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Flexural Nonlinear Natural Frequency Analysis of Rotational Functionally Graded Sandwich Rectangular Plates with Uniform and Inhomogeneous Pore Distributions in Thermal Environments 认领 引用
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作者 Dazhi Zhang Yongqiang Li 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2025年第4期664-676,共13页
This study investigates the nonlinear dynamic properties of rotating functionally graded sandwich rectangular plates in a thermal environment.The nonlinear vibration equations for a rotating metal-ceramic functionally... This study investigates the nonlinear dynamic properties of rotating functionally graded sandwich rectangular plates in a thermal environment.The nonlinear vibration equations for a rotating metal-ceramic functionally graded sandwich rectangular plate in a thermal environment are derived using classical thin plate theory and Hamilton’s principle,considering geometric nonlinearity,temperature-dependent material properties,and power law distribution of components through the thickness.With cantilever boundary conditions,the flexural nonlinear differential equations of the rectangular sandwich plate are obtained via the Galerkin method.Since the natural vibration differential equations exhibit nonlinear characteristics,the multiscale method is employed to derive the expression for nonlinear natural frequency.An example analysis reveals how the natural frequency of a functionally graded sandwich rectangular plate varies with rotational speed and temperature.Results show that the nonlinear/linear frequency ratio increases with rotational angular velocity Ω and thickness-to-length ratio h/a,follows a cosine-like periodic pattern with the setting angle,and shows a sharp decrease followed by a rapid increase with increasing width-to-length ratio b/a.The derived analytical solutions for nonlinear frequency provide valuable insights for assessing the dynamic characteristics of functionally graded structures. 展开更多
关键词 Rectangular plate Sandwich Functionally graded material Nonlinear natural frequency Rotational motion
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THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅰ)—RECTANGULAR PLATES WITH FOUR CLAMPED EDGES AND WITH THREE CLAMPED EDGES 认领 引用 被引量：2
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作者 付宝连 李农 《Applied Mathematics and Mechanics(English Edition)》 SCIE 1989年第8期727-749,共23页
In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates w... In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another. 展开更多
关键词 RECTANGULAR PLATES WITH FOUR CLAMPED EDGES AND WITH THREE CLAMPED EDGES THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES
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STUDY ON THE DYNAMIC BEHAVIOR OF AXIALLY MOVING RECTANGULAR PLATES PARTIALLY SUBMERSED IN FLUID 认领 引用 被引量：7
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作者 Yanqing Wang Wei Du +1 位作者 Xiaobo Huang Senwen Xue 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2015年第6期706-721,共16页
The natural frequencies, complex modes and critical speeds of an axially moving rectangular plate, which is partially immersed in a fluid and subjected to a pretension, are investigated. The effects of free surface wa... The natural frequencies, complex modes and critical speeds of an axially moving rectangular plate, which is partially immersed in a fluid and subjected to a pretension, are investigated. The effects of free surface waves, compressibility and viscidity of the fluid are neglected in the analysis. The subsection functions are used to describe the discontinuous characteristics of the system due to partial immersion. The classical thin plate theory is adopted to formulate the equations of motion of a vibrating plate. The velocity potential and Bernoulli＇s equation are used to describe the fluid pressure acting on the moving plate. The effect of fluid on the vibrations of the plate may be equivalent to the added mass on the plate. The effects of distance ratio, moving speed, immersed-depth ratio, boundary conditions, stiffness ratio and aspect ratio of the plate as well as the fluid-plate density ratios on the free vibrations of the moving plate-fluid system are investigated. 展开更多
关键词 partially immersed axially moving rectangular plates fluid-structure interaction free vibration
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EXACT SOLUTIONS FOR FREE IN-PLANE VIBRATIONS OF RECTANGULAR PLATES 认领 引用 被引量：5
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作者 Bo Liu Yufeng Xing 《Acta Mechanica Solida Sinica》 SCIE EI 2011年第6期556-567,共12页
All possible exact solutions are successfully obtained in terms of 10 sets of distinct eigensolutions for the free in-plane vibration of isotropic rectangular plates.The plates have simply supported condition at two o... All possible exact solutions are successfully obtained in terms of 10 sets of distinct eigensolutions for the free in-plane vibration of isotropic rectangular plates.The plates have simply supported condition at two opposite edges and any combination of classical boundary conditions at the other two edges.The exact solutions are validated through both mathematical proof and comparisons with the solutions of differential quadrature method.Some unusual phenomena are revealed in free in-plane vibrations of rectangular plates due to one of the eigenvalues being zero.This work constitutes an improved version of very recent corresponding work by the same authors lint.J.Mech.Sci.,2009,51:246-255.Both the solution forms and solving procedures in the previous work are substantially simplified.Some new results are also given,which are useful for validation purpose in future. 展开更多
关键词 rectangular plate in-pane free vibration frequency mode shape exact solution
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Analytical solution of rectangular plate with in-plane variable stiffness 认领 引用 被引量：2
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作者 于天崇 聂国隽 +1 位作者 仲政 褚福运 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第4期395-404,共10页
The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. T... The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form, and Poisson＇s ratio is constant. A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation, and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads. The validity of the present solution is shown by comparing the present results with those of the classical solution. The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples. The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness. 展开更多
关键词 in-plane variable stiffness power form Levy-type solution rectangular plate
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ON THE BENDING, VIBRATION AND STABILITY OF LAMINATED RECTANGULAR PLATES WITH TRANSVERSELY ISOTROPIC LAYERS 认领 引用 被引量：2
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作者 丁皓江 陈伟球 徐荣桥 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第1期17-24,共8页
A method based on newly presented state space formulations is developed for analyzing the bending, vibration and stability of laminated transversely isotropic rectangular plates with simply supported edges. By introdu... A method based on newly presented state space formulations is developed for analyzing the bending, vibration and stability of laminated transversely isotropic rectangular plates with simply supported edges. By introducing two displacement functions and two stress functions, two independent state equations were constructed based on the three-dimensional elasticity equations for transverse isotropy. The original differential equations are thus decoupled with the order reduced that will facilitate obtaining solutions of various problems. For the simply supported rectangular plate, two relations between the state variables at the tap and bottom surfaces were established. In particular, for the free vibration ( stability) problem, it is found that there exist two independent classes: One corresponds to the pure in-plane vibration (stability) and the other to the general bending vibration (stability). Numerical examples are finally presented and the effects of same parameters are discussed. 展开更多
关键词 transverse isotropy rectangular plate state space method
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Unified Solution Method of Rectangular Plate Elastic Bending 认领 引用 被引量：12
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作者 许琪楼 姬同庚 +2 位作者 姜锐 唐国明 姬鸿恩 《Journal of Southeast University(English Edition)》 CAS 2002年第3期241-248,共8页
The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition a... The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of... 展开更多
关键词 bending of elastic thin plate rectangular plate unified solution method
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Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method 认领 引用 被引量：1
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作者 Qiuhong Li Wenhao Huang +3 位作者 Joey Sanchez Ping Wang Qiang Ding Jiufa Wang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第3期2093-2121,共29页
Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved ... Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics. 展开更多
关键词 Rectangular plate with cutouts the independent coordinate coupling method elastic boundary conditions free vibration analysis
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Three-dimensional analysis of a thick FGM rectangular plate in thermal environment 认领 引用 被引量：9
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作者 陈伟球 边祖光 丁皓江 《Journal of Zhejiang University Science》 2003年第1期1-7,共7页
The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the materia... The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the material constants were further considered as functions of temperature. A solution method based on state-space formulations with a laminate approximate model was proposed. For a thin plate, the method was clarified by comparison with the thin plate theory. The influences of material inhomogeneity and temperature-dependent characteristics were finally discussed through numerical examples. 展开更多
关键词 Functionally graded material (FGM) State space method Simply supported rectangular plate
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THE PROBLEMS OF NONLINEAR BENDING FOR ORTHOTROPIC RECTANGULAR PLATE WITH FOUR CLAMPED EDGES 认领 引用 被引量：2
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作者 黄家寅 秦圣立 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第3期221-246,共26页
In this paper,under the non-uniformtransverse load,the problems of nonlinear bending for orthotropic rectangular plate are studied by using'the method of twovariable'[1]and 'the method of mixing perturbati... In this paper,under the non-uniformtransverse load,the problems of nonlinear bending for orthotropic rectangular plate are studied by using'the method of twovariable'[1]and 'the method of mixing perturbation'[2].The uniformly valid asymptotic solutions of Nth-order for ε1 and Mth-order for ε2 for ortholropic rectangular plale with four clamped edges are oblained. 展开更多
关键词 orthotropic rectangular plate,nonlinear bending,method of twovariable,method of mixing perturbation uniformly valid asymptotic solutions
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A SET OF 12-PARAMETER RECTANGULAR PLATE ELEMENT WITH HIGH ACCURACY 认领 引用 被引量：4
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作者 Chen Shaochun\ Luo Laixing 《Applied Mathematics(A Journal of Chinese Universities)》 1999年第4期433-439,共7页
Using the method of undetermined function, a set of 12 parameter rectangular plate element with double set parameter and geometry symmetry is constructed. Their consistency error are O(h\+2) , one order higher than th... Using the method of undetermined function, a set of 12 parameter rectangular plate element with double set parameter and geometry symmetry is constructed. Their consistency error are O(h\+2) , one order higher than the usual 12 parameter rectangular plate elements. 展开更多
关键词 Rectangular plate elem ent double setparam eter m ethod high accuracy
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Study on magneto-elastic-plastic deformation characteristics of ferromagnetic rectangular plate with simple supports 认领 引用 被引量：2
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作者 Yuanwen Gao 《Acta Mechanica Sinica》 SCIE EI CAS 2009年第1期139-147,共9页
In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation techniq... In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration offer- romagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45°for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto--elastic-plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses. 展开更多
关键词 Ferromagnetic rectangular plate Deformation characteristics Magneto-elastic-plastic coupling - Plastic yield
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Growth of Voids in a Hyperelastic Rectangular Plate 认领 引用 被引量：1
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作者 程昌钧 任九生 《Journal of Shanghai University(English Edition)》 2005年第3期194-200,共7页
The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility... The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility condition of the material. The solution was approximately obtained from the minimum potential energy principle. The growth of voids was discussed. One can see that an initial central circular-cylinder void becomes an elliptic-cylinder void, but an initial non-centeral circular-cylinder void becomes an elliptic-like cylinder void and the center of void has a shift. The stress distributions along the edges of voids were given and the phenomenon of stress concentration was observed. The influences of the distribution manner and size of voids, as well as the distance between them on the growth of voids were analyzed. 展开更多
关键词 hyperelastic rectangular plate finite deformation potential energy principle growth of voids stress concentration.
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THEORY AND EXPERIMENTAL INVESTIGAION OF FLEXURAL WAVE PROPAGATION IN THIN RECTANGULAR PLATE WITH PERIODIC STRUCTURE 认领 引用 被引量：5
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作者 Wen Jihong Yu Dianlong Wang Gang Zhao Hongang Liu Yaozong 《Chinese Journal of Mechanical Engineering》 EI CAS 2005年第3期385-388,共4页
With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane... With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane-wave expansion （PWE） method, and directional band gaps are found in the ΓX direction. The acceleration frequency response in the ΓX direction of such a plate with finite structure is simulated with the finite element method and verified with a vibration experiment. The frequency ranges of sharp drops in the calculated and measured acceleration frequency response curves are in basic agreement with those in the band structures. Thin plate is a widely used component in the engineering structures. The existence of band gaps in such periodic structures gives a new idea in vibration control of thin plates. 展开更多
关键词 Phononic crystals Flexural wave band gaps Thin rectangular plate
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RECIPROCAL THEOREM METHOD FOR THE FORCED VIBRATIONOF ELASTIC THICK RECTANGULAR PLATES 认领 引用
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作者 李慧剑 付宝连 谭文峰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第2期191-205,共15页
In this paper, reciprocal theorem method (RTM) is generalized to solve the problems for the forced vibration of thick rectangular plates based on the Reissner's theory. The paper derives the dynamic basic solution... In this paper, reciprocal theorem method (RTM) is generalized to solve the problems for the forced vibration of thick rectangular plates based on the Reissner's theory. The paper derives the dynamic basic solution of thick rectangular; and the exact analytical solution of the steady-state responses of thick rectangular plates with three clamped edges and one free edge under harmonic uniformly distributed disturbing forces is found by RTM. It is regarded as a simple, convenient and general method for calculating the steady-stare responses of forced vibration of thick rectangular plates. 展开更多
关键词 reciprocal theorem method dynamic basic solution thick rectangular plate forced vibration
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Analytical solutions of steady vibration of free rectangular plate on semi-infinite elastic foundation 认领 引用
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作者 王春玲 黄义 贾继红 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第2期173-182,共10页
The method of double Fourier transform Was employed in the analysis of the semi-infinite elastic foundation with vertical load. And an integral representations for the displacements of the semi-infinite elastic founda... The method of double Fourier transform Was employed in the analysis of the semi-infinite elastic foundation with vertical load. And an integral representations for the displacements of the semi-infinite elastic foundation was presented. The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semiinfinite elastic foundation. Some computational results and the analysis on the influence of parameters were presented. 展开更多
关键词 semi-infinite elastic foundation rectangular plate with four free edges,steady vibration interaction analytical solution
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TRANSVERSELY ISOTROPIC HYPER-ELASTIC MATERIAL RECTANGULAR PLATE WITH VOIDS UNDER A UNIAXIAL EXTENSION 认领 引用
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作者 程昌钧 任九生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第7期763-773,共11页
The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper_elastic material with the generalized neo_Hookean strain energy function under a uniaxial extensio... The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper_elastic material with the generalized neo_Hookean strain energy function under a uniaxial extension are studied. The deformation functions of plates with voids that are symmetrically distributed in a certain manner are given and the functions are expressed by two parameters by solving the differential equations.The solution may be approximately obtained from the minimum potential energy principle. Thus, the analytic solutions of the deformation and stress of the plate are obtained. The growth of the voids and the distribution of stresses along the voids are analyzed and the influences of the degree of anisotropy, the size of the voids and the distance between the voids are discussed. The characteristics of the growth of the voids and the distribution of stresses of the plates with one void, three or five voids are obtained and compared. 展开更多
关键词 transversely isotropic hyper_elastic material rectangular plate with voids finite deformation potential energy principle growth of voids
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EFFECT OF DAMAGE ON NONLINEAR DYNAMIC PROPERTIES OF VISCOELASTIC RECTANGULAR PLATES 认领 引用
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作者 郑玉芳 傅衣铭 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第3期319-326,共8页
The nonlinear dynamic behaviors of viscoelastic rectangular plates including the damage effects under the action of a transverse periodic load were studied. Using the von Karman equations, Boltzmann superposition prin... The nonlinear dynamic behaviors of viscoelastic rectangular plates including the damage effects under the action of a transverse periodic load were studied. Using the von Karman equations, Boltzmann superposition principle and continuum damage mechanics, the nonlinear dynamic equations in terms of the mid_plane displacements for the viscoelastic thin plates with damage effect were derived. By adopting the finite difference method and Newmark method, these equations were solved. The results were compared with the available data. In the numerical calculations, the effects of the external loading parameters and geometric dimensions of the plate on the nonlinear dynamic responses of the plate were discussed. Research results show that the nonlinear dynamic response of the structure will change remarkably when the damage effect is considered. 展开更多
关键词 rectangular plate viscoelasticity damage effect geometric nonlinearity
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THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅲ)--CANTILEVER RECTANGULAR PLATES 认领 引用
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作者 Fu Bao-lian Li Nong 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第7期663-680,共18页
In this paper,applying the method of the reciprocal theorem,we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic... In this paper,applying the method of the reciprocal theorem,we give the stationary solutions of the forced vibration of cantilever rectangular plates under uniformly distributed harmonic load and concentrated harmonic load acting at any point of the plates,the figures and tables of number value of bending moment and the deflection amplitudes as well. 展开更多
关键词 the method of reciprocal theorem forced vibration cantilever rectangular plate the amplitude of bending moment the amplitude of deflection
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NONLINEAR BENDING OF SIMPLY SUPPORTED SYMMETRIC LAMINATED CROSS-PLY RECTANGULAR PLATES 认领 引用
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作者 刘人怀 何陵辉 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第9期801-807,共7页
Based on the von Karman-type theory of plates, nonlinear bending problems of simply supported symmetric laminated cross-ply rectangular plates under the combined action of pressure and inplane load are investigated in... Based on the von Karman-type theory of plates, nonlinear bending problems of simply supported symmetric laminated cross-ply rectangular plates under the combined action of pressure and inplane load are investigated in this paper. The solution which satisfies the governing equations and boundary conditions is obtained by using the double Fourier series method. 展开更多
关键词 laminated rectangular plate nonlinear bending governing equation
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