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Nonlinear vibrations of a composite circular plate with a rigid body
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作者 Ying MENG Xiaoye MAO +1 位作者 Hu DING Liqun CHEN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第6期857-876,共20页
The influence of weights is usually ignored in the study of nonlinear vibrations of plates.In this paper,the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is pr... The influence of weights is usually ignored in the study of nonlinear vibrations of plates.In this paper,the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented.The nonlinear governing equations are derived from the generalized Hamilton's principle and the von Kármán plate theory.The equilibrium configurations due to weights are determined and validated by the finite element method(FEM).A nonlinear model for the vibration around the equilibrium configuration is established.Moreover,the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated.The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model.This leads to interesting phenomena.For example,considering weights increases the natural frequency.Furthermore,when the influence of weights is considered,the vibration response of the plate becomes asymmetrical. 展开更多
关键词 composite circular plate WEIGHT nonlinear vibration equilibrium configuration natural frequency
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CHAOTIC MOTION OF AN ELASTIC CIRCULAR PLATE
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作者 韩强 胡海岩 杨桂通 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 1998年第2期55-59,共5页
The chaotic motion of a harmonically forced circular plate is studied in the paper. The virtual displacement principle is used to derive the dynamic equation of motion, with the effect of large deflection of plate tak... The chaotic motion of a harmonically forced circular plate is studied in the paper. The virtual displacement principle is used to derive the dynamic equation of motion, with the effect of large deflection of plate taken into account. By means of Garlerkin approach and Melnikov function method, the critical condition for chaotic motion is obtained. A demonstrative example is discussed through the Poincare mapping, phase portrait and time history. 展开更多
关键词 circular plate CHAOS Melnikov function Poincare mapping
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DIFFERENTIAL QUADRATURE FOR AXISYMMETRIC GEOMETRICALLY NONLINEAR ANALYSIS OF CIRCULAR PLATES
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作者 王鑫伟 周光明 贾德财 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 1995年第2期134-142,共9页
New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bendin... New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated. 展开更多
关键词 circular plates nonlinear analysis axisymmetric bodies differential quadrature large deflection
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NEW SOLUTION SYSTEM FOR CIRCULAR SECTOR PLATE BENDING AND ITS APPLICATION 被引量:15
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作者 Yao, W Zhong, WX Su, B 《Acta Mechanica Solida Sinica》 SCIE EI 1999年第4期307-315,共9页
Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So ... Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So the Hamiltonian system can also be applied to plate bending problems by introducing bending moment functions. The new method presents the analytical solution for the circular sector plate. The results show that the new method is effective. 展开更多
关键词 circular sector plate Hamiltonian system bending moment functions ANALOGY
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Nonlinear Resonance of the Rotating Circular Plate under Static Loads in Magnetic Field 被引量:10
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作者 HU Yuda WANG Tong 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2015年第6期1277-1284,共8页
The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating ci... The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering. 展开更多
关键词 circular plate main resonance magnetic filed static load modified multiple scale method
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Magnetoelastic combined resonance and stability analysis of a ferromagnetic circular plate in alternating magnetic field 被引量:4
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作者 Yuda HU Bingbing MA 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2019年第7期925-942,共18页
The nonlinear combined resonance problem of a ferromagnetic circular plate in a transverse alternating magnetic field is investigated. On the basis of the deformation potential energy, the strain potential energy, and... The nonlinear combined resonance problem of a ferromagnetic circular plate in a transverse alternating magnetic field is investigated. On the basis of the deformation potential energy, the strain potential energy, and the kinetic energy of the circular plate, the Hamilton principle is used to induce the magnetoelastic coupling transverse vibration dynamical equation of the ferromagnetic circular plate. Based on the basic electromagnetic theory, the expressions of the magnet force and the Lorenz force of the circular plate are presented. A displacement function satisfying clamped-edge combined with the Galerkin method is used to derive the Duffing vibration differential equation of the circular plate. The amplitude-frequency response equations of the system under various combined resonance forms are obtained by means of the multi-scale method, and the stability of the steady-state solutions is analyzed according to the Lyapunov theory. Through examples, the amplitude-frequency characteristic curves with different parameters, the amplitude of resonance varying with magnetic field intensity and excitation force, and the time-course response diagram, phase diagram, Poincar′e diagram of the system vibration are plotted, respectively. The effects of different parameters on the amplitude and stability of the system are discussed. The results show that the electromagnetic parameters have a significant effect on the multi-valued attribute and stability of the resonance solutions, and the system may exhibit complex nonlinear dynamical behavior including multi-period and quasi-periodic motion. 展开更多
关键词 MAGNETOELASTICITY FERROMAGNETIC circular plate COMBINED RESONANCE multi- scale method ALTERNATING magnetic field
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AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES 被引量:6
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作者 Guojun Nie Zheng Zhong 《Acta Mechanica Solida Sinica》 SCIE EI 2007年第4期289-295,共7页
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
关键词 two-directional functionally graded materials circular and annular plates axisym-metric bending semi-analytical numerical method integrated design
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Nonlinear vibration analysis of a circular composite plate harvester via harmonic balance 被引量:6
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作者 Tian-Chen Yuan Jian Yang Li-Qun Chen 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2019年第4期912-925,共14页
Alumped parameter transversevibration model of a composite plate harvester is analyzed via harmonic balance approaches. The harvester is mainly composed of a piezoelectriccircular composite clamped by two steel rings ... Alumped parameter transversevibration model of a composite plate harvester is analyzed via harmonic balance approaches. The harvester is mainly composed of a piezoelectriccircular composite clamped by two steel rings and a proof mass on the plate.The lumped parameter model is a 1.5 degree-of-freedom strongly nonlinear system with a higher order polynomial stiffness. Aharmonic balance approach is developed to analyze the system, and the resulting algebraic equations are numerically solved by adopting an arc-length continuation technique. Anincremental harmonic balance approach is also developedfor the lumped parameter model. The two approaches yieldthe same results.The amplitude-frequency responses produced by the harmonic balance approach are validated by the numericalintegrations and the experimental data. The investigation reveals that there coexist hardening and softening characteristics in the amplitude-frequency response curves under sufficiently large excitations. The harvester with thecoexistenceof hardening and softening nonlinearitiescan outperform not only linear energy harvesters but also typical hardening nonlinear energy harvesters. 展开更多
关键词 Piezoelectricenergy HARVESTER circular composite plate TRANSVERSE NONLINEAR vibration Harmonic BALANCE Arc-length CONTINUATION
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Hydroelastic Response of A Circular Plate in Waves on A Two-Layer Fluid of Finite Depth 被引量:3
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作者 林强 卢东强 Ronald W.YEUNG 《China Ocean Engineering》 SCIE EI CSCD 2014年第5期671-686,共16页
The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interf... The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the platecovered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode. 展开更多
关键词 wave diffraction two-layer fluid ORTHOGONALITY matched eigenfunction circular elastic plate flexural waves
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DYNAMIC BEHAVIORS OF CONDUCTIVE CIRCULAR PLATE IN TIME-VARYING MAGNETIC FIELDS 被引量:4
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作者 Yuanwen Gao1 Bang Xu(Key Laboratory of Mechanics on Western Disaster and Environment,College of Civil Engineering and Mechanics,Lanzhou University,Lanzhou 730000,China) 《Acta Mechanica Solida Sinica》 SCIE EI 2010年第1期66-76,共11页
In this study, we proposed an analytical solution for eddy currents as well as electromagnetic forces of a conductive circular plate in a time varying magnetic field. Specifically, an analytical series solution for ed... In this study, we proposed an analytical solution for eddy currents as well as electromagnetic forces of a conductive circular plate in a time varying magnetic field. Specifically, an analytical series solution for eddy currents in a circular plate subjected to an axisymmetrie time varying magnetic field has been proposed based on the T-method that has been widely used in the eddy current analysis of conductive and superconductive structures. Accordingly, the dynamic response, the dynamic instability and the magnetic damping of a circular plate in a transverse transient magnetic field as well as a stationary in-plane magnetic field have also been obtained. The analytical series solution proposed in this work as well as the subsequent numerical analysis not only confirmed the emergence of dynamic instability of a circular plate in a strong transverse magnetic field, but also demonstrated the existence of magneto-damping of a circular conductive plate in an in-plane magnetic field. The method developed in this paper provides a potential new possible way by which the analysis of the electromagnetic coupling problems of conductive structures can be simplified. 展开更多
关键词 dynamic response circular conductive plate series solution for eddy current Bessel function
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VIBRATION PROBLEMS OF FLEXIBLE CIRCULAR PLATES WITH INITIAL DEFLECTION 被引量:3
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作者 王晋莹 陈科进 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1993年第2期177-184,共8页
In this paper, the differential equations of flexible circular plates with initial deflection are derived. The stability of motion is investigated in phase plane. The periodical solutions of nonlinear vibration for ci... In this paper, the differential equations of flexible circular plates with initial deflection are derived. The stability of motion is investigated in phase plane. The periodical solutions of nonlinear vibration for circular plates with initial deflection are obtained by use of Galerkin method and Lindstedt-Poincare perturbation method. The effect of initial deflection on the dynamic behavior of the flexible plates are also discussed. 展开更多
关键词 flexible circular plate initial deflection nonlinear-vibration perturbation method trajectories
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NONLINEAR VIBRATION OF CIRCULAR SANDWICH PLATE UNDER THE UNIFORMED LOAD 被引量:3
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作者 杜国君 李慧剑 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第2期217-226,共10页
The differential equations of the axisymmetric large amplitude free vibration for circular sandwich plates under static load are derived, and a set of nonlinearly coupled algebraic and differential eigenvalue equation... The differential equations of the axisymmetric large amplitude free vibration for circular sandwich plates under static load are derived, and a set of nonlinearly coupled algebraic and differential eigenvalue equations of the problem are formulated following an assumed time mode approach suggested. The analytic solutions are presented and a relation for amplitude frequency-load of the plates with edge clamped is derived by modified iteration method. The effects of static load on vibrations of plates are investigated. 展开更多
关键词 circular sandwich plate uniformed load nonlinear amplitude frequency-load characteristic relation
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Nonlinear vibration analysis of a circular micro-plate in two-sided NEMS/MEMS capacitive system by using harmonic balance method 被引量:4
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作者 Milad Saadatmand Alireza Shooshtari 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2019年第1期129-143,I0004,共16页
In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman pl... In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors. 展开更多
关键词 NONLINEAR vibration Two-sided MEMS CAPACITOR circular plate Harmonic balance method
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EXACT SOLUTIONS FOR FREE VIBRATION OF TRANSVERSELY ISOTROPIC PIEZOELECTRIC CIRCULAR PLATES 被引量:2
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作者 丁皓江 徐荣桥 陈伟球 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2000年第2期141-147,共7页
By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. ... By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. Three-dimensional exact solutions are then obtained under two specified boundary conditions, which can be used for both axisymmetric and non-axisymmetric cases. Numerical results are finally presented. 展开更多
关键词 exact solution piezoelectric circular plate free vibration
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ANALYTICAL EVALUATION OF PERMANENT DEFLECTION OF A THIN CIRCULAR PLATE STRUCK NORMALLY AT ITS CENTER BY A PROJECTILE 被引量:2
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作者 Chen Liebin Yang Jialing 《Acta Mechanica Solida Sinica》 SCIE EI 2007年第2期117-122,共6页
The permanent deflection of a thin circular plate struck normally at its center by a projectile is studied by an approximate theoretical analysis, FEM simulation and experiment. The plate made of rate sensitive and st... The permanent deflection of a thin circular plate struck normally at its center by a projectile is studied by an approximate theoretical analysis, FEM simulation and experiment. The plate made of rate sensitive and strain-hardening material undergoes serious local deformation but is not perforated during the impact. The theoretical analysis is based on an energy approach, in which the Cowper-Symonds equation is used for the consideration of strain rate sensitive effects and the parameters involved are determined with the aid of experimental data. The maximum permanent deflections predicted by the theoretical model are compared with those of FEM simulation and published papers obtained both by theory and experiment, and good agreement is achieved for a wide range of thickness of the plates and initial impact velocities. 展开更多
关键词 thin circular plate finite deflection impact strain rate sensitive STRAIN-HARDENING
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EXACT SOLUTIONS FOR FREE VIBRATIONS OF TRANSVERSELY ISOTROPIC CIRCULAR PLATES 被引量:2
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作者 Ding, HJ Xu, RQ 《Acta Mechanica Solida Sinica》 SCIE EI 2000年第2期105-111,共7页
By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of... By virtue of the general solution of dynamic elasticity equations for transverse isotropy as well as the variable separation method, three-dimensional exact solutions of circular plates are obtained under two types of boundary conditions. The solutions can consider both axisymmetric and non-axisymmetric cases. Solutions based on the classical plate theory and Mindlin plate theory are also presented under the corresponding boundary conditions. Numerical results are finally presented and comparisons between the three theories are made. 展开更多
关键词 free vibration transversely isotropic circular plate exact solution general solution
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TORSIONAL VIBRATIONS OF A RIGID CIRCULAR PLATE ON SATURATED STRATUM OVERLAYING BEDROCK 被引量:3
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作者 CaiYuanqiang WuDazhi XuChangjie 《Acta Mechanica Solida Sinica》 SCIE EI 2005年第2期142-149,共8页
The torsional vibration of a rigid plate resting on saturated stratum overlaying bedrock has been analysed for the first time. The dynamic governing differential equations for saturated poroelastic medium are solved b... The torsional vibration of a rigid plate resting on saturated stratum overlaying bedrock has been analysed for the first time. The dynamic governing differential equations for saturated poroelastic medium are solved by employing the technology of Hankel transform. By taking into account the boundary conditions, the dual integral equations of torsional vibration of a rigid circular plate are established, which are further converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficients of the foundation on saturated stratum, the contact shear stress under the foundation and the angular amplitude of the foundation are evaluated. Numerical results indicate that, when the dimensionless height is bigger than 5, saturated stratum overlaying bedrock can be treated as saturated half space approximately. When the dimensionless frequency is low, the permeability of the soil must be taken into account. Furthermore, when the vibration frequency is a constant, the height of the saturated stratum has a slight effect on the dimensionless contact shear stress under the foundation. 展开更多
关键词 saturated stratum overlaying bedrock torsional vibration rigid circular plate dynamical compliance coefficients contact shear stress
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Pure bending of simply supported circular plate of transversely isotropic functionally graded material 被引量:6
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作者 LI Xiang-yu DING Hao-jiang CHEN Wei-qiu 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第8期1324-1328,共5页
This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial d... This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM). 展开更多
关键词 Transversely isotropic Functionally graded materials (FGMs) Pure bending problem Simply supported circular plate Axisymmetric deformation
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Nonlinear vibration and buckling of circular sandwich plate under complex load 被引量:2
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作者 杜国君 马建青 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第8期1081-1091,共11页
The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory, and then acc... The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained. 展开更多
关键词 circular sandwich plate nonlinear vibration BUCKLING complex load amplitude frequency-load characteristic relation
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Upper bound analysis of ultimate pullout capacity of shallow 3-D circular plate anchors based on nonlinear Mohr-Coulomb failure criterion 被引量:7
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作者 ZHAO Lian-heng TAN Yi-gao +2 位作者 HU Shi-hong DENG Dong-ping YANG Xin-ping 《Journal of Central South University》 SCIE EI CAS CSCD 2018年第9期2272-2288,共17页
Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules,the three-dimensional(3-D)axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultim... Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules,the three-dimensional(3-D)axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultimate pullout capacity(UPC)is determined.A derivative function of the projection function for projecting the 3-D axisymmetric failure surface on plane is deduced using the variation theory.By using difference principle,the primitive function of failure surface satisfying boundary condition and numerical solution to its corresponding ultimate pullout capacity function are obtained.The influences of nonlinear Mohr-Coulomb parameters on UPC and failure mechanism are studied.The result shows that UPC decreases with dimensionless parameter m and uniaxial tensile strength increases but increases when depth and radius of plate anchor,surface overload,initial cohesion,geomaterial density and friction angle increase.The failure surface is similar to a symmetrical spatial funnel,and its shape is mainly determined by dimensionless parameter m;the surface damage range expands with the increase of radius and depth of the plate anchor as well as initial cohesion but decreases with the increase of dimensionless parameter m and uniaxial tensile strength as well as geomaterial density.As the dimensionless parameter m=2.0,the numerical solution of UPC based on the difference principle is proved to be feasible and effective through the comparison with the exact solution.In addition,the comparison between solutions of UPC computed by variation method and those computed by upper bound method indicate that variation method outperforms upper bound method. 展开更多
关键词 shallow circular plate anchors ultimate pullout capacity variation analysis nonlinear Mohr-Coulomb failure criterion upper bound limit analysis
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