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基于复数矢径的波叠加法解声辐射问题 总被引:9,自引:0,他引:9
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。 相似文献
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利用满足Laplace方程,线性化自由面条件及无穷远处条件的Havelock兴波源涵数,建立了关于常航速稳态船波势函数的边界积分方程.针对这个积分方程,建立了相应的数值计算方法,编制了一般三维问题的边界元法计算机程序,可用来计算全潜和半潜物体的稳态绕流场及船舶兴波阻力. 相似文献
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伸缩虚拟边界元法解二维Helmholtz外问题 总被引:1,自引:0,他引:1
以位势理论为基础,提出了求解Helmholtz外问题的伸缩虚拟边界元法.给出了该方法在全波数域内获得唯一解的严格数学证明,其核心是通过伸缩虚拟边界使对偶内问题的特征频率(本征值)避开与波数重合,从而保证了解的唯一性,同以往前人提出的几种解法途径相比,该法简单得多;通过诸多边界曲线形状和不同边界量的声辐射算例,从计算精度、稳定性以及克服解的非唯一性等方面,对该方法进行了检验.计算结果表明:对远场或近场辐射声压,该方法都具有非常高的效率和精度. 相似文献
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本文基于非局部弹性理论及辛叠加方法,得到放置在黏弹性介质上四角点支撑矩形纳米板稳态受迫振动问题的解析解.将纳米板受迫振动问题导入哈密顿体系,得到哈密顿控制方程,在无需任何预设函数的情况下可直接对哈密顿控制方程进行求解,得到简支纳米板稳态受迫振动问题在辛空间展开形式的解析解.进而通过边界叠加,可求出四角点支撑纳米板稳态受迫振动的解析解.数值算例中验证了本文应用辛叠加方法得到解析解的准确性,并以石墨烯纳米板为例,分析了非局部参数和黏弹性介质参数对四角点支撑石墨烯纳米板稳态受迫振动的影响.结果表明,非局部参数和黏弹性介质参数的变化会影响石墨烯纳米板的共振频率及共振幅值. 相似文献
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The breaking up of gas filament in liquid is important in many industrial and scientific applications. In this study, a transient axisymmetric model with the level set method is built up to examine the dynamics of a contracting gas filament, and to determine the effects of the aspect ratio, Ohnesorge (Oh) number, and viscosity ratio on its breakup mode. The filament undergoes no break, middle break, or end-pinching modes with increasing aspect ratio at either a low or a high Oh number, and one critical initial aspect ratio is observed for each Oh number. The fate of the filament is determined by the interaction of capillary waves on its surface, and can be predicted accurately by using the one-dimensional wave superposition method. The decreasing viscosity ratio of liquid over gas reduces the critical initial aspect ratio for the fate transition between the no break and breakup modes, and this effect is reduced at a low viscosity ratio. These findings may be helpful in fabricating gas bubbles and their breakup suppression. 相似文献
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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. 相似文献
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计算特征向量摄动量的混合基展开法 总被引:1,自引:0,他引:1
在结构修改和模型校正中,模态展开法是计算特征向量摄动量的常用方法之一,但当高阶模态被截断时,它会带来很大的截断误差。本文利用已知的有限阶模态,构造了N维欧氏空间的一个新基-混合基,并将特征向量的摄动量在新基上展开来计算特征向量的一、二阶 摄动量。该方法使得不管截模态个数的多少,其精度总与全模态展开法相同,且计算量都远少于全模记展开法;与改进的部分民开法相比,本方法不要求所截留的模态边连续的低阶模态 相似文献
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By observing experimentally obtained photoelastic fringe patterns and applying classical solutions for an infinite plate containing
a circular hole under remote tension and the modified Hertz contact theory, a replaced superposition method is proposed. In
this paper we use this method to investigate the state of stress around a near-surface circular hole in a semi-infinite plate
under a concentrated load. The well-matched conditions between the reconstructed and experimental photoelastic fringe patterns
indicate the applicability of the proposed method.
This paper was presented, in part, at a symposium honoring Dr. Christian P. Burger, Novel Applications of Experimental Methods in Mechanicsheld at the 2003 SEM Annual Conference and Exposition on Experimental and Applied Mechanics, June 2–4, 2003, Charlotte, North
Carolina. 相似文献
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A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free
field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized
on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method
with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed
into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements
of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on
the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed
method has high accuracy and good stability.
The project supported by the National Natural Science Foundation of China (50478014), the National 973 Program (2007CB714200)
and the Beijing Natural Science Foundation (8061003).
The English text was polished by Yunming Chen. 相似文献
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The objective is to present exact analytical solutions of longitudinal impact analysis for slender conical rods struck by a particle and a new method is proposed for conical rod-particle impact analysis, in which the superposition method is used and the response of the rod is presented. These analytical results are exact and can be used to validate the numerical methods or other analytical results. The numerical example shows that one of the advantages of the present method is that the analytical form is very simple. The result is that mass ratio and some variables describing the geometrical shape of rods such as taper, length and radius play an important role in impact dynamic system. 相似文献
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The article gives a semi-discrete method for solving high-dimension wave equation. By the method, high-dimension wave equation
is converted by means of discretization into I-D wave equation system which is well-posed. The convergence of the semidiscrete
method is given. The numerical calculating results show that the speed of convergence is high. 相似文献
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Lanczos向量叠加法的改进及其在高层结构动力分析中的应用 总被引:1,自引:1,他引:0
本文柔度法形成高层建筑结构的动力方程,在对现有Lancoz向量叠加法改进后,建立了用改进的Lanczos向量叠加法进行高层建筑结构的动力计算的具体步骤与原则。 相似文献
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H. M. Wang H. J. Ding Y. M. Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2005,74(9):581-599
The dynamic solution of a multilayered spherically isotropic piezoelectric hollow sphere subjected to radial dynamic loads is obtained. By the method of superposition, the solution is divided into two parts: one is quasi-static and the other is dynamic. The quasi-static part is derived by the state-space method, and the dynamic part is obtained by the method of separation of variables coupled with the initial parameter method as well as the orthogonal expansion technique. By using the quasi-static and dynamic parts, the electric boundary conditions as well as the electric continuity conditions, a Volterra integral equation of the second kind with respect to a function of time is derived, which can be solved successfully by means of the interpolation method. The displacements, stresses and electric potentials are finally obtained. The present method is suitable for a multilayered spherically isotropic piezoelectric hollow sphere consisting of arbitrary layers and subjected to arbitrary spherically symmetric dynamic loads. Finally, numerical results are presented and discussed. 相似文献
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研究了梁中的非线性弯曲波的传播特性,同时考虑了梁的大挠度引起的几何非线性效应和
梁的转动惯性导致的弥散效应,利用Hamilton变分法建立了梁中非线性弯曲波的波动方程.
对该方程进行了定性分析,在不同的条件下,该方程在相平面上存在同宿轨道或异宿轨道,
分别对应于方程的孤波解或冲击波解. 利用Jacobi椭圆函数展开法,对该非线性方程进行
求解,得到了非线性波动方程的准确周期解及相对应的孤波解和冲击波解,讨论了这些解存
在的必要条件,这与定性分析的结果完全相同. 利用约化摄动法从非线性弯曲波动方程中导
出了非线性Schr\"{o}dinger方程,从理论上证明了考虑梁的大挠度和转动惯性时梁中存在
包络孤立波. 相似文献
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以Miner、Boltsman叠加原理为代表的线性叠加原理在探讨低应力水平的蠕变叠加作用时存在很大困难,文章对此进行了分析讨论,并在此基础上建议了一种非线性叠加原理,在实际应用中得到了很好的验证. 相似文献