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考虑需求弹性的电力-交通网络双层博弈模型——基于拟变分不等式

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中国电机工程学报 2024年第6期44卷 2185-2196,I0008页

作者：谢仕炜陈铠悦张亚超谢龙韬吴秋伟福州大学电气工程与自动化学院福建省福州市350108 清华大学深圳国际研究生院清华-伯克利深圳学院广东省深圳市518055

电动汽车数量的激增势必给城市电网和交通网带来巨大冲击,研究如何准确描述电动汽车行为对电力-交通网络的影响具有重大价值和意义。充分考虑电动汽车需求弹性及其充电行为,并针对问题的复杂性引入拟变分不等式理论来解决耦合网络博弈... 详细信息

电动汽车数量的激增势必给城市电网和交通网带来巨大冲击,研究如何准确描述电动汽车行为对电力-交通网络的影响具有重大价值和意义。充分考虑电动汽车需求弹性及其充电行为,并针对问题的复杂性引入拟变分不等式理论来解决耦合网络博弈行为建模及求解的难题。首先,建立含电动汽车弹性需求和充电行为的混合交通流模型;基于此,提出表征弹性混合交通用户均衡状态的拟变分不等式框架,并证明均衡状态与拟变分不等式的等价性。其次,提出含充电负荷的配电网二阶锥规划模型,并建立电力网和交通网之间的耦合关系。基于此,采用不动点映射的思想将电力-交通耦合网络的作用机理描述为双层博弈问题;针对内、外层博弈问题的特点,分别设计外层不动点迭代算法及内层黏性投影逼近算法,形成求解双层博弈均衡状态的完整方法。最后,仿真基于福州地区测试系统验证建模和求解方法的有效性,表明考虑电动汽车弹性需求行为对耦合网络均衡状态分析的必要性。

关键词：拟变分不等式弹性需求电力-交通耦合网络双层博弈

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随机分布非椭球夹杂压电复合材料变分上下界

力学季刊 2024年第1期45卷 70-87页

作者：王宁谢龙涛宁波大学机械工程与力学学院浙江宁波315211

压电复合材料因其具有高机电耦合系数和压电常数及低密度和高声阻抗,被广泛应用于水声工程、医学和超声检测的领域.人们通过预测压电复合材料有效模量界限可以更好地优化压电复合材料的结构。目前,对于压电复合材料有效模量上下界的研... 详细信息

压电复合材料因其具有高机电耦合系数和压电常数及低密度和高声阻抗,被广泛应用于水声工程、医学和超声检测的领域.人们通过预测压电复合材料有效模量界限可以更好地优化压电复合材料的结构。目前,对于压电复合材料有效模量上下界的研究普遍集中于包含椭球形夹杂的压电复合材料,而对于非椭球形夹杂的压电复合材料研究甚少.本文在传统的Hashin-Shtrikman变分上下界方法的基础上,利用体现夹杂物分布特性及形状的微结构参数,求解横观各向同性压电复合材料有效模量的上下界.该方法适用于任意形状夹杂:当椭球域与椭球形夹杂形状相同时,该方法与传统的压电复合材料Hashi-Shtrikman上下界方法一致.当椭球域与椭球形夹杂物形状不同且夹杂含量较低时,本方法所得到的部分有效模量的上下界更紧凑.此外,本文计算了横观各向同性的压电基体含正方体夹杂的复合材料有效模量上下界,结果表明材料整体表现为横观各向同性且与椭球形夹杂时的有效模量上下界差异较小,本文建立了考虑夹杂物分布和夹杂物形状的压电复合材料上下界的计算方法,对压电复合材料的研究有一定的参考价值。

关键词： Hashin-Shtrikman上下界压电复合材料 Hill张量

Correction Factors of the Approximate Theories for Axisymmetric Modes of Longitudinal Waves in Circular Rods

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Acta Mechanica Solida Sinica 2022年第5期35卷 824-833页

作者： longtao xie Chunlei Bian Ji Wang Piezoelectric Device Laboratory School of Mechanical Engineering and MechanicsNingbo UniversityNingbo315211China TXC-NBU Joint Center of Research School of Mechanical Engineering and MechanicsNingbo UniversityNingbo315211China

The longitudinal waves guided by rods are widely used in broad engineering *** theories are required to improve the understanding of the longitudinal wave propagation in finite rods in *** correction factors are commonly used in the vibration analyses of beams and plates,but are seldom adopted to the longitudinal wave propagation in rods in a similar *** this paper,the longitudinal and radial displacements in axisymmetric problems of circular rods are expanded in infinite power series of the radial *** using Hamilton’s principle,an infinite one-dimensional system of equations of motion is *** high-order components of stress and strain,and their relations are introduced to obtain the infinite one-dimensional system for the axisymmetric wave propagation in elastic rods.A proper truncation of the infinite equations leads to an approximate theory of a specific *** improve the truncated equations,some high-order components of strain are multiplied by the correction *** correction factors for the first-to fourth-order approximations are systematically determined to ensure that the cutoff frequencies are the same as the exact values calculated by the Pochhmammer–Chree *** frequency spectra,via the well-known Pochhmammer–Chree equation and the approximate theories of order one to four,are presented for comparison in a region where the longitudinal wave is not attenuating and the wavelength in the axial direction is longer than the diameter of the *** to the approximate theories without correction factors,the approximate theories with correction factors show some advantages in accuracy when the branches are high.

关键词： Symmetric wave Approximate theory of rods Correction factor Frequency

Variational bounds of the effective moduli of piezoelectric composites

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Science China(Physics,Mechanics & Astronomy) 2012年第11期55卷 2106-2113页

作者： WAN YongPing xie longtao ZHONG Zheng School of Aerospace Engineering and Applied Mechanics Tongji UniversityShanghai 200092China

The classical Hashin-Shtrikman variational principle was re-generalized to the heterogeneous piezoelectric *** auxiliary problem is very much simplified by selecting the reference medium as a linearly isotropic elastic *** electromechanical fields in the inhomogeneous piezoelectrics are simulated by introducing into the homogeneous reference medium certain eigenstresses and eigen electric fields.A closed-form solution can be obtained for the disturbance fields,which is convenient for the manipulation of the energy *** an application,a two-phase piezoelectric composite with nonpiezoelectric matrix is *** of upper and lower bounds for the overall electromechanical moduli of the composite can be *** bounds are shown better than the Voigt-Reuss type ones.

关键词： variational bound piezoelectric composite effective modulus

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压电晶体谐振器非线性厚度拉伸振动研究

机械制造 2024年第6期62卷 24-27,31页

作者：李斌斌谢龙涛宁波大学机械工程与力学学院浙江宁波315211

基于压电理论的三维运动方程和边界条件,能够精确得到描述压电晶体板的振动。由于压电特性、各向异性及非线性,方程非常复杂,解析求解几乎不可能。考虑压电谐振器晶体板的结构特点,以一维无限大压电晶体板为研究对象,分析压电晶体谐振... 详细信息

基于压电理论的三维运动方程和边界条件,能够精确得到描述压电晶体板的振动。由于压电特性、各向异性及非线性,方程非常复杂,解析求解几乎不可能。考虑压电谐振器晶体板的结构特点,以一维无限大压电晶体板为研究对象,分析压电晶体谐振器非线性厚度拉伸振动。针对边界短路的非线性厚度拉伸振动,通过伽辽金法求解微分方程,得到振动振幅、晶体材料高阶弹性常数与非线性频率漂移之间的关系。并且利用解耦方法,通过振动幅值建立恒定电流与频率漂移之间的联系。

关键词：压电晶体谐振器非线性拉伸振动研究

Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales

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Applied Mathematics and Mechanics(English Edition) 2022年第5期43卷 653-666页

作者： Yang ZHENG Bin HUANG Lijun YI Tingfeng MA longtao xie Ji WANG Key Laboratory of Impact and Safety Engineering Ministry of EducationNingbo UniversityNingbo 315211Zhejiang ProvinceChina Piezoelectric Device Laboratory Faculty of Mechanical Engineering&MechanicsNingbo UniversityNingbo 315211Zhejiang ProvinceChina

This paper presents a nonlinear thickness-shear vibration model for onedimensional infinite piezoelectric plate with flexoelectricity and geometric *** constitutive equations with flexoelectricity and governing equations are derived from the Gibbs energy density function and variational *** displacement adopted here is assumed to be antisymmetric through the thickness due to the thickness-shear vibration *** the shear strain gradient through the thickness is considered in the present *** geometric nonlinearity,the governing equations are converted into differential equations as the function of time by the Galerkin *** method of multiple scales is employed to obtain the solution to the nonlinear governing equation with first order *** results show that the nonlinear thickness-shear vibration of piezoelectric plate is size dependent,and the flexoelectric effect has significant influence on the nonlinear thickness-shear vibration frequencies of micro-size thin *** geometric nonlinearity also affects the thickness-shear vibration frequencies *** results show that flexoelectricity and geometric nonlinearity cannot be ignored in design of accurate high-frequency piezoelectric devices.

关键词： thickness-shear vibration piezoelectric plate size effect flexoelectric effect

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

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Theoretical & Applied Mechanics Letters 2020年第2期10卷 120-124页

作者： Ji Wang Shaoyun Wang longtao xie Yangyang Zhang Lili Yuan Jianke Du Han Zhang Piezoelectric Device Laboratory School of Mechanical Engineering and MechanicsNingbo UniversityNingbo315211 ZhejiangChina Noise and Vibration Laboratory Institute of AcousticsChinese Academy of Sciences100190 BeijingChina

It is well-known that Rayleigh wave,also known as surface acoustic wave(SAW),solutions in semiinfinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the *** of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation.A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical *** is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius,confirming the existence of surface acoustic waves is irrelevant to coordinate *** the other hand,the solutions can be treated as plane waves in regions far away from the ***,the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.

关键词： Axisymmetric Rayleigh wave Solid Propagation Velocity

Analysis of Vibration Frequencies of Piezoelectric Ceramic Rings as Ultrasonic Transducers in Welding of Facial Mask Production

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Transactions of Nanjing University of Aeronautics and Astronautics 2021年第1期38卷 124-131页

作者： WU Jinghui ZHAO Shengquan xie longtao WANG Ji Piezoelectric Device Laboratory School of Mechanical Engineering&MechanicsNingbo UniversityNingbo 315211P.R.China

The explosive demands for facial masks as vital personal protection equipment(PPE)in the wake of Covid-19 have challenged many industries and enterprises in technology and capacity,and the piezoelectric ceramic(PZT)transducers for the production of facial masks in the welding process are in heavy *** the earlier days of the epidemic,the supply of ceramic transducers cannot meet its increasing demands,and efforts in materials,development,and production are mobilized to provide the transducers to mask producers for quick *** simplest solution is presented with the employment of Rayleigh-Ritz method for the vibration analysis,then different materials can be selected to achieve the required frequency and energy *** fully tailored method and results can be utilized by the engineers for quick development of the PZT transducers to perform precise function in welding.

关键词： piezoelectric ceramic(PZT) transducer facial mask welding personal protection equipment(PPE)

基于GIS的农田土壤重金属空间分布及污染评价——以南京市江宁区某乡镇为例

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土壤学报 2020年第2期57卷 316-325页

作者：谢龙涛潘剑君白浩然张培育康翔王飞朱燕香南京农业大学资源与环境科学学院南京210095 南京农业大学公共管理学院南京210095

土壤污染近年来备受瞩目,我国已出台多项法律法规来规范防治,合理评价不同地区土壤重金属的污染情况,具有现实和长远意义。2017年11—12月在研究区采集的29个表层土壤(0~20 cm),分析测定土壤pH、有机质和8种重金属元素砷(As)、镉(Cd)、... 详细信息

土壤污染近年来备受瞩目,我国已出台多项法律法规来规范防治,合理评价不同地区土壤重金属的污染情况,具有现实和长远意义。2017年11—12月在研究区采集的29个表层土壤(0~20 cm),分析测定土壤pH、有机质和8种重金属元素砷(As)、镉(Cd)、铬(Cr)、铜(Cu)、汞(Hg)、镍(Ni)、铅(Pb)和锌(Zn)的含量,采用最新发布的《土壤环境质量—农用地土壤污染风险管控标准(试行)》(GB 15618-2018)进行污染评价,运用GIS地统计学方法分析重金属空间分布特征。结果表明,研究区土壤pH呈现酸性至中性;有机质平均含量为17.73 mg·kg–1,较为缺乏;8种重金属元素(As、Cd、Cr、Cu、Hg、Ni、Pb、Zn)的平均含量分别为8.27、0.17、70.84、24.74、0.20、32.07、28.48和73.57 mg·kg–1,除As外,其他重金属含量均超过南京市江宁区土壤环境背景值,但未超过国家现行标准,总体无重金属污染。其中Cd、Cu和Hg元素在局部地区达到了警戒线,风险区主要分布在西南部和南部,呈现带状分布,农业生产上需引起重视。

关键词： GIS 土壤重金属表层土壤空间分布污染评价