旋转相似载荷下轴对称结构弹性响应的快速算法:旋转叠加法及其应用

基于叠加原理,采用坐标旋转和线性叠加的方法,建立了求解旋转相似载荷下轴对称结构弹性响应的快速算法--旋转叠加法.文章首先给出了"旋转相似载荷"的定义,推导了相关计算公式,然后给出了一个应用实例,验证了算法的正确性和有效性,最后对相关问题进行了讨论.旋转叠加法巧妙利用了叠加原理和结构的轴对称性,对同一结构只需一次分析,即...     

利用叠加理论研究固-液声子晶体纵波的能带结构

采用相干叠加原理推导出一种研究一维固-液有限周期声子晶体中纵波的透射率公式,建立了一种研究一维固-液有限周期声子晶体能带的新方法——波叠加理论。将波叠加理论和转移矩阵法进行了比较研究,结果表明波叠加理论和转移矩阵法得出的结果是一致的。波叠加理论不仅具有转移矩阵法的优点,而且又克服了转移矩阵法的不足。因此波叠加理论是一种研究一维固-液有限周期声子晶体中纵波能带的更为有效的方法。     

声子晶体中SH波缺陷模的相干叠加理论

利用波的相干叠加原理推导出一维掺杂声子晶体中SH波缺陷模的透射率公式和频率公式,即建立了缺陷模的相干叠加法。将相干叠加法与转移矩阵法和共振理论进行了比较研究,结果表明缺陷模的相干叠加法具备转移矩阵法和共振理论各自的优点,又克服了转移矩阵法和共振理论各自的不足。相干叠加法是研究一维掺杂声子晶体中SH波缺陷模的一种更有效的方法。     

用边缘荷载格林函数方法计算含裂纹Reissner型有限板的弯曲

本文在文献[1]所得到的受边缘荷载格林函数基本解方法基础上,利用叠加原理,通过边界积分方程的方法,分析了含裂纹Reissner型板的弯曲断裂问题。计算表明方法正确,便于应用。     

开口正方形板的应力分析(一)

根据Muskhelishvili的方法,给出了借助于多项式将正方形孔保角映射到单位圆的边值问题的通解,并通过叠加原理给出了双连通域边值问题的解。做为例子给出了开口正方形板在剪力作用下的应力分布。     

三边简支一边自由混凝土矩形薄板的热弯曲

基于薄板的小挠度理论和叠加原理,考虑横向变温情况,将温度作用下的三边简支一边自由矩形薄板看作是面内温差作用下的四边简支矩形薄板和自由边上挠度作用下的三边简支一边自由矩形薄板的叠加,得到了温度作用下三边简支一边自由混凝土矩形薄板的挠度和弯矩解析解.首先通过在自由边界上试设具有待定参数的挠度函数,采用李维解法推导出三边简支一边自由矩形薄板在自由边界挠度作用下的挠度方程;其次利用横向变温作用下四边简支矩形薄板的求解得到待定参数;再采用叠加原理得出横向变温作用下三边简支一边自由矩形薄板的挠度和弯矩解析解;最后利用MATLAB编制程序得到了横向变温作用下三边简支一边自由矩形薄板的计算系数用表,为工程结构中三边简支一边自由混凝土矩形薄板在热环境下的设计计算提供了理论依据.     

求解轴对称结构侧向冲击响应的一种快速算法

轴对称结构在侧向冲击载荷下的动力响应分析,一般采用解析、半解析法或者直接进行有限元数值模拟,这些方法均有一定的局限性.本文依据线性动力学问题的叠加原理,提出了一种基于有限元分析和线性叠加的快速算法.该方法首先采用多条母线对载荷进行离散,然后采用有限元计算结构在单个"载荷单元"作用下的动力响应,最后采用坐标旋转和线性叠加的方法计算得到结构在复杂分布载荷作用下的响应.算例表明,本文提出的算法是正确、有效的,并且具有快速、简便、灵活的特点.     

巧解铅球最佳出手角

利用运动叠加原理通过对铅球运动的恰当分解, 提出了一种计算最佳出 手角的新方法, 并与传统方法就两种不同情形进行了对比, 说明了新方法的物理思想.     

一种新的振动叠加气动耦合加载技术

飞机机动飞行时,机体结构受到随机振动叠加气动的耦合载荷作用,有可能迅速产生破坏。为了考核在这种振动环境下飞机的结构强度及使用寿命能否达到设计要求,需要提供有效的地面试验验证手段和可靠的试验数据。本文研究了一种振动叠加气动的耦合载荷加载技术,通过液压球头传递振动载荷,同时通过气囊施加气动载荷,并设计进行了原理性验证试验。试验结果表明,这种耦合载荷加载技术可以避免过多改变试件自身的振动特性,同时可精确实现振动叠加气动的耦合载荷加载,真实模拟试验件的振动工作环境。此项技术可应用于现代战机的地面结构强度研究。     

用叠加法求阶梯轴的变形

当一根梁只有横向外力及力偶而无轴向外力作用时,计算梁的弯矩和建立弹性曲线方程,我们都利用了梁的“小变形假设”,因此在几种载荷作用时,梁在任意截面处的转角和挠度,可以按照力的独立作用原理,将各个载荷单独作用时在梁上所引起的该截面的转角和挠度进行叠加而求得。从本质上来说,叠加法不是一个独立的方法,它只是利用     

WAVE SUPERPOSITION METHOD BASED ON VIRTUAL SOURCE BOUNDARY WITH COMPLEX RADIUS VECTOR FOR SOLVING ACOUSTIC RADIATION PROBLEMS

By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.     

基于复数矢径的波叠加法解声辐射问题

利用波叠加法与结构动力分析中的相似性，提出了一种在波叠加法中克服解非唯一的通用方法，即在虚拟源强系统中加入一定的虚拟阻尼从而能获得全波数域内的唯一解，并以此为基础提出了一种新的加入虚拟阻尼的方法——复数矢径波叠加法。文中给出了脉动球和摆动球两个数值算例，计算结果表明：本文方法不仅能有效解决数值求解过程中解非唯一的问题，且计算时间只与标准波叠加法相当，计算精度却比同类方法高。     

Dynamics of an exponentially damped solid rod: Analytic solution and finite element formulations

This paper presents the analytic solution together with two finite element formulations to obtain the dynamic response of an exponentially damped solid rod. The analysis is carried out in time domain, the material being modeled by the standard linear viscoelastic solid model. On the one hand, the analytic solution is reached by means of modal superposition by two different ways: with and without internal variables. On the other hand, two different finite element formulations are proposed: the first one is conceived for direct integration methods, and the other one is developed to apply modal superposition. The interest of modal superposition method lies on investigating the influence of non-viscous modes.     

Solution of bending of cantilever rectangular plates under uniform surface-load by the method of two-direction trigonometric series

The bending of a cantilever rectangular plate is a very complicated problem in thetheory of plates.For a long time,there have been only approximate solutions for thisproblem by energy methods and numerical methods.since 1979,Prof.F.V.Chang of Tsing Hua University obtained,by the method ofsuperposition,a series of analytic solutions for cantilever rectangular plates under uniformload and concentrated load.In this paper,the two-direction trigonometric series is used to obtain the solution forthe bending of cantilever rectangular plates under uniform load.The obtained results arecompared with the results by the method of superposition.The comparison shows that theresults of these two methods are in good agreement,hence they are mutually confirmed to becorrect.     

Winkler地基上四边自由正交各向异性矩形薄板弯曲问题的辛叠加解

研究Winkler地基上正交各向异性矩形薄板弯曲方程所对应的Hamilton正则方程, 计算出其对边滑支条件下相应Hamilton算子的本征值和本征函数系, 证明该本征函数系的辛正交性以及在Cauchy主值意义下的完备性, 进而给出对边滑支边界条件下Hamilton正则方程的通解, 之后利用辛叠加方法求出Winkler地基上四边自由正交各向异性矩形薄板弯曲问题的解析解. 最后通过两个具体算例验证了所得解析解的正确性.     

Superposition principles for small amplitude oscillatory shearing of nematic mesophases

The linear viscoelasticty of Leslie-Ericksen monodomain liquid crystals subjected to a bend distortion through a small amplitude oscillatory shear flow driven by harmonic wall stress is analyzed, using numerical and asymptotic methods. The viscoelastic material functions were derived using a new scaling approach that extracts the material parameters that control superposition. Small and high frequency superposition schemes for linear viscoleasticity were derived. The schemes were successfully applied to collapse the predicted loss and storage linear viscoelastic moduli of seven experimental data sets. Comparisons between different shear flows (simple shear and capillary Poiseuille) and different director distortion modes (splay and bend) shows that the superposition schemes are applicable to shear flows in any single director distortion mode.     

基于频率相关黏性阻尼模型的复模态叠加法

黏性阻尼模型存在每周期耗散能量与外激励频率相关的缺陷, 复阻尼模型时域计算结果存在发散现象. 为克服上述两种阻尼模型的不足, 在复阻尼模型基础上, 依据时频域转化原则推导了频率相关黏性阻尼模型. 频率相关黏性阻尼模型不仅具有每周期耗散能量与外激励频率无关的优点, 还保证了结构位移时程的稳定收敛. 混合结构由具有不同阻尼特性的材料组成, 其阻尼矩阵为非比例矩阵, 无法直接采用实模态叠加法. 根据频率相关黏性阻尼模型与复阻尼模型的转换关系, 提出了适用于混合结构的基于频率相关黏性阻尼模型的复模态叠加法. 算例分析结果表明, 与基于黏性阻尼模型的复模态叠加法相比, 基于频率相关黏性阻尼模型的复模态叠加法不仅计算结果唯一, 且不增加矩阵维度, 具有较高的计算效率. 小阻尼情况下, 两种方法的计算结果近似相等, 且与复阻尼模型的频域计算结果一致. 当阻尼比较大时, 两种方法的计算结果差异增大, 但频率相关黏性阻尼模型的复模态叠加法与复阻尼模型的频域计算结果仍保持一致.      

On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years. The method has yielded many new analytic solutions due to its rigorousness. In this study, the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge. The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied. The solution procedure incorporates separation of variables, symplectic eigen solution and superposition. The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems. The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use. The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.     

Matlab编程实现求解基于振型叠加法的多自由度动力学系统的时域和频域响应

给出了求解多自由度动力学系统响应的M atlab程序,这些程序基于振型叠加法可用于求解由质量矩阵M和刚度矩阵K以及常见阻尼矩阵描述的线性离散系统的时域和频域解.对于无阻尼系统,用户可以选择数值解或符号解析解(以时间或频率表示),并利用复模态叠加法计算了阻尼系统的数值解.总结了模态叠加方法下动力学响应的求解,并在简短的M atlab程序中实现.以三自由度系统和悬臂梁模型为例说明了程序的应用.这些程序也可用于工程应用中,通过对商用有限元软件包产生的质量和刚度进行后处理,产生感兴趣的时域和频域响应.     

On new symplectic superposition method for exact bending solutions of rectangular cantilever thin plates

A novel superposition method based on the symplectic geometry approach is presented for exact bending analysis of rectangular cantilever thin plates. The basic equations for rectangular thin plate are first transferred into Hamilton canonical equations. By the symplectic geometry method, the analytic solutions to some problems for plates with slidingly supported edges are derived. Then the exact bending solutions of rectangular cantilever thin plates are obtained using the method of superposition. The symplectic superposition method developed in this paper is completely rational compared with the conventional analytical ones because the predetermination of deflection functions, which is indispensable in existing methods, is dispelled.