共查询到18条相似文献,搜索用时 265 毫秒
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多自由度复模态理论的摄动方法(二)——重特征值及高阶摄动 总被引:1,自引:1,他引:1
本文是《多自由度复模态理论的摄动方法(一)一阶摄动》[1]的继续,讨论重特征值及高阶摄动修正问题,对于有重特征值的实模态摄动修正已有论述,本文将论述复特征值的修正。一般而言,一阶摄动已有足够精度,但当参数变化范围稍大时,需要二阶或更高阶的摄动修正,Meirovitch等人讨论了无阻尼,非陀螺系统的二阶摄动修正,并用于响应计算。当阻尼系数增大时,复特征值的误差将随之增大。本文将给出二阶摄动修正及任意阶摄动修正,从而得到二阶及二阶以上的复特征值及复特征矢量的近似公式。Aubrun采用Jacobin公式讨论了有阻尼系统的摄动解,给出了一阶及二阶的阻尼,频率修正公式及一阶复模态,但是由于非按照正规的摄动方法来求解,其一阶阻尼系数与本文虽一致,但对频率则无修正,阻尼对复模态的修正也只有虚部而无实部。为了改善收敛速度,本文提出了将阻尼阵中可对角化部分作为与质量,刚度阵同量级列入方程,而不可对角化部分列入一阶摄动量。这种改进的摄动法以复特征值及实振型为零阶近似,从而可以提高精度改善收敛速度,使对阻尼阵作为一阶小量的限制放宽。作为复模态理论摄动法的应用,讨论了陀螺特征值问题。文末并给出了简单的算例。 相似文献
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非对称矩阵特征值问题密集模态重分析方法 总被引:1,自引:0,他引:1
本文提出了一种非对称矩阵特征值问题的密集模态重分析方法,它将原密集特征问题表达为与其临近的某一重特征值的小摄动。从而密集模态的重分析问题就转重频模态的重分析问题。 相似文献
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本文采用以模态迭加原理为基础的实模态分析技术及初参数优选法对汽车车架的模态参数进行了识别,讨论了振动特征值问题中关于非重特征值和重特征值的矩阵摄动法,提出了利用有弹性元件悬挂的结构振动测试数据来得到自由——自由结构的模态参数的摄动修正方法.文中还给出了一些数值例子来说明此方法的应用,同时得到了一些重要结论. 相似文献
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基于有限元分析的特征值反问题求解的逆摄动方法 总被引:2,自引:0,他引:2
本文研究特征值反问题的求解方法,根据广义特征值反问题理论和有限元法的特点,以转子系统平面梁单元有限元模型结构分析的特征值反问题求解为例,给出一种新的逆摄动方法,给出了本逆摄动法较完整的理论基础,给出了其逆摄动参数的显式计算公式及相应的取值方法,本逆摄动法也可推广到其他单元类型的有限元模型特征值反问题的求解。 相似文献
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密集模态摄动的新方法 总被引:11,自引:0,他引:11
本文提出了一种密集模态结构系统(M_0,K_0)振动分析的矩阵摄动新方法.它将密集模态结构系统特征解的摄动问题转化为重特征值的摄动问题.文中给出了一个数值例子. 相似文献
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本文给出了一种适用于迭代计算的矩阵摄动法,它是进行广义特征值问题Ax=λBx的摄动重分析的一种高精度算法,同时也可用于改进由其它矩阵摄动分析方法提供的近似解的精度。实际算例表明,当结构参数修改量不太大时,采用这种摄动迭代法进行特征值问题的精确重分析是十分有效的。 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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对非自伴随系统的振动重分析问题,提出了一种简单的通用方法。从子空间缩聚出发,基于复矩阵的奇异值分解定理,推导了同时适用于孤立 特征值,相重特征值和相近特征值三种复特征值情况的一阶和二阶摄动公式。算例表明,该方法通用性好,且具有足够的精度。 相似文献
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多自由度系统复模态理论的摄动方法——(一)一阶摄动 总被引:2,自引:1,他引:2
除了阻尼矩阵满足一定条件外,有阻尼多自由度线性系统运动方程,在一般情况下不能通过实模态变换而解耦。因此,许多情况下工程结构动力分析需要寻求系统的复模态和复特征值,为此如Foss.Frazy and Bishop等提出的惯用方法又太复杂和不经济。本文采用基于实模态理论的摄动方法,耒求解系统的复模态和复特征值,考虑到阻尼力比惯性力和弹性恢复力要小是符合工程实际的,把系统的模态和特征值按不同的量级展成级数,从而建立起各阶渐近方程,其零阶方程对应于无阻尼系统可按实模态理论求解,如果需要,可按高阶方程逐次求解得到复模态和复特征值各阶渐近修正。本方法不仅计算方便而且经济,其结果易于从零阶和一阶近似中得到复模态和复特征值,对于自由振动运动方程同样可以解耦。利用已得到的一阶复模态的结果,讨论了自由振动和强迫振动问题。文末给出了算例以说明本方法的计算精度。 相似文献
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In existing studies, the well-known Hencky problem, i.e. the large deflection problem of axisymmetric deformation of a circular membrane subjected to uniformly distributed loads, has been analyzed generally on small-rotation-angle assumption and solved by using the common power series method. In fact, the problem studied and the method adopted may be effectively expanded to meet the needs of larger deformation. In this study, the classical Hencky problem was extended to the problem without small-rotation-angle assumption and resolved by using the perturbation idea combining with power series method. First, the governing differential equations used for the solution of stress and deflection in the perturbed system were established. Taking the load as a perturbation parameter, the stress and deflection were expanded with respect to the parameter. By substituting the expansions into the governing equations and corresponding boundary conditions, the perturbation solution of all levels were obtained, in which the zero-order perturbation solution exactly corresponds to the small-rotation-angle solution, i.e. the solution of the unperturbed system. The results indicate that if the perturbed and unperturbed systems as well as the corresponding differential equations may be distinguished, the perturbation method proposed in this study can be extended to solve other nonlinear differential equations, as long as the differential equation of unperturbed system may be obtained by letting a certain parameter be zero in the corresponding equation of perturbed system. 相似文献
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This paper presents a new method for perturbation analysis of vibration modes with close frequencies. The main idea of this method is to transform the perturbation analysis problem of vibration modes with close frequencies into a perturbation problem associated with repeated frequencies. A numerical example is given to demonstrate the good agreement of eigensolutions obtained by this method with the exact solutions.This project is supported by National Natural Science Foundation of China 相似文献
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A Universal Matrix Perturbation Technique for Complex Modes 总被引:1,自引:0,他引:1
IntroductionMatrixperturbationmethodsforthedynamicreanalysisofself_adjointsystemshavebeenwelldeveloped[1] .However,manysystemsgiverisetogeneralnon_self_adjointformulations.Importantexamplesareaeroelasticstabilityofsystems,arbitrarilydampedorgyroscopicsys… 相似文献
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Summary Singular fields and higher order fields near a sharp notch in a power-law material under longitudinal shear are investigated. Using the perturbation method the whole set of eigenvalues is determined. The higher order eigensolutions are constructed by use of the dominant singular solution. Some examples, including the special case of a crack are discussed for different boundary conditions.
Dedicated to Prof. Dr.-Ing. F. G. Kollmann on the occasion of his sixtieth Birthday 相似文献
Felder höherer Ordnung an Riß- und Kerbspitzen unter nichtebener Schubbelastung in Materialien mit Potenzverfestigungsgesetz
Übersicht Untersucht werden singuläre Felder und Felder höherer, Ordnung an Spitzkerben unter nichtebener Schubbelastung in Materialien mit Potenzgesetz. Die Eigenwerte werden mittels der Störungsrechnung ermittelt. Die Bestimmung der Eigenlösungen höherer Ordnung erfolgt unter Verwendung der dominierenden singulären Lösung. Einige Beispiele, die auch den Spezialfall des Risses einschließen, werden für unterschiedliche Randbedingungen diskutiert.
Dedicated to Prof. Dr.-Ing. F. G. Kollmann on the occasion of his sixtieth Birthday 相似文献
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Chun Nam Wong Hong-Zhong Huang Jingqi Xiong Hua Long Lan 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(4):451-472
A general method is formulated to estimate damage location and extent from the explicit perturbation terms in specific set
of eigenvectors and eigenvalues. At first, perturbed orthonormal equation is generated from the perturbation of eigenvectors
and eigenvalues to obtain the k-th explicit perturbation coefficients. At second, perturbed eigenvalue equation is generated from the perturbation of eigenvector
and eigenvalue, and first-order expansion of the stiffness matrix to obtain other explicit perturbation coefficients. Stiffness
parameters are computed from these equations using an optimization method. The algorithm is iterative and terminates under
certain criteria. A fixed–fixed modular beam with various numbers of elements is used as test structure to investigate the
applicability of the developed approach. By comparison with the Euler–Bernoulli beam, discretization errors are analyzed.
In six elements beam, first-order algorithm converges faster for small percentage damage. Second-order algorithm is more efficient
for medium percentage damage. For large percentage damage, the second-order algorithm converges more effectively. Meanwhile,
for eight elements large percentage damage and ten elements small percentage damage, second-order algorithm converges faster
to the termination criterion. 相似文献