In order to overcome the limitations of traditional microperforated plate with narrow sound absorption bandwidth and a single structure,two multi-cavity composite sound-absorbing materials were designed based on the s...In order to overcome the limitations of traditional microperforated plate with narrow sound absorption bandwidth and a single structure,two multi-cavity composite sound-absorbing materials were designed based on the shape of monoclinic crystals:uniaxial oblique structure(UOS)and biaxial oblique structure(BOS).Through finite element simulation and experimental research,the theoretical models of UOS and BOS were verified,and their sound absorption mechanisms were revealed.At the same time,the influence of multi-cavity composites on sound absorption performance was analyzed based on the theoretical model,and the influence of structural parameters on sound absorption performance was discussed.The research results show that,in the range of 100-2000 Hz,UOS has three sound absorption peaks and BOS has five sound absorption peaks.The frequency range of the half-absorption bandwidth(α>0.5)of UOS and BOS increases by 242% and 229%,respectively.Compared with traditional microperforated sound-absorbing structures,the series and parallel hybrid methods significantly increase the sound-absorbing bandwidth of the sound-absorbing structure.This research has guiding significance for noise control and has broad application prospects in the fields of transportation,construction,and mechanical design.展开更多
Using the plane-wave expansion (PWE)method , the band gaps of the two-dimension phononic crystals composed of square, triangle and honeycomb arrays aluminum cylinders in the air are calculated numerically. The band st...Using the plane-wave expansion (PWE)method , the band gaps of the two-dimension phononic crystals composed of square, triangle and honeycomb arrays aluminum cylinders in the air are calculated numerically. The band structures of three lattices were compared and analyzed. It is concluded that the band-gap of honeycomb lattices is located at lower frequency fields, compared with square and triangle lattices. When the filling fraction is between 0.091 and 0.6046, the honeycomb lattices have larger band gaps and gain an advantage over square and triangle lattices. In addition, the gap map is introduced to illustrate the influences of filling fraction on the number, the relative width and the limit frequency of the band-gap.展开更多
A new ansatz is presentedfor analytic study of the properties of the Holstein model. New analytic resultsfor the polaronic band structure, ground state energy, phonon distribution, hopping probability of electron, and...A new ansatz is presentedfor analytic study of the properties of the Holstein model. New analytic resultsfor the polaronic band structure, ground state energy, phonon distribution, hopping probability of electron, and effectivemasses, of the Holstein molecular crystal model, are given in one dimension. All the analytic results obtained are inaccord with the numerical results completed recently and valid both in the adiabatic and nonadiabatic regimes, andaccurate enough in the region of validity.展开更多
Experiments were performed on the crystallization of a CuSO4 solution upon the action of the temperature gradient with the forming of mono crystals three wedges crystal system （prisms）. We found that the fractal dim...Experiments were performed on the crystallization of a CuSO4 solution upon the action of the temperature gradient with the forming of mono crystals three wedges crystal system （prisms）. We found that the fractal dimension of crystals equals 2.45, which is consistent with the literature data. Crystal growth is represented as the N-rd translation of each side of the crystal lattice with its own speed and with relation to the formation of similar structures--fractals. A mathematical model of ultrasonic crystallization of a CuSO4 solution was proposed. The model is based on the combined use of differential transport equations of momentum, mass, energy and sound waves and a method of similarity and dimensional analysis. The calculated formulas for the concentration of Ccr, the equivalent diameter of the formed crystals dcr and the intensity of internal energy source Ф, associated with the interaction of crystals with the hydro mechanical, heat and sound fields were obtained. Fractal interpretation of ultrasonic crystallization of the CuSO4 solution was made. It was found that on the growth of crystal size d^r directly affects translation N, i.e., an increase in the number of sets of crystals of infinitely small size e, correspond to the size of the crystal lattice. In turn, translation of crystals depends on the geometry of the crystallizer and the physical parameters of external force fields, acting on the CuSO4 solution. A connection of results of the mathematical modeling with the results of fractal analysis of the ultrasonic crystallization of solutions was established.展开更多
This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semi...This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.展开更多
基金Project(52202455)supported by the National Natural Science Foundation of ChinaProject(23A0017)supported by the Key Project of Scientific Research Project of Hunan Provincial Department of Education,China。
文摘In order to overcome the limitations of traditional microperforated plate with narrow sound absorption bandwidth and a single structure,two multi-cavity composite sound-absorbing materials were designed based on the shape of monoclinic crystals:uniaxial oblique structure(UOS)and biaxial oblique structure(BOS).Through finite element simulation and experimental research,the theoretical models of UOS and BOS were verified,and their sound absorption mechanisms were revealed.At the same time,the influence of multi-cavity composites on sound absorption performance was analyzed based on the theoretical model,and the influence of structural parameters on sound absorption performance was discussed.The research results show that,in the range of 100-2000 Hz,UOS has three sound absorption peaks and BOS has five sound absorption peaks.The frequency range of the half-absorption bandwidth(α>0.5)of UOS and BOS increases by 242% and 229%,respectively.Compared with traditional microperforated sound-absorbing structures,the series and parallel hybrid methods significantly increase the sound-absorbing bandwidth of the sound-absorbing structure.This research has guiding significance for noise control and has broad application prospects in the fields of transportation,construction,and mechanical design.
文摘Using the plane-wave expansion (PWE)method , the band gaps of the two-dimension phononic crystals composed of square, triangle and honeycomb arrays aluminum cylinders in the air are calculated numerically. The band structures of three lattices were compared and analyzed. It is concluded that the band-gap of honeycomb lattices is located at lower frequency fields, compared with square and triangle lattices. When the filling fraction is between 0.091 and 0.6046, the honeycomb lattices have larger band gaps and gain an advantage over square and triangle lattices. In addition, the gap map is introduced to illustrate the influences of filling fraction on the number, the relative width and the limit frequency of the band-gap.
文摘A new ansatz is presentedfor analytic study of the properties of the Holstein model. New analytic resultsfor the polaronic band structure, ground state energy, phonon distribution, hopping probability of electron, and effectivemasses, of the Holstein molecular crystal model, are given in one dimension. All the analytic results obtained are inaccord with the numerical results completed recently and valid both in the adiabatic and nonadiabatic regimes, andaccurate enough in the region of validity.
文摘Experiments were performed on the crystallization of a CuSO4 solution upon the action of the temperature gradient with the forming of mono crystals three wedges crystal system （prisms）. We found that the fractal dimension of crystals equals 2.45, which is consistent with the literature data. Crystal growth is represented as the N-rd translation of each side of the crystal lattice with its own speed and with relation to the formation of similar structures--fractals. A mathematical model of ultrasonic crystallization of a CuSO4 solution was proposed. The model is based on the combined use of differential transport equations of momentum, mass, energy and sound waves and a method of similarity and dimensional analysis. The calculated formulas for the concentration of Ccr, the equivalent diameter of the formed crystals dcr and the intensity of internal energy source Ф, associated with the interaction of crystals with the hydro mechanical, heat and sound fields were obtained. Fractal interpretation of ultrasonic crystallization of the CuSO4 solution was made. It was found that on the growth of crystal size d^r directly affects translation N, i.e., an increase in the number of sets of crystals of infinitely small size e, correspond to the size of the crystal lattice. In turn, translation of crystals depends on the geometry of the crystallizer and the physical parameters of external force fields, acting on the CuSO4 solution. A connection of results of the mathematical modeling with the results of fractal analysis of the ultrasonic crystallization of solutions was established.
基金supported by the National Natural Science Foundation of China(Grant Nos.12122205 and 11772119)the Six Talent Peaks Project in Jiangsu Province of China(Grant No.2019-KTHY-009).
文摘This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.
