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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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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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Analyses of dynamic characteristics of a fluid-filled thin rectangular porous plate with various boundary conditions 认领 引用 被引量：1
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作者 Yu Xiang Honghua Jiang Jing Lu 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2017年第1期87-97,共11页
Based on the classical theory of thin plate and Biot theory,a precise model of the transverse vibrations of a thin rectangular porous plate is proposed.The first order differential equations of the porous plate are de... Based on the classical theory of thin plate and Biot theory,a precise model of the transverse vibrations of a thin rectangular porous plate is proposed.The first order differential equations of the porous plate are derived in the frequency domain.By considering the coupling effect between the solid phase and the fluid phase and without any hypothesis for the fluid displacement,the model presented here is rigorous and close to the real materials.Owing to the use of extended homogeneous capacity precision integration method and precise element method,the model can be applied in higher frequency range than pure numerical methods.This model also easily adapts to various boundary conditions.Numerical results are given for two different porous plates under different excitations and boundary conditions. 展开更多
关键词 Thin rectangular porous plate Blot theory Vibration First order differential equations Extended homogeneous capacity high precision integration method
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THEORETIC SOLUTION OF RECTANGULAR THIN PLATE ON FOUNDATION WITH FOUR EDGES FREE BY SYMPLECTIC GEOMETRY METHOD 认领 引用 被引量：1
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作者 钟阳 张永山 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第6期833-839,共7页
The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firs... The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution. 展开更多
关键词 elastic foundation rectangular thin plate symplectic geometry method theoretic solution
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BASIC EQUATIONS OF THE PROBLEM OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE WITH VARIABLE THICKNESS 认领 引用
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作者 黄家寅 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第7期812-816,共5页
Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bendin... Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given. 展开更多
关键词 orthotropic rectangular thin plate with variable thickness nonlinear unsymmetrical bending equilibrium equation compatibility equation basic equation dimensionless equation
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UNIFORMLY VALID ASYMPTOTIC SOLUTIONS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE OF FOUR CLAMPED EDGES WITH VARIABLE THICKNESS 认领 引用
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作者 黄家寅 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第7期817-826,共10页
By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate wi... By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained. 展开更多
关键词 orthotropic rectangular thin plate with variable thickness four clampled edge nonlinear unsymmetrical bending method of modified two-variable method of mixing perturbation uniformly valid asymptotic solution
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A procedure of the method of reverberation ray matrix for the buckling analysis of a thin multi-span plate 认领 引用 被引量：2
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作者 Zhiwei LI Guohua NIE 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2020年第7期1055-1068,共14页
A procedure of the method of reverberation ray matrix(MRRM)is developed to perform the buckling analysis of thin multi-span rectangular plates having internal line supports or stiffeners.A computation algorithm for th... A procedure of the method of reverberation ray matrix(MRRM)is developed to perform the buckling analysis of thin multi-span rectangular plates having internal line supports or stiffeners.A computation algorithm for the reverberation ray matrix in the MRRM is derived to determine the buckling loading.Specifically,the analytical solutions are presented for the buckling of the structure having two opposite simply-supported or clamped-supported edges with spans,while the constraint condition of two remaining edges may be in any combination of free,simply-supported,and clamped boundary conditions.Furthermore,based on the analysis of matrices relating to the unknown coefficients in the solution form for the deflection in terms of buckling modal functions,some recursive equations(REs)for the MRRM are introduced to generate a reduced reverberation ray matrix with unchanged dimension when the number of spans increases,which promotes the computation efficiency.Several numerical examples are given,and the present results are compared with the known solutions to illustrate the validity and accurateness of the MRRM for the buckling analysis. 展开更多
关键词 multi-span thin rectangular plate buckling method of reverberation ray matrix(MRRM) recursive equation(RE)
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Element-free Galerkin method for free vibration of rectangular plates with interior elastic point supports and elastically restrained edges 认领 引用 被引量：1
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作者 王砚 王忠民 阮苗 《Journal of Shanghai University(English Edition)》 2010年第3期187-195,共9页
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for t... The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed. 展开更多
关键词 element free method rectangular thin plates interior elastic point supports elastically restrained edges free vibration
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ANALYSIS OF GLOBAL DYNAMICS IN A PARAMETRICALLY EXCITED THIN PLATE 认领 引用
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作者 张伟 《Acta Mechanica Sinica》 SCIE EI CAS 2001年第1期71-85,共15页
The global bifurcations and chaos of a simply supported rectangular thin plate with parametric excitation are analyzed. The formulas of the thin plate are derived by von Karman type equation and Galerkin's approac... The global bifurcations and chaos of a simply supported rectangular thin plate with parametric excitation are analyzed. The formulas of the thin plate are derived by von Karman type equation and Galerkin's approach. The method of multiple scales is used to obtain the averaged equations. Based on the averaged equations, the theory of the normal form is used to give the explicit expressions of the normal form associated with a double zero and a pair of pure imaginary eigenvalues by Maple program. On the basis of the normal form, a global bifurcation analysis of the parametrically excited rectangular thin plate is given by the global perturbation method developed by Kovacic and Wiggins. The chaotic motion of thin plate is also found by numerical simulation. 展开更多
关键词 rectangular thin plate global bifurcations normal form chaos
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基于假设振型法对驾驶室顶板的振动分析 认领 引用
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作者 孟杰 马孝昌 史尚昆 《太原科技大学学报》 2026年第4期336-341,347,共6页
工程车辆驾驶室的动态振动响应会严重影响乘坐舒适性,分析驾驶室壁板的振动特性具有重要意义。提出了一种研究薄板振动特性的有效解析方法,将假设振型法应用到工程车辆驾驶室板件的运动方程中,通过建立结构体系的拉格朗日运动方程,推导... 工程车辆驾驶室的动态振动响应会严重影响乘坐舒适性,分析驾驶室壁板的振动特性具有重要意义。提出了一种研究薄板振动特性的有效解析方法,将假设振型法应用到工程车辆驾驶室板件的运动方程中,通过建立结构体系的拉格朗日运动方程,推导出用广义坐标表示的系统动力学方程,确定了结构的质量矩阵与刚度矩阵,最后根据特征值来计算系统的固有频率和振型函数,并与有限元计算结果进行了比较。随后进行了受迫振动分析,计算了矩形薄板在外部激励下的振动特性,并通过试验进行了验证。结果表明理论计算的数值结果与有限元分析结果以及试验结果吻合较好,并且计算效率比有限元高53.4%,其研究结果可对其他任意边界的不同类型薄板的振动特性分析提供参考,同时也为工程车辆驾驶室的减振提供思路。 展开更多
关键词 假设振型法 矩形薄板 拉格朗日方程 有限元分析
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Hydroelastic Analysis of Very Large Floating Structures Using Plate Green Functions 认领 引用 被引量：8
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作者 闫红梅 崔维成 刘应中 《海洋工程：英文版》 2003年第2期151-162,共12页
Great attention has been paid to the development of very large floating structures. Owing to their extreme large size and great flexibility, the coupling between the structural deformation and fluid motion is signific... Great attention has been paid to the development of very large floating structures. Owing to their extreme large size and great flexibility, the coupling between the structural deformation and fluid motion is significant. This is a typical problem of hydroelasticity. Efficient and accurate estimation of the hydroelastic response of very large floating structures in waves is very important for design. In this paper, the plate Green function and fluid Green function are combined to analyze the hydroelastic response of very large floating structures. The plate Green function here is a new one proposed by the authors and it satisfies all boundary conditions for free-free rectangular plates on elastic foundations. The results are compared with some experimental data. It is shown that the method proposed in this paper is efficient and accurate. Finally, various factors affecting the hydroelastic response of very large floating structures are also studied. 展开更多
关键词 hydroelastic response very large floating structure fluid Green function plate Green function thin plate theory free-free rectangular plate
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基于约束等效的背栓式石材幕墙自振频率解及裂缝损伤识别 认领 引用 被引量：5
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作者 杨煌涛 朱元臣 +1 位作者 丛浩楠 王建民 《工业建筑》 2025年第7期30-38,共9页
针对背栓式石材幕墙面板所具有的四边外伸、四点局部背栓(面)约束的相对复杂的构造特征,目前没有相关自振频率理论解用以验证数值模拟和指导试验测试分析。综合考虑实际背栓式石材幕墙面板的约束特征,首先简化等效为沿面板某一方向的线... 针对背栓式石材幕墙面板所具有的四边外伸、四点局部背栓(面)约束的相对复杂的构造特征,目前没有相关自振频率理论解用以验证数值模拟和指导试验测试分析。综合考虑实际背栓式石材幕墙面板的约束特征,首先简化等效为沿面板某一方向的线性约束,再等同于两端外伸简支梁,最后根据无限自由度振动理论得到两端外伸梁自振频率理论解。背栓式石材幕墙模态试验结果表明:试验值与理论解较为接近,并通过数值模拟进行辅助验证;考虑幕墙面板裂缝缺陷,背栓式石材幕墙面板简化模型的相应自振频率与带裂缝的理论解整体也能得到吻合验证。背栓式石材幕墙面板(包括部分带裂缝的面板)所得到的部分振型自振频率理论解可用于验证模拟分析及试验测试结果。 展开更多
关键词 背栓式石材幕墙 自振频率 理论解 数值模拟 矩形薄板
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相邻两边固支其余边自由正交各向异性矩形薄板屈曲的辛叠加解 认领 引用
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作者 王菁龙 额布日力吐 《振动与冲击》 EI CSCD 北大核心 2025年第2期112-119,共8页
运用辛叠加方法求出相邻两边固支其他两边自由(two adjacent edges clamped and the other edges free, CCFF)正交各向异性矩形薄板屈曲问题的级数展开解。首先,将原屈曲问题的控制方程转化为哈密顿系统,通过分析边界条件,将原屈曲问题... 运用辛叠加方法求出相邻两边固支其他两边自由(two adjacent edges clamped and the other edges free, CCFF)正交各向异性矩形薄板屈曲问题的级数展开解。首先,将原屈曲问题的控制方程转化为哈密顿系统,通过分析边界条件,将原屈曲问题分解为两个子屈曲问题,再利用辛本征函数展开法分别求得两个子屈曲问题的通解;然后,利用叠加方法得到原屈曲问题的辛叠加解;最后,应用所得辛叠加解分别计算了单/双向载荷作用下的CCFF各向同性和正交各向异性矩形薄板的屈曲问题。计算结果表明,所得辛叠加解是正确的并且其收敛速度较快。 展开更多
关键词 辛叠加方法 正交各向异性矩形薄板 哈密顿系统 屈曲 辛叠加解
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非线性弹性地基上矩形薄板的主参数共振 认领 引用 被引量：22
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作者 杨志安 赵雪娟 席晓燕 《岩土力学》 EI CAS 北大核心 2005年第12期1921-1925,共5页
分析非线性弹性地基上受参数激励小挠度矩形薄板的主参数共振问题,由冯卡门方程和伽辽金方法得到系统的非线性振动方程,它是杜分-马休型方程,应用非线性振动的多尺度法得到平均方程。数值计算结果表明:阻尼系数、地基系数、几何参数对... 分析非线性弹性地基上受参数激励小挠度矩形薄板的主参数共振问题,由冯卡门方程和伽辽金方法得到系统的非线性振动方程,它是杜分-马休型方程,应用非线性振动的多尺度法得到平均方程。数值计算结果表明:阻尼系数、地基系数、几何参数对主参数共振曲线影响明显。 展开更多
关键词 非线性弹性地基 Galerkin方法 多尺度法 矩形薄板 主参数共振
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矩形薄板在面内随机参数激励下的随机分岔研究 认领 引用 被引量：7
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作者 葛根 王洪礼 许佳 《振动与冲击》 EI CSCD 北大核心 2011年第9期253-258,共6页
建立了四边简支的矩形薄板在受面内随机激励时的振动模型,并用Galerkin法将该系统化简为二自由度常微分非线性动力学方程组。得出系统的广义能量(Hamilton函数)表达式后,又利用拟不可积Hamilton系统平均理论将方程等价为一个一维的Ito... 建立了四边简支的矩形薄板在受面内随机激励时的振动模型,并用Galerkin法将该系统化简为二自由度常微分非线性动力学方程组。得出系统的广义能量(Hamilton函数)表达式后,又利用拟不可积Hamilton系统平均理论将方程等价为一个一维的Ito随机扩散过程,并通过计算该系统的最大Lyapunov指数来研究系统的局部随机稳定性,同时利用基于随机扩散过程的奇异边界理论研究了模型的全局稳定性,最后通过稳态概率密度函数的形状变化探讨了系统参数变化对系统随机Hopf分岔的影响。数值模拟结果验证了理论分析的正确性。 展开更多
关键词 矩形薄板 随机稳定性 随机Hopf分岔
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矩形薄板在面内随机参数激励下的随机稳定性与分岔研究 认领 引用 被引量：6
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作者 葛根 王洪礼 许佳 《振动与冲击》 EI 北大核心 2009年第9期91-94,194,共4页
根据小挠度薄板的弹性理论建立了矩形薄板的受面内随机激励的振动模型,并用Galerkin变分法将其化简为常微分非线性动力学方程。又利用拟不可积Hamilton平均理论将方程等价为一个一维的Ito随机微分方程,并通过计算系统的最大Lyapunov指... 根据小挠度薄板的弹性理论建立了矩形薄板的受面内随机激励的振动模型,并用Galerkin变分法将其化简为常微分非线性动力学方程。又利用拟不可积Hamilton平均理论将方程等价为一个一维的Ito随机微分方程,并通过计算系统的最大Lyapunov指数来研究系统的局部随机稳定性,同时利用奇异边界理论研究了模型的全局稳定性,最后通过稳态概率密度函数的形状研究了系统参数对发生的随机Hopf分岔现象的影响,发现随机Hopf分岔在两个关键值附近发生,数值模拟结果验证了理论分析的正确性。 展开更多
关键词 矩形薄板 Galerkin变分法 随机稳定性 随机Hopf分岔
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焊接残余应力对非线性矩形薄板解的稳定性影响的研究 认领 引用 被引量：3
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作者 高永毅 唐果 +1 位作者 万文 邹声华 《机械强度》 CAS CSCD 北大核心 2016年第6期1289-1293,共5页
根据非线性振动和高等板壳理论,以具有对接焊接残余应力的非线性矩形薄板为研究对象,研究了焊接残余应力对非线性构件解的稳定性影响;得出了具有焊接残余应力的非线性矩形簿板周期解的稳定和不稳定区域随焊接残余应力大小变化而变化和... 根据非线性振动和高等板壳理论,以具有对接焊接残余应力的非线性矩形薄板为研究对象,研究了焊接残余应力对非线性构件解的稳定性影响;得出了具有焊接残余应力的非线性矩形簿板周期解的稳定和不稳定区域随焊接残余应力大小变化而变化和在不同频率范围内,焊接残余应力对周期解稳定性的影响不同以及焊接残余应力整体上是使周期解的稳定区域减少的结论;其结论对具有焊接残余应力的非线性矩形簿板的设计具有一定的指导意义。 展开更多
关键词 焊接残余应力 非线性矩形薄板 周期解 稳定性
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任意边界条件下矩形板薄板自由振动特性分析 认领 引用 被引量：19
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作者 杜圆 李海超 +1 位作者 庞福振 缪旭弘 《振动与冲击》 EI CSCD 北大核心 2019年第19期70-76,共7页
提出一种基于改进傅里叶级数的方法,对矩形薄板在任意边界条件下自由振动特性进行求解。通过将薄板振动的位移函数表示成二维傅里叶余弦级数和辅助级数的线性组合,克服传统傅里叶级数法中薄板位移函数边界处不连续的缺陷;基于位移函数... 提出一种基于改进傅里叶级数的方法,对矩形薄板在任意边界条件下自由振动特性进行求解。通过将薄板振动的位移函数表示成二维傅里叶余弦级数和辅助级数的线性组合,克服传统傅里叶级数法中薄板位移函数边界处不连续的缺陷;基于位移函数列出矩形薄板拉格朗日方程,然后通过Hamilton原理求解得到矩形薄板自由振动频率与相应位移函数的系数。计算结果与文献及有限元解吻合良好,方法准确可靠;此外,通过改变边界约束弹簧刚度模拟任意边界条件;大量计算表明,固支边界条件与弹性边界条件组合中,随着固支边条界范围增大,矩形薄板无量纲频率参数呈增大趋势;简支及自由边界条件与弹性边界条件组合中,随着弹性边条界的增多,矩形薄板无量纲频率参数呈增大趋势。 展开更多
关键词 矩形薄板 振动特性 改进傅里叶级数 弹性边界条件
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静水荷载作用下矩形薄板力学特性研究及其应用 认领 引用 被引量：8
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作者 高俊 党发宁 +2 位作者 李海斌 马宗源 任劼 《应用力学学报》 CAS CSCD 北大核心 2018年第5期1029-1036,共8页
基于平面闸门研究了两种边界条件下矩形薄板在水荷载作用下的挠度、内力、应力的分布规律。利用单三角级数分别构造了两对边简支一边固支一边自由以及三边固支一边自由矩形薄板在水压力作用下的挠曲变形函数,并依据最小势能原理求解了... 基于平面闸门研究了两种边界条件下矩形薄板在水荷载作用下的挠度、内力、应力的分布规律。利用单三角级数分别构造了两对边简支一边固支一边自由以及三边固支一边自由矩形薄板在水压力作用下的挠曲变形函数,并依据最小势能原理求解了挠曲变形函数系数,最后根据薄板小挠度弯曲理论得到了两种边界条件下矩形薄板的内力与应力函数,并对挠度、内力、应力的分布规律进行了比较分析。结果表明,在相同静水压力作用下,两对边简支一边固支一边自由和三边固支一边自由矩形薄板的挠度以及内力分布规律不尽相同,其中三边固支一边自由矩形薄板挠度及背水面出现的最大拉应力值较两对边简支一边固支一边自由矩形薄板的要小。 展开更多
关键词 矩形薄板 最小势能原理 挠曲函数 力学特性
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缺陷对薄板结构振动模态影响的数值与实验分析 认领 引用 被引量：2
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作者 姜益军 姜珊 +2 位作者 陶楠 杨福俊 何小元 《振动工程学报》 EI CSCD 北大核心 2017年第4期564-569,共6页
利用有限元法和电子散斑干涉技术研究了缺陷对矩形薄铝板的振动模态的影响。通过数值模拟和实验测量同时得到了1块完整和4块带有缺陷大小与位置均不同的铝板1~10阶的振型图;铝板的边界条件为长对边自由,短对边固支。结果表明:缺陷的存... 利用有限元法和电子散斑干涉技术研究了缺陷对矩形薄铝板的振动模态的影响。通过数值模拟和实验测量同时得到了1块完整和4块带有缺陷大小与位置均不同的铝板1~10阶的振型图;铝板的边界条件为长对边自由,短对边固支。结果表明:缺陷的存在对薄板结构的共振振型影响较大,而对共振频率的影响较小。共振振型随裂缝的大小、位置和方位的不同而有所变化。研究也表明,有限元计算出的模态形状与实验测量得到的结果一致性较好。 展开更多
关键词 振动测量 模态振型 含裂缝薄矩形板 电子散斑干涉 有限元法
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