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Eigenvalues for the Clamped Plate Problem of L_(ν)^(2) Operator on Complete Riemannian Manifolds
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作者 Ling Zhong ZENG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第9期2223-2243,共21页
L_(ν) operator is an important extrinsic differential operator of divergence type and has profound geometric settings.In this paper,we consider the clamped plate problem of L_(ν)^(2)operator on a bounded domain of t... L_(ν) operator is an important extrinsic differential operator of divergence type and has profound geometric settings.In this paper,we consider the clamped plate problem of L_(ν)^(2)operator on a bounded domain of the complete Riemannian manifolds.A general formula of eigenvalues of L_(ν)^(2) operator is established.Applying this general formula,we obtain some estimates for the eigenvalues with higher order on the complete Riemannian manifolds.As several fascinating applications,we discuss this eigenvalue problem on the complete translating solitons,minimal submanifolds on the Euclidean space,submanifolds on the unit sphere and projective spaces.In particular,we get a universal inequality with respect to the L_(II) operator on the translating solitons.Usually,it is very difficult to get universal inequalities for weighted Laplacian and even Laplacian on the complete Riemannian manifolds.Therefore,this work can be viewed as a new contribution to universal estimate. 展开更多
关键词 Mean curvature flows L_(ν)^(2)operator clamped plate problem EIGENVALUES Riemannian manifolds translating solitons
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Eigenvalue inequalities for the clamped plate problem of L_(ν)^(2) operator 被引量:1
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作者 Lingzhong Zeng 《Science China Mathematics》 SCIE CSCD 2022年第4期793-812,共20页
The ■ operator is introduced by Xin(2015), which is an important extrinsic elliptic differential operator of divergence type and has profound geometric meaning. In this paper, we extend the ■ operator to a more gene... The ■ operator is introduced by Xin(2015), which is an important extrinsic elliptic differential operator of divergence type and has profound geometric meaning. In this paper, we extend the ■ operator to a more general elliptic differential operator ■, and investigate the clamped plate problem of the bi-■ operator,which is denoted by ■ on the complete Riemannian manifolds. A general formula of eigenvalues for the ■ operator is established. Applying this formula, we estimate the eigenvalues on the Riemannian manifolds. As some further applications, we establish some eigenvalue inequalities for this operator on the translating solitons with respect to the mean curvature flows, submanifolds of the Euclidean spaces, unit spheres and projective spaces. In particular, for the case of translating solitons, all of the eigenvalue inequalities are universal. 展开更多
关键词 mean curvature flows L^(2)_(ν)operator clamped plate problem EIGENVALUES Riemannian manifolds translating solitons
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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 被引量:5
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作者 付宝连 李农 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 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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Quasi-Green’s function method for free vibration of clamped thin plates on Winkler foundation
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作者 李善倾 袁鸿 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第3期265-276,共12页
The quasi-Green's function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green's function is established by the fundamental solution and the boundary equa... The quasi-Green's function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green's function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of tile problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green's formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method. 展开更多
关键词 Green's function integral equation clamped thin plate Winkler foundation free vibration
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Analytical solutions for a uniformly loaded circular plate with clamped edges
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作者 丁皓江 李翔宇 陈伟球 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2005年第10期1163-1168,共6页
A bi-harmonic potential function was constructed in this study. Love solution was employed to obtain analytical solutions of uniformly loaded plates with two different types of clamped edges. The treatment of clamped ... A bi-harmonic potential function was constructed in this study. Love solution was employed to obtain analytical solutions of uniformly loaded plates with two different types of clamped edges. The treatment of clamped boundary conditions was the same as that adopted by Timoshenko and Goodier (1970). The analytical solution for the first type of clamped boundary condition is identical with that obtained by Luo et al.(2004), and the solutions for both types were compared with the FEM results and the calculations of thin plate theory. 展开更多
关键词 Three-dimensional analytical solution Circular plates with clamped edges Bi-harmonic functions Axisymmetricdeformation
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THE BENDING OF A THICK RECTANGULAR PLATE WITH THREE CLAMPED EDGES AND ONE FREE EDGE
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作者 程昌钧 杨骁 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第6期543-559,共17页
The exact solution of the bending of a thick rectangular plate with three clamped edges and one free edge under a uniform transverse load is obtained by means of the concept of generalized simply-supported boundary[1]... The exact solution of the bending of a thick rectangular plate with three clamped edges and one free edge under a uniform transverse load is obtained by means of the concept of generalized simply-supported boundary[1] in Reissner's theory of thick plates. The effect of the thickness h of a plate on the bending is studied and the applicable range of Kirchhoffs theory for bending of thin plates is considered. 展开更多
关键词 THE BENDING OF A THICK RECTANGULAR plate WITH THREE clamped EDGES AND ONE FREE EDGE
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Mechanical Properties of Moso Bamboo Connections with External Clamp Steel Plates 被引量:1
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作者 Shidong Nie Song Ran +3 位作者 Di Wu Jieyu Chen Hui Wang Qike Wei 《Journal of Renewable Materials》 SCIE EI 2022年第2期487-510,共24页
The Moso bamboo,a renewable green building material used in various new green buildings,have received exten-sive attention with the promotion of the concept of green buildings.To explore the mechanical properties of M... The Moso bamboo,a renewable green building material used in various new green buildings,have received exten-sive attention with the promotion of the concept of green buildings.To explore the mechanical properties of Moso bamboo connections with external clamp steel plates,the 16 specimens were designed by changing the bolt diameters and the end distances of the bolt holes.Their static tension tests were conducted to investigate bearing capacities and failure modes of different connection configurations.Based on test results,three failure modes of these connections were obtained,including the shear failure of bolt shank,bearing failure of bolt hole and punch-ing shear failure of the Moso bamboo.The influence of bolt diameters and end distances of bolt holes on bearing capacities of the connections was quantitatively analyzed.Based on a simplified mechanical model,the analytical models were deduced for the bolt shear failure and the bearing failure of bolt holes.The results showed that the predictive values are in substantial agreement with the experimental results.Finally,the design and manufacturing suggestions are recommended for this Moso bamboo connections. 展开更多
关键词 Moso bamboo connections external clamp steel plates load-carrying capacities failure modes the 5%d offset method mechanical model
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ESTIMATES ON EIGENVALUES FOR THE BIHARMONIC OPERATOR ON A BOUNDED DOMAIN IN H^n(-1) 被引量:3
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作者 黄广月 李兴校 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1383-1388,共6页
In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the (k + 1)th eigenvalue in terms of the first kth eigenvalues in... In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the (k + 1)th eigenvalue in terms of the first kth eigenvalues independent of the domains. 展开更多
关键词 universal inequality EIGENVALUE hyperbolic space clamped plate problem
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Calculation method of first collapse span with superhigh water material backfill mining 被引量:3
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作者 ZHANG Li-ya DENG Ka-zhong 《Journal of Coal Science & Engineering(China)》 2012年第4期374-378,共5页
It is critical for the material to be of active supporting capacity before initial collapse ot mare root wltn supermgn water material backfill mining, and the maximum bending moment should be first calculated in order... It is critical for the material to be of active supporting capacity before initial collapse ot mare root wltn supermgn water material backfill mining, and the maximum bending moment should be first calculated in order to determine the initial collapse span. In the light of principal of virtual work, the simple expression of deflection, bending moment of elastic clamped plate were deduced under the condition of vertical uniform distributed load, horizontal pressure and supporting by elastic foundation, and then, the maximal bending moment expression was derived too. At the same time, the influence degree on square clamped plate by adding horizontal pressure and elastic foundation were analyzed. The results show that the effect of horizontal pressure on maximal bending moment can be ignored when the value of horizontal pressure is two orders of magni- tude less than that of coeificient of elastic stiffness existing elastic foundation. 展开更多
关键词 first collapse span superhigh water material backfill mining elastic clamped plate principal of virtual work
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GREEN QUASIFUNCTION METHOD FOR FREE VIBRATION OF CLAMPED THIN PLATES 被引量:5
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作者 Shanqing Li Hong Yuan 《Acta Mechanica Solida Sinica》 SCIE EI 2012年第1期37-45,共9页
The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This fu... The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Two examples demonstrate the validity of the present method.Comparison with both the series solution and ANSYS finite-element solution shows fine agreement.The present method is a novel and effective mathematical one. 展开更多
关键词 Green function integral equation R-function clamped thin plates free vibration
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