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natural frequency analysis of laminated piezoelectric beams with arbitrary polarization directions

Applied Mathematics and Mechanics(English Edition) 2024年第11期45卷 1949-1964页

作者： Zhi LI Cuiying FAN Mingkai GUO Guoshuai QIN Chunsheng LU Dongying LIU Minghao ZHAO School of Mechanics and Safety Engineering Zhengzhou UniversityZhengzhou450001China School of Electromechanical Engineering Henan University of TechnologyZhengzhou450001China School of Civil and Mechanical Engineering Curtin UniversityPerthWestern Australia6845Australia School of Civil Engineering Guangzhou UniversityGuangzhou510006China Henan Province Industrial Science&Technology Institute for Anti-fatigue Manufacturing Zhengzhou450001China Henan Province Engineering Research Center of Anti-fatigue Manufacturing Technology Zhengzhou450001China

Piezoelectric devices exhibit unique properties that vary with different vibration modes,closely influenced by their polarization *** paper presents an analysis on the free vibration of laminated piezoelectric beams with varying polarization directions,using a state-space-based differential quadrature ***,based on the electro-elasticity theory,the state-space method is extended to anisotropic piezoelectric materials,establishing state-space equations for arbitrary polarized piezoelectric beams.A semi-analytical solution for the natural frequency is then obtained via the differential quadrature *** study commences by examining the impact of a uniform polarization direction,and then proceeds to analyze six polarization schemes relevant to the current research and ***,the effects of geometric dimensions and gradient index on the natural frequencies are *** numerical results demonstrate that varying the polarization direction can significantly influence the natural frequencies,offering distinct advantages for piezoelectric elements with different *** research provides both theoretical insights and numerical methods for the structural design of piezoelectric devices.

关键词： piezoelectric laminated beam free vibration arbitrary polarization state-space equation differential quadrature method natural frequency

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natural frequency of tapered high pier considering pile-soil interaction

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Journal of Central South University 2010年第3期17卷 635-641页

作者：赵明华杨晶杨明辉 Geotechnical Engineering Institute Hunan University

In seismic design of tapered high pier, the analysis of natural vibration frequency is of great importance. According to the engineering features of tapered high pier in mountainous area, a vibration calculation model was set up considering the tapered pier characteristics and pile-soil interaction. Based on Southwell frequency composition theory, it consists of elastic deformation of bridge pier and the rigid deformation of group piles, which are respectively solved by the finite-element method and energy method, and then the natural frequency is derived. The comparison between the measured and calculated results shows that the calculation errors with and without considering pile-soil interaction are 4.9% and 14.7%, respectively. Additionally, the main parameters (pier height, section variation coefficient and lateral foundation horizontal proportional coefficient) affecting natural frequency were investigated. The result shows that natural frequency ascends with the increase of the lateral foundation horizontal proportional coefficient; and it is quite necessary to consider the pile-soil interaction in natural frequency calculation of tapered high pier.

关键词： tapered pier natural frequency energy method finite-element method Southwell frequency composition theory

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natural frequency FOR RECTANGULAR ORTHOTROPIC CORRUGATED-CORE SANDWICH PLATES WITH ALL EDGES SIMPLY-SUPPORTED

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Applied Mathematics and Mechanics(English Edition) 2001年第9期22卷 1019-1027页

作者： WU Hui(吴晖) YU Huan-ran(俞焕然) Department of Mechanics Lanzhou University Lanzhou 730000 P R China Department of Mechanics Lanzhou University Lanzhou 730000 P R China

A simple approach to reduce the governing equations for orthotropic corrugated core sandwich plates to a single equation containing only one displacement function is presented, and the exact solution of the natural frequencies for rectangular corrugated-core sandwich plates with all edges simply-supported is obtained. Furthermore, two special cases of practical interests are discussed in details.

关键词： rectangular sandwich plates corrugated-core orthotropic natural frequency displacement functional exact solution

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natural frequency OF COMPONENT UNDER INFLUENCE OF WELDING RESIDUAL STRESS

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Transactions of Nonferrous Metals Society of China 1996年第1期6卷 135-140页

作者： Gao Yongyi Lin Lichuan Department of Physics Xiangtan Teacher's CollegeXiangtan 411100 Central South Univesity of Technology Changsha 410083

According to the distribution feature of welding residual stress on plate with welding seam along axis,a mathematical model of the welding residual stress is established.A formula of natural frequency of four boundary simply-supported quadrate thin plate with welding residual stress is *** conclusions have been *** are:(1)if there is welding residual stress,all natural frequencies of component are in increase,(2)change of high rank natural frequency under the influence of residual stress is larger than that of low rank natural frequency,and the higher the rank number is the larger the absolute amount of change of natural frequency is.

关键词： mathematical model residual stress natural frequency welding quadrate thin plate

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natural frequency of Full-Prestressed Concrete Beam

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Transactions of Tianjin University 2007年第5期13卷 354-359页

作者：张耀庭李瑞鸽 School of Civil Engineering and Mechanics Huazhong University of Science and Technology Civil Engineering Department Pingdingshan Institute of TechnologyPingdingshan 467001China

Dynamic tests of three bonded and two unbonded full-prestressed concrete beams were carried *** purpose was to seek the relation between prestressing force and natural *** results indicate that the frequency of prestressed concrete(PSC)beam increases with the increase in prestressing force *** results are different from the dynamic characteristics of isotropic material beam subjected to compressive axial force which were put forward by Clough et *** reason is that the beams were considered as isotropic,homogeneous,linear elastic material in the traditional analysis ***,more accurate results are required in the analysis of frequency of PSC *** constitutive mode of PSC member is analyzed based on microstructure of concrete in this *** orthotropic linear elastic mode is used to analyze the relation between dynamic frequency and prestressing force of concrete beam,at the same time the equivalent stiffness of prestressed tendon relating to the prestressing force is added to the bending deformation stiffness of the *** analytical value agrees well with the test result,indicating that the current analysis method in this paper is feasible to full-prestressed concrete beam.

关键词： full-prestressed concrete beam prestressing force natural frequency anisotropic material

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Applications of different criteria in structural damage identification based on natural frequency and static displacement

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Science China(Technological Sciences) 2016年第11期59卷 1746-1758页

作者： YANG Chen HOU XinBin WANG Li ZHANG XingHua Qian Xuesen Laboratory of Space Technology China Academy of Space Technology

This paper presents a damage identification method that consists of a fusion sensitivity matrix that contains information on dynamic and static responses. Based on natural frequency and static displacement, the study defines and considers damage criteria such as 1D and 2D single and fusion load cases. To overcome the lack of sufficient information on damage identification in large-scale structures, the authors consider multiple responses to and objective descriptions of uncertainties and various *** to the finite element model and the structural responses described and measured, the fusion methods and damage criteria treat uncertainty as non-probability intervals. As long as we know the bounds of uncertain parameters, the intervals of the elemental stiffness parameters in undamaged and damaged models can be obtained by interval technology. Two numerical examples—a damage-criteria numerical example and a 5-span with 25-bar truss structure in a space solar power station—are proposed. Both examples indicate the veracity of the interval method.

关键词： damage identification fusion sensitivity matrix damage criteria natural frequency static displacement interval analysis space solar power station

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Analysis of natural frequency for imaging interface in liquid lens

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Chinese Physics B 2021年第10期30卷 418-421页

作者： Na Xie College of Electronic and Optical Engineering and College of Microelectronics Nanjing University of Posts and TelecommunicationsNanjing 210023China

Transmission beam can be modulated at the liquid-liquid interface inside an electrowetting liquid *** fluctuation characteristics of the interface has a decisive effect on the beam modulation.A closed cylinder in capillary constant scale is analyzed and the natural frequencies of a flat interface are obtained using capillary wave *** in modes 0 and 1 are in good agreement with previous experiments in the *** influences of the radius,the height ratio and the height-to-diameter ratio of a liquid lens on the interface eigenfrequencies are analyzed.

关键词： natural frequency liquid-liquid interface capillary wave liquid lens

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Design for a specified natural frequency of elastically constrained axially graded bars

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Acta Mechanica Sinica 2010年第2期26卷 313-316页

作者： Isaac Elishakoff Jason Yost Department of Mechanical Engineering Florida Atlantic University

This study derives some closed-form analytic as well as numeric solutions for the axially graded elasticallyconstrained bar with polynomial varying modulus of elasticity, along the axial coordinate. The solutions allo... 详细信息

关键词： Graded bars Vibration natural frequency

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NONLINEAR natural frequency OF SHALLOW CONICAL SHELLS WITH VARIABLE THICKNESS

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Applied Mathematics and Mechanics(English Edition) 2005年第3期26卷 277-282页

作者：王新志韩明君赵永刚叶开沅 School of Sciences Lanzhou University of Technology Lanzhou 730050 P.R.China School of Physics Lanzhou University Lanzhou 730000 P.R.China

The nonlinear dynamical variation equation and compatible equation of the shallow conical shell with variable thickness are obtained by the theory of nonlinear dynamical variation equation and compatible equation of the circular thin plate with variable thickness. Assuming the thin film tension is composed of two items. The compatible equation is transformed into two independent equations. Selecting the maximum amplitude in the center of the shallow conical shells with variable thickness as the perturbation parameter, the variation equation and the differential equation are transformed into linear expression by theory of perturbation variation method. The nonlinear natural frequency of shallow conical shells with circular bottom and variable thickness under the fixed boundary conditions is solved. In the first approximate equation, the linear natural frequency of shallow conical shells with variable thickness is obtained. In the third approximate equation, the nonlinear natural frequency of it is obtained. The figures of the characteristic curves of the natural frequency varying with stationary loads, large amplitude, and variable thickness coefficient are plotted. A valuable reference is given for dynamic engineering.

关键词： variable thickness natural frequency non-linearity perturbation variation method

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Assessment of natural frequency of installed offshore wind turbines using nonlinear finite element model considering soil-monopile interaction

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Journal of Rock Mechanics and Geotechnical Engineering 2018年第2期10卷 333-346页

作者： Djillali Amar Bouzid Subhamoy Bhattacharya Lalahoum Otsmane Department of Civil Engineering Faculty of Technology University Saad Dahled of Blida Department of Civil and Environmental Engineering Tomas Telford Building University of Surrey Department of Material Engineering Faculty of Sciences and TechnologyUniversity of Médéa

A nonlinear finite element model is developed to examine the lateral behaviors of monopiles, which support offshore wind turbines(OWTs) chosen from five different offshore wind farms in Europe. The simulation is using this model to accurately estimate the natural frequency of these slender structures, as a function of the interaction of the foundations with the subsoil. After a brief introduction to the wind power energy as a reliable alternative in comparison to fossil fuel, the paper focuses on concept of natural frequency as a primary indicator in designing the foundations of OWTs. Then the range of natural frequencies is provided for a safe design purpose. Next, an analytical expression of an OWT natural frequency is presented as a function of soil-monopile interaction through monopile head springs characterized by lateral stiffness KL, rotational stiffness KRand cross-coupling stiffness KLRof which the differences are discussed. The nonlinear pseudo three-dimensional finite element vertical slices model has been used to analyze the lateral behaviors of monopiles supporting the OWTs of different wind farm sites considered. Through the monopiles head movements(displacements and rotations), the values of KL, KRand KLRwere obtained and substituted in the analytical expression of natural frequency for comparison. The comparison results between computed and measured natural frequencies showed an excellent agreement for most cases. This confirms the convenience of the finite element model used for the accurate estimation of the monopile head stiffness.

关键词： Nonlinear finite element analysis Vertical slices model Monopiles under horizontal loading natural frequency Monopile head stiffness Offshore wind turbines(OWTs)

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