一种用于非线性振动系统的模态分析方法

本文提出了一种用于非线性振动系统的模态分析方法,将求解非线性系统模态的问题化为求解非线性特征值、特征向量的问题,利用模态研究系统的响应,文中分析了非线性保守系统、非线性自治系统和非线性非自治系统的线性模态,导出了三个模态包含原理。     

Multidimensional modal analysis of liquid nonlinear sloshing in right circular cylindrical tank

The multidimensional modal theory proposed by Faltinsen,et al.(2000) is applied to solve liquid nonlinear free sloshing in right circular cylindrical tank for the first time. After selecting the leading modes and fixing the order of magnitudes baaed on the Narimanov-Moiseev third order asymptotic hypothesis,the general infinite dimensional modal system is reduced to a five dimensional asymptotic modal system (the system of second order nonlinear ordinary differential equations coupling the generalized time dependent coordinates of free surface wave elevation).The numerical integrations of this modal system discover most important nonlinear phenomena,which agree well with both pervious analytic theories and experimental observations. The results indicate that the multidimensional modal method is a very good tool for solving liquid nonlinear sloshing dynamics and will be developed to investigate more complex sloshing problem in our following work.     

Iterative methods for scattering problems in isotropic or anisotropic elastic waveguides

We consider the time-harmonic problem of the diffraction of an incident propagative mode by a localized defect, in an infinite elastic waveguide. We propose several iterative algorithms to compute an approximate solution of the problem, using a classical finite element discretization in a small area around the perturbation, and a modal expansion in the unbounded straight parts of the guide. Each algorithm can be related to a so-called domain decomposition method, with an overlap between the domains. Specific transmission conditions are used, so that at each step of the algorithm only the sparse finite element matrix has to be inverted, the modal expansion being obtained by a simple projection, using a bi-orthogonality relation. The benefit of using an overlap between the finite element domain and the modal domain is emphasized. An original choice of transmission conditions is proposed which enhances the effect of the overlap and allows us to handle arbitrary anisotropic materials. As a by-product, we derive transparent boundary conditions for an arbitrary anisotropic waveguide. The transparency of these new boundary conditions is checked for two- and three-dimensional anisotropic waveguides. Finally, in the isotropic case, numerical validation for two- and three-dimensional waveguides illustrates the efficiency of the new approach, compared to other existing methods, in terms of number of iterations and CPU time.     

利用多维模态理论分析圆柱贮箱液体非线性晃动

将多维模态理论应用到求解作横向运动圆柱贮箱中液体的非线性晃动问题. 首先通过压力积分变分原理推导出描述液体作非线性晃动的一般形式无穷维模态系统,然后根据Narimanov-Moiseev三阶渐近假设关系,通过选取二阶主模态和三阶次模态,将无穷维模态系统降为五维渐近模态系统. 通过对这个模态系统的数值积分可以看出一些典型的非线性特征(如波峰大于波谷、节径移动等).      

OPERATIONAL MODAL ANALYSIS SCHEMES USING CORRELATION TECHNIQUE

For some large-scale engineering structures in operating conditions, modal parameters estimation must base itself on response-only data. This problem has received a considerable amount of attention in the past few years. It is well known that the cross-correlation function between the measured responses is a sum of complex exponential functions of the same form as the impulse response function of the original system. So this paper presents a time-domain operating modal identification global scheme and a frequency-domain scheme from output-only by coupling the cross-correlation function with conventional modal parameter estimation. The outlined techniques are applied to an airplane model to estimate modal parameters from response-only data.     

Fatigue growth modeling of cracks emanating from a circular hole in infinite plate

This paper presents a numerical approach of fatigue growth analysis of cracks emanating from a hole in infinite elastic plate subjected to remote loads. It involves a generation of Bueckner’s principle and a hybrid displacement discontinuity method (a boundary element method) proposed recently by the senior author of the paper. Because of an intrinsic feature of the boundary element method, a general crack growth problem can be solved in a single region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is modeled conveniently by adding new boundary elements on the incremental crack extension to the previous crack boundaries. As an example, fatigue growth process of an inclined crack in an infinite plate under uniaxial cycle load is modeled to illustrate the effectiveness of the numerical approach. In addition, fatigue growth of cracks emanating from a circular hole in infinite elastic plate subjected to remote loads is investigated by using the numerical approach. Many numerical results are given     

对边夹支无限长板受法向荷载的解析解

本文用积分变换和留数理论得出了对边夹支无限长板受法向荷载的解析解。     

Nonlinear sloshing of liquid in rigid cylindrical container with a rigid annular baffle: free vibration

In this paper, the free nonlinear sloshing of liquid in a rigid partially liquid-filled cylindrical container with a rigid annular baffle is investigated. The liquid domain is firstly divided into four simple sub-domains so that the liquid velocity potential in each sub-domain has continuous boundary conditions of class \(\hbox {C}^{1}\) . Then, based on the Bateman–Luke variational principle, the equivalent variational formulation of the free boundary problem for the liquid in a baffled container is derived. By introducing the generalized time-dependent coordinates, the surface wave height and the velocity potential are expanded in the form of generalized Fourier series. Substituting the series expression of surface wave height and velocity potential into the variational formulation enables us to obtain the infinite dimensional modal system. Finally, based on the Moiseev asymptotic relations, the infinite dimensional modal system is reduced to a finite dimensional modal system. Good agreements have been achieved by comparing the present results with those obtained from the Gavrilyuk’s solutions. The effects of baffle parameters and initial conditions on the nonlinear sloshing of liquid are discussed in detail.     

亏损系统模态优化控制Riccati方程的求解方法

讨论亏损重复特征值的Ｒｉｃｃａｔｉ方程的模态控制算法．由于亏损特征值的Ｊｏｒｄａｎ块矩阵的阶数ｍ小于状态方程的阶数ｎ,即ｍ＜＜ｎ;所提出的模态控制算法可极大地减少计算工作量．其中的数值例子说明了该方法的有效性．     

使用阻尼材料结构的试验模态分析

高分子聚合物做为阻尼材料的使用，使结构的模态分析出现特殊问题，本文介绍试验模态分析中的若干问题，包括模态阶次、模态参数的拟合、模态结构阻尼系数与粘性阻尼系数之间的关系，灵敏度分析等     

Modal parameter identification based on ARMAV and state–space approaches

An accurate prediction for the response of civil and mechanical engineering structures subject to ambient excitation requires the information of dynamic properties of these structures including natural frequencies, damping ratios and mode shapes. Since the excitation force is not available as a measured signal, we need to develop techniques which are capable of accurately extracting the modal parameters from output-only data. This article presents the results of modal parameter identification using two time-domain methods as follows: the autoregressive moving average vector (ARMAV) method and the state–space method. These methods directly work with the recorded time signals and allow the analysis of structures where only the output is measured, while the input is unmeasured and unknown. The equivalence between ARMAV and state–space approaches for the problem of modal parameter identification of vibrating systems is shown in the article. Using only the singular value decomposition of a block Hankel matrix of sample covariances, it is shown that these two approaches give identical modal parameters in the case where the block Hankel matrix has full row rank. The time-domain modal identification algorithms have a serious problem of model order determination: when extracting structural modes these algorithms always generate spurious modes. A modal indicator to differentiate spurious and structural modes is presented. Numerical and experimental examples are given to show the effectiveness of the ARMAV or state–space approaches in modal parameter identification using response data only.     

饱和多孔介质化学-热-弹性模型及应用

本文基于热局部非平衡(LTNE)条件和加权平均温度概念,并假设孔隙流体由溶质和溶剂两组元组成,对页岩（饱和多孔介质）,推导给出了一种LTNE条件下的化学-热-弹性模型,同时讨论了耦合方程组的解耦求解问题．作为模型的应用,考虑无限大平面含一圆形孔的情况,研究了冷/热对流以及溶质摩尔分数突变边界条件下圆孔附近的孔隙压力和化-热应力问题,用Laplace变换得到了平面轴对称情况下有关力学变量的表达式．数值分析了圆孔边界上冷/热对流的Biot数和溶质摩尔分数改变量对圆孔附近孔隙压力和化-热应力的影响．结果表明：在Biot数为中等值(1~5)范围内,LTNE效应是非常明显的;化学作用对孔隙压力和固相应力的影响不可忽视．     

A new matrix perturbation method for analytical solution of the complex modal eigenvalue problem of viscously damped linear vibration systems

A new matrix perturbation analysis method is presented for efficient approximatesolution of the complex modal quadratic generalized eigenvalue problem of viscouslydamped linear vibration systems.First,the damping matrix is decomposed into the sum of aproportional-and a nonproportional-damping parts,and the solutions of the real modaleigenproblem with the proportional dampings are determined,which are a set of initialapproximate solutions of the complex modal eigenproblem.Second,by taking thenonproportional-damping part as a small modification to the proportional one and using thematrix perturbation analysis method,a set of approximate solutions of the complex modaleigenvalue problem can be obtained analytically.The result is quite simple.The new methodis applicable to the systems with viscous dampings-which do not deviate far away from theproportional-damping case.It is particularly important that the solution technique be alsoeffective to the systems with heavy,but not over,dampings.The solution formul     

Slightly open, penny-shaped crack in an infinite solid under biaxial compression

This paper addresses the problem of a slightly open, penny-shaped crack in an infinite solid under in-plane biaxial compression. It presents an analytical model using the equations of elastic stability to determine the stress intensity factor for a specific shape of a slightly open crack surface. This model employs mathematical techniques appropriate for mixed boundary value problems.     

FEM-based reconstruction of sound pressure field damped by partially absorbing boundary conditions

This paper presents an inverse formulation of the acoustic boundary value problem featuring arbitrary admittance boundary conditions. The problem is discretised by using finite elements to reconstruct the sound pressure field of a cavity based on a preferably small number of measurements. For that, a modal approach is investigated to handle the generally under-determined and ill-conditioned system of equations. The viability of the algorithm is tested to reconstruct sound pressure field inside a two-dimensional sedan passenger compartment.     

Non-linear vibrations of free-edge thin spherical shells: modal interaction rules and 1:1:2 internal resonance

This paper is devoted to the derivation and the analysis of vibrations of shallow spherical shell subjected to large amplitude transverse displacement. The analog for thin shallow shells of von Kármán’s theory for large deflection of plates is used. The validity range of the approximations is assessed by comparing the analytical modal analysis with a numerical solution. The specific case of a free edge is considered. The governing partial differential equations are expanded onto the natural modes of vibration of the shell. The problem is replaced by an infinite set of coupled second-order differential equations with quadratic and cubic non-linear terms. Analytical expressions of the non-linear coefficients are derived and a number of them are found to vanish, as a consequence of the symmetry of revolution of the structure. Then, for all the possible internal resonances, a number of rules are deduced, thus predicting the activation of the energy exchanges between the involved modes. Finally, a specific mode coupling due to a 1:1:2 internal resonance between two companion modes and an axisymmetric mode is studied.     

Applied alternating method to analyze the stress concentration around interacting multiple circular holes in an infinite domain

This paper presents an efficient alternating method for analyzing the interactions among multiple circular holes in a two-dimensional infinite domain. An analytical solution is derived for a single circular hole in an infinite domain subjected to the arbitrary tractions across the circle boundary to achieve this purpose. This analytical solution correlates with a successive iterative superposition process capable of satisfying the prescribed boundary condition for each circular hole of the problem. In addition, several perforated plate problems are solved to demonstrate the proposed methods validity. The computed results and the available referenced solutions closely corresponds to each other and indicates the methods accuracy and efficiency.     

核电结构土-结相互作用分析分区混合计算方法

土-结构相互作用分析是核电结构进行抗震设计和安全评估的重要环节.在核电结构的土-结相互作用分析中,阻尼和非线性是影响结构反应的重要因素. 若采用频域分析,可以方便考虑阻尼,但需通过等效线性化来考虑非线性,不适合于强震作用下的土体非线性.若采用时域分析的逐步积分方法,适合于考虑非线性,但材料阻尼一般采用瑞利阻尼模型,除了紧靠指定阻尼比的少数几个振型外,其他振型的反应将受到瑞利阻尼模型所确定的大阻尼所抑制,造成地震反应与真实情形有较大差异.若采用时域分析的模态叠加法,可合理计入阻尼效应,但模态叠加法不能考虑非线性.因此,如何合理考虑阻尼和非线性是核电结构土-结相互作用分析需要关注的问题.基于此,本文提出一种模态叠加和时步积分结合的土-结相互作用分区算法.其中,出于安全性考虑,地震作用下核电主体结构一般不允许进入非线性,因此结构可采用模态叠加方法,以便合理考虑结构阻尼;土体和基础采用显式时步积分法,可考虑土体非线性;通过人工边界条件考虑无限域的影响 (辐射阻尼).通过简单算例对该方法进行了验证,并用于CAP1400核电结构的土-结相互作用分析中,对比分析了采用模态阻尼和瑞利阻尼时核电结构和场地反应的差异,结果表明结构阻尼模型对场地的反应影响不大,但对结构反应影响明显,在实际工程中应合理选取阻尼模型.      

无限长圆管非轴对称问题的Donnell理论的解析解

本文根据圆柱壳体的Ｄｏｎｎｅｌｌ近似理论，用富氏积分变换和留数理论得出了无限胀圆管受非轴对称法向荷载的解析解。     

用声信号识别构件模态频率

本文提出一种新的模态分析方法—用声信号识别构件模态频率.传声器不与结构表面接触,消除了附加质量的影响.同时,结合时间序列谱分析法改善并提高了响应谱的精度.