The concept of two-direction refinable functions and two-direction wavelets is introduced.We investigate the existence of distributional(or L2-stable) solutions of the two-direction refinement equation: φ(x)=∑p+kφ(...The concept of two-direction refinable functions and two-direction wavelets is introduced.We investigate the existence of distributional(or L2-stable) solutions of the two-direction refinement equation: φ(x)=∑p+kφ(mx-k)+∑p-kφ(k-mx) where m ≥ 2 is an integer. Based on the positive mask {pk+} and negative mask {p-k}, the conditions that guarantee the above equation has compactly distributional solutions or L2-stable solutions are established. Furthermore, the condition that the L2-stable solution of the above equation can generate a two-direction MRA is given. The support interval of φ(x) is discussed amply. The definition of orthogonal two-direction refinable function and orthogonal two-direction wavelets is presented, and the orthogonality criteria for two-direction refinable functions are established. An algorithm for constructing orthogonal two-direction refinable functions and their two-direction wavelets is presented. Another construction algorithm for two-direction L2-refinable functions, which have nonnegative symbol masks and possess high approximation order and regularity, is presented. Finally, two construction examples are given.展开更多
Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using ...Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.展开更多
This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. The...This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.展开更多
In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate. Unlike any other theory, the number of unknown functions involve...In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Two common types of functionally graded sandwich plates, namely, the sandwich with fimctionally graded facesheet and homogeneous core and the sandwich with homogeneous facesheet and functionally graded core, are considered. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinu- soidal loading has been obtained by using the Navier method. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded sandwich plates.展开更多
An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties ...An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.展开更多
A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress the...A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).展开更多
目的 探讨基于心理状态评估的精细化护理对突发性耳聋患者的影响。方法 选取厦门大学附属第一医院耳鼻咽喉头颈外科2022年9月—2023年9月收治的90例突发性耳聋患者为研究对象。采取随机数表法分为对照组与观察组,各45例。对照组给予常...目的 探讨基于心理状态评估的精细化护理对突发性耳聋患者的影响。方法 选取厦门大学附属第一医院耳鼻咽喉头颈外科2022年9月—2023年9月收治的90例突发性耳聋患者为研究对象。采取随机数表法分为对照组与观察组,各45例。对照组给予常规心理护理,观察组给予基于心理状态评估的精细化护理。比较2组疾病不确定感量表(uncertainty in illness scale,MUIS)评分、听力功能、汉密尔顿焦虑量表(Hamilton anxiety scale,HAMA)评分、汉密尔顿抑郁量表(Hamilton depression scale,HAMD)评分、匹兹堡睡眠质量指数(Pittsburgh sleep quality index,PSQI)评分、健康调查简表(the MOS item short from health survey,SF-36)评分及满意度评分。结果 护理后,观察组MUIS评分为(34.23±5.47)分,低于对照组的(39.37±5.89)分,差异有统计学意义(P<0.001)。观察组听力功能缺损分贝、纯音气道听阈值分别为(7.06±2.36)d B、(25.76±4.19)dB,均低于对照组的(13.35±3.19)dB、(34.56±4.44)d B,差异有统计学意义(P<0.001)。观察组HAMA、HAMD评分分别为(7.86±2.16)分、(8.26±2.19)分,均低于对照组的(10.35±2.39)分、(11.13±2.24)分,差异有统计学意义(P<0.001)。观察组PSQI评分为(8.83±1.39)分,低于对照组的(11.02±1.55)分,差异有统计学意义(P<0.001)。观察组生理机能、社会功能、生理职能、情感职能、精神健康、精力、健康状况、躯体疼痛评分分别为(84.06±6.36)分、(81.76±6.29)分(、76.86±6.36)分(、79.76±6.79)分(、80.23±6.47)分、(79.57±6.78)分、(81.87±6.25)分、(83.69±6.11)分,均高于对照组的(77.35±6.59)分、(74.56±6.44)分、(71.35±6.19)分、(74.56±6.44)分(、74.37±5.89)分(、74.08±6.47)分(、75.03±6.37)分、(76.84±6.21)分,差异有统计学意义(P<0.001)。观察组护理满意度评分为(92.26±4.34)分,高于对照组的(89.37±4.02)分,差异有统计学意义(P<0.001)。结论 对突发性耳聋患者实施基于心理状态评估的精细化护理可有效减轻患者自身不确定感,改善其听力功能,并能提供更为全面的心理干预措施,有效改善患者心理状态、睡眠质量及生活质量,利于其早期获得康复,进而可取得较高的满意度。展开更多
The four-decade quest for synthesizing ambient-stable polymeric nitrogen,a promising high-energy-density material,remains an unsolved challenge in materials science.We develop a multi-stage computational strategy empl...The four-decade quest for synthesizing ambient-stable polymeric nitrogen,a promising high-energy-density material,remains an unsolved challenge in materials science.We develop a multi-stage computational strategy employing density functional tight-binding-based rapid screening combined with density functional theory refinement and global structure searching,effectively bridging computational efficiency with quantum accuracy.This integrated approach identifies four novel polymeric nitrogen phases(Fddd,P3221,I4m2,and𝑃P6522)that are thermodynamically stable at ambient pressure.Remarkably,the helical𝑃6522 configuration demonstrates exceptional thermal resilience up to 1500 K,representing a predicted polymeric nitrogen structure that maintains stability under both atmospheric pressure and high-temperature extremes.Our methodology establishes a paradigm-shifting framework for the accelerated discovery of metastable energetic materials,resolving critical bottlenecks in theoretical predictions while providing experimentally actionable targets for polymeric nitrogen synthesis.展开更多
基金This work was Supported by the Natural Science Foundation of Guangdong Province (Grant Nos.06105648,05008289,032038)the Doctoral Foundation of Guangdong Province (Grant No.04300917)
文摘The concept of two-direction refinable functions and two-direction wavelets is introduced.We investigate the existence of distributional(or L2-stable) solutions of the two-direction refinement equation: φ(x)=∑p+kφ(mx-k)+∑p-kφ(k-mx) where m ≥ 2 is an integer. Based on the positive mask {pk+} and negative mask {p-k}, the conditions that guarantee the above equation has compactly distributional solutions or L2-stable solutions are established. Furthermore, the condition that the L2-stable solution of the above equation can generate a two-direction MRA is given. The support interval of φ(x) is discussed amply. The definition of orthogonal two-direction refinable function and orthogonal two-direction wavelets is presented, and the orthogonality criteria for two-direction refinable functions are established. An algorithm for constructing orthogonal two-direction refinable functions and their two-direction wavelets is presented. Another construction algorithm for two-direction L2-refinable functions, which have nonnegative symbol masks and possess high approximation order and regularity, is presented. Finally, two construction examples are given.
基金Project supported by the National Natural Science Foundation of China (No.10432030).
文摘Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.
基金supported by the Natural Science Foundation China(11126343)Guangxi Natural Science Foundation(2013GXNSFBA019010)+1 种基金supported by Natural Science Foundation China(11071152)Natural Science Foundation of Guangdong Province(10151503101000025,S2011010004511)
文摘This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2（R^s）. Then, two theorems are given for constructing biorthogonal （orthogonal） two-direction refinable functions in L^2（R^s） and their biorthogonal （orthogonal） two-direction wavelets, respectively. From the constructed biorthogonal （orthogonal） two-direction wavelets, symmetric biorthogonal （orthogonal） multiwaveles in L^2（R^s） can be obtained easily. Applying the projection method to biorthogonal （orthogonal） two-direction wavelets in L^2（R^s）, we can get dual （tight） two-direction wavelet frames in L^2（R^m）, where m ≤ s. From the projected dual （tight） two-direction wavelet frames in L^2（R^m）, symmetric dual （tight） frames in L^2（R^m） can be obtained easily. In the end, an example is given to illustrate theoretical results.
文摘In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Two common types of functionally graded sandwich plates, namely, the sandwich with fimctionally graded facesheet and homogeneous core and the sandwich with homogeneous facesheet and functionally graded core, are considered. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinu- soidal loading has been obtained by using the Navier method. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded sandwich plates.
文摘An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.
基金the National Natural Science Foundation of China(Nos.11602204 and 12102373)the Fundamental Research Funds for the Central Universities of China(Nos.2682022ZTPY081 and 2682022CX056)the Natural Science Foundation of Sichuan Province of China(Nos.2023NSFSC0849,2023NSFSC1300,2022NSFSC1938,and 2022NSFSC2003)。
文摘A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).
文摘目的 探讨基于心理状态评估的精细化护理对突发性耳聋患者的影响。方法 选取厦门大学附属第一医院耳鼻咽喉头颈外科2022年9月—2023年9月收治的90例突发性耳聋患者为研究对象。采取随机数表法分为对照组与观察组,各45例。对照组给予常规心理护理,观察组给予基于心理状态评估的精细化护理。比较2组疾病不确定感量表(uncertainty in illness scale,MUIS)评分、听力功能、汉密尔顿焦虑量表(Hamilton anxiety scale,HAMA)评分、汉密尔顿抑郁量表(Hamilton depression scale,HAMD)评分、匹兹堡睡眠质量指数(Pittsburgh sleep quality index,PSQI)评分、健康调查简表(the MOS item short from health survey,SF-36)评分及满意度评分。结果 护理后,观察组MUIS评分为(34.23±5.47)分,低于对照组的(39.37±5.89)分,差异有统计学意义(P<0.001)。观察组听力功能缺损分贝、纯音气道听阈值分别为(7.06±2.36)d B、(25.76±4.19)dB,均低于对照组的(13.35±3.19)dB、(34.56±4.44)d B,差异有统计学意义(P<0.001)。观察组HAMA、HAMD评分分别为(7.86±2.16)分、(8.26±2.19)分,均低于对照组的(10.35±2.39)分、(11.13±2.24)分,差异有统计学意义(P<0.001)。观察组PSQI评分为(8.83±1.39)分,低于对照组的(11.02±1.55)分,差异有统计学意义(P<0.001)。观察组生理机能、社会功能、生理职能、情感职能、精神健康、精力、健康状况、躯体疼痛评分分别为(84.06±6.36)分、(81.76±6.29)分(、76.86±6.36)分(、79.76±6.79)分(、80.23±6.47)分、(79.57±6.78)分、(81.87±6.25)分、(83.69±6.11)分,均高于对照组的(77.35±6.59)分、(74.56±6.44)分、(71.35±6.19)分、(74.56±6.44)分(、74.37±5.89)分(、74.08±6.47)分(、75.03±6.37)分、(76.84±6.21)分,差异有统计学意义(P<0.001)。观察组护理满意度评分为(92.26±4.34)分,高于对照组的(89.37±4.02)分,差异有统计学意义(P<0.001)。结论 对突发性耳聋患者实施基于心理状态评估的精细化护理可有效减轻患者自身不确定感,改善其听力功能,并能提供更为全面的心理干预措施,有效改善患者心理状态、睡眠质量及生活质量,利于其早期获得康复,进而可取得较高的满意度。
基金supported by the National Natural Science Foundation of China(Grant Nos.11974154,and 12304278)the Taishan Scholars Special Funding for Construction Projects(Grant No.tstp20230622)+1 种基金the Natural Science Foundation of Shandong Province(Grant Nos.ZR2022MA004,ZR2023QA127,and ZR2024QA121)the Special Foundation of Yantai for Leading Talents above Provincial Level。
文摘The four-decade quest for synthesizing ambient-stable polymeric nitrogen,a promising high-energy-density material,remains an unsolved challenge in materials science.We develop a multi-stage computational strategy employing density functional tight-binding-based rapid screening combined with density functional theory refinement and global structure searching,effectively bridging computational efficiency with quantum accuracy.This integrated approach identifies four novel polymeric nitrogen phases(Fddd,P3221,I4m2,and𝑃P6522)that are thermodynamically stable at ambient pressure.Remarkably,the helical𝑃6522 configuration demonstrates exceptional thermal resilience up to 1500 K,representing a predicted polymeric nitrogen structure that maintains stability under both atmospheric pressure and high-temperature extremes.Our methodology establishes a paradigm-shifting framework for the accelerated discovery of metastable energetic materials,resolving critical bottlenecks in theoretical predictions while providing experimentally actionable targets for polymeric nitrogen synthesis.
