover point appears at a lower wave number and wave velocity is higher. These findings are useful for magnetoelectric transducer applications.
基金supported by the National Natural Science Foundation of China (Nos.10672108,10572069 and 10820101048)
文摘This paper investigates shear horizontal (SH) waves propagating in a periodically layered structure that consists of piezoelectric (PE) layers perfectly bonded with piezomagnetic (PM) layers alternately. The explicit dispersion relations are derived for the two cases when the propagation directions of SH waves are normal to the interface and parallel to the interface, respectively. The asymptotic expressions for dispersion relations are also given when the wave number is extremely small. Numerical results for stop band effect and phase velocity are presented for a periodic system of alternating BaTiO3 and Terfenol-D layers. The influence of volume fraction on stop band effect and dispersion behaviors is discussed and revealed.
基金The National Science and Technology Major Project of China under contract No.2016ZX05057015the National Natural Science Foundation of China under contract Nos 41376038 and 40406009+3 种基金the NSFC-Shandong Joint Fund for Marine Science Research Centers of China under contract No.U1606405the National Program on Global Change and Air-Sea Interaction of China under contract Nos GASI-03-01-01-02,GASI-02-IND-STSsum and GASI-IPOVAI-01-05the Public Science and Technology Research Funds Projects of Ocean of China under contract No.200905024the National Key Scientific Instrument and Equipment Development Projects of China under contract No.2012YQ12003908
文摘The South China Sea (SCS), in particular the northern SCS, is one of ocean areas where energetic internal solitary waves (ISWs)occur most frequently (Cai et al., 2012; Zheng, 2017). Based on the re-appearance period (RP) at an observation station, Ramp et al.(2004) divided the ISWs into two types:Type-a and Type-b. Type-a ISWs arrive regularly at the same time every day, i.e., the RP is about 24 h, and Type-b ISWs arrive about one hour late every day, i.e., the RP is about 25 h.
基金Project supported by the Anhui Key Laboratory of Information Materials and Devices (Anhui University),China
文摘In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.
基金supported by the National Natural Science Foundation of China(11401122)Science and technology project of Qufu Normal University(xkj201607)
文摘This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations {iu +uxx = uv + |u|^2u, vtt-vxx=(|u|^2)xx.First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of [15, 16, 19].
文摘A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency.
基金financially supported by the funding of an independent research project from the Chinese State Key Laboratory of Ocean Engineering(Grant No.GKZD010068/084)
文摘In this study we have for the first time proposed a novel transformed linear simulation method for the estimation of wave crest amplitudes distribution and freak wave occurrence in a short crested mixed sea with a bimodal 3D spectrum. For implementing the proposed transformed linear simulation method, a Hermite transformation model expressed in a monotonic cubic polynomial has been constructed so that the first four moments of the original true process match the corresponding moments of the transformed model. The proposed novel simulation method has been applied to forecast the freak wave occurrence in two short crested mixed sea states, one with a directional wave spectrum based on the measured surface elevation data at the coast of Yura, and the other one with a typical directional bimodal Torsethaugen wave spectrum. It is shown in the two cases that the proposed novel simulation method can offer more accurate forecasting results than those obtained from the traditional linear simulation method or by using Rayleigh distribution model. It is also demonstrated in this article that the proposed novel simulation method is more efficient than the nonlinear simulation method.
文摘The elastic wave propagation phenomena in two-dimensional periodic beam lattices are studied by using the Bloch wave transform. The numerical modeling is applied to the hexagonal and the rectangular beam lattices, in which, both the in-plane (with respect to the lattice plane) and out-of-plane waves are considered. The dispersion relations are obtained by calculating the Bloch eigenfrequencies and eigenmodes. The frequency bandgaps are observed and the influence of the elastic and geometric properties of the primitive cell on the bandgaps is studied. By analyzing the phase and the group velocities of the Bloch wave modes, the anisotropic behaviors and the dispersive characteristics of the hexagonal beam lattice with respect to the wave prop- agation are highlighted in high frequency domains. One im- portant result presented herein is the comparison between the first Bloch wave modes to the membrane and bend- ing/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the hexagonal beam lattice. It is shown that, in low frequency ranges, the homog- enized plate model can correctly represent both the in-plane and out-of-plane dynamic behaviors of the beam lattice, its frequency validity domain can be precisely evaluated thanks to the Bloch modal analysis. As another important and original result, we have highlighted the existence of the retro- propagating Bloch wave modes with a negative group veloc- ity, and of the corresponding "retro-propagating" frequency bands.
基金supported in part by National Natural Science Foundation of China (Grant No 10772110)
文摘A general solution, including three arbitrary functions, is obtained for a (2~l)-dimensional modified dispersive water-wave (MDWW) equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.
文摘We extend the multiple-scattering theory (MST) for elastic wave scattering and propagating in two-dimensional composite. The formalism for the band structure calculation is presented by taking into account the full vector character of the elastic wave. As a demonstration of application of the formalism we calculate the band structure of elastic wave propagating in a two-dimensional periodic arrangement of cylinders. The results manifest that the MST shows great promise in complementing the plane-wave (PW) approach for the study of elastic wave.
基金Project supported by the National Natural Science Foundation of China (Nos. 10972182,10772147,and 10632030)the National Basic Research Program of China (No. 2006CB 601202)+4 种基金the National 111 Project of China (No. B07050)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (No. GZ0802)the Doctoral Foundation of Northwestern Polytechnical University (No. CX200908)the China Postdoctoral Science Foundation (No. 20090450170)the Northwestern Polytechnical University Foundation for Fundamental Research (No. JC200938)
文摘The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.