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1.
Dynamic equilibrium equations of structural systems with non‐proportional damping are coupled through the damping terms. Such coupling invalidates application of the classical modal superposition method. In this paper, a mode‐superposition pseudo‐force method is proposed. The coupled equilibrium equations are solved by an iterative process in which the coupling terms are treated as pseudo‐forces. A scale factor for each mode of the system is obtained by optimizing the iteration convergence. Through these uniquely solved scale factors, the modified modal equations not only converge much faster but also yield results with higher accuracy. A proof of the convergence of the iterative process is also presented. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
2.
Spectral analysis of systems with non-classical damping using classical mode superposition technique
A spectral method for random vibration analysis of a structural system with non-proportional damping is presented using classical (undamped) mode superposition technique. The method obtains the frequency response function of the system by solving the dynamic equilibrium equations in generalized co-ordinates through an iterative process. The iterative solution is written in closed form and the proof for convergence of the iterative process is given. Numerical examples show the convergence characteristics of the process and an excellent accuracy of the obtained results. The method turns out to be computationally more efficient than the conventional methods of spectral analysis using damped mode shapes and frequencies. 相似文献
3.
Non-proportional damping may be defined as a form of linear viscous damping which introduces coupling between the undamped modal co-ordinate equations of motion. The standard mode superposition method of earthquake response analysis therefore cannot be employed with non-proportionally damped structures. In this paper, several methods for analysing the dynamic response of non-proportional damped structures are outlined. It is concluded that the most efficient procedure is to express the response in terms of a truncated set of undamped modal coordinates and to integrate directly the resulting coupled equations. The effectiveness of the method is demonstrated by a numerical example. 相似文献
4.
基于复模态的有限元模型修正算法 总被引：2，自引：0，他引：2
针对地下结构地震响应分析中无限地基辐射阻尼问题，引入复模态情况下的具有非简化的堆积阻尼矩阵的阻尼模型，并针对具有集中质量阵的阻尼模型提出了合并与质量有关的阻尼和堆积阻尼的思想，并据此提出了一种修正此类有限元模型的两步法，首先从复模态参数中提取实模态参数，采用基于模态残余力的识别算法修正刚度矩阵，然后根据复模态参数和已得的刚度矩阵来识别阻尼模型中的刚度参与系数和质量阻尼堆积阻尼联合矩阵。 相似文献
5.
Diagonal damping matrices were computed for three systems which have non-proportional damping matrices. These diagonal damping matrices were computed on three bases, as follows: 1. After normalizing the equations of motion by the modal matrix, the diagonal terms are retained ignoring the non-diagonal terms. 2. Diagonal damping matrix is established by the optimization algorithm which minimizes the mean square error of the frequency response. 3. Diagonal damping is determined from the normalized differential equation by matching the peaks of the coupled and uncoupled system. The frequency responses for the three cases of one of the three systems are presented together with a comparison of the energy dissipation. 相似文献
6.
钢结构与混凝土结构阻尼比不同,混凝土房屋与其顶上钢塔组成了非比例阻尼结构系统。本文用非经典振型分解法求解该类结构系统的线弹性地震响应,发现只用前几阶振型响应迭加的结果即可逼近直接积分法的精确度。 相似文献
7.
Non-classically damped structural systems do not easily lend themselves to the modal superposition method because these systems yield coupled second-order differential equations. In this paper, a variety of new computationally efficient iterative methods for determining the response of such systems are developed. The iterative approaches presented here differ from those presented earlier in that they are computationally superior and/or are applicable to the determination of the responses of broader classes of structural systems. Numerical examples, which are designed to evaluate the efficacy of these schemes, show the vastly improved rates of convergence when compared to earlier iterative schemes. 相似文献
8.
R. W. Traill-Nash 《地震工程与结构动力学》1981,9(2):153-169
When damping in a system is both significantly high and its distribution is non-classical the solution of dynamical problems by conventional modal analysis is complicated by the presence of coupling between the normal co-ordinates. Further, the convergence of a solution may be erratic with successive modal additions, leading to the need to include a larger number of modes than would otherwise be expected. In this paper methods of modal analysis in structural dynamics are discussed and their derivations briefly given. These include the conventional mode displacement method and the force summation method, employing normal modes, and the analogous procedures with damped modes. In the latter, dynamic response equations are not coupled. Dynamic loading solutions by the four approaches, each taking account of the non-classical damping distribution, are demonstrated with a simple model representing a structure on a compliant foundation. The results strongly suggest that the use of damped modes with force summation could be the most effective procedure when damping is non-classical. 相似文献
9.
Closed‐form solution for seismic response of adjacent buildings connected by hydraulic actuators with linear quadratic Gaussian (LQG) controllers is presented in this paper. The equations of motion of actively controlled adjacent buildings against earthquake are first established. The complex modal superposition method is then used to determine dynamic characteristics, including modal damping ratio, of actively controlled adjacent buildings. The closed‐form solution for seismic response of the system is finally derived in terms of the complex dynamic characteristics, the pseudo‐excitation method and the residue theorem. By using the closed‐form solution, extensive parametric studies can be carried out for the system of many degrees of freedom. The beneficial parameters of LQG controllers for achieving the maximum response reduction of both buildings using reasonable control forces can be identified. The effectiveness of LQG controllers for this particular application is evaluated in this study. The results show that for the adjacent buildings of different dynamic properties, if the parameters of LQG controllers are selected appropriately, the modal damping ratios of the system can be significantly increased and the seismic responses of both buildings can be considerably reduced. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
10.
非比例阻尼线性体系地震反应计算的振型分解反应谱法 总被引：2，自引：0，他引：2
汪梦甫 《地震工程与工程振动》2007,27(1):31-37
以非比例阻尼线性体系地震反应计算实数形式的一般解答为基础,推导得到了非比例阻尼线性体系水平地震作用计算的多种形式,建立了非比例阻尼线性体系地震反应计算振型分解反应谱法的基本过程与步骤。最后,以一个五层剪切型结构为例,通过与各种常用直接积分方法计算结果的比较,证实了本文非比例阻尼线性体系地震反应计算实数形式的一般解答的高精度与可靠性。通过对多种形式地震作用所得地震效应的比较,证实了非比例阻尼线性体系地震反应振型分解反应谱方法的可靠性及可行性。 相似文献
11.
A method to determine the approximate normal modes and the modal damping for torsionally coupled buildings on an elastic foundation is presented. The modal damping is determined by an iterative procedure which matches the approximate normal mode solution with the rigorous solution. The response quantity to be matched is selected in a consistent and logical manner. The normal modes and the damping ratios thus found are then used to determine the seismic response of the interaction system by the response spectrum technique. 相似文献
12.
Computational algorithms based on the pseudo-force method (PFM) and the tangent spectrum method (TSM) for the seismic analysis of elasto-plastic MDOF structures by mode superposition are presented. The emphasis is put on the effect of the truncation of higher modes on the convergence of the ductility demand and energy dissipated during the earthquake. Eigenvectors and load-dependent vectors have been used in comparative analyses. Applications on a flexible 25-storey building and a stiff, 5-storey shear building indicate that, for a flexible structure, the ductility demand computed from the PFM is more sensitive to basis truncation than that computed from the TSM. However, for the stiff structure, the opposite behaviour is observed. The results indicate that the use of load-dependent vectors in inelastic analyses maintains the computational advantages found for elastic analyses in previous investigations. Although the PFM is more stable and computationally more effective than the TSM, it does not provide any information on the evolution of tangent modal properties in time that reflects dynamic response modification as the structure becomes inelastic. 相似文献
13.
The equations of motion of a structure in undamped modal coordinates may have non-zero off-diagonal terms in the damping matrix. Although these terms are commonly neglected, studies have shown that they may have a significant influence on the response to dynamic loads. In this paper, two independent criteria are developed to determine when these damping terms will affect the structure's modal properties and response. It is found that even small off-diagonal damping values can be significant if the structure has closely spaced natural frequencies. To quantify and understand the influence of these damping terms, closed-form analytical expressions are derived for the modal properties and harmonic and stochastic response of structures with closely spaced natural frequencies. One conclusion is that off-diagonal damping terms will decrease a modal damping ratio for each pair of closely spaced modes. This is significant, since a response analysis performed by neglecting these off-diagonal terms will underestimate the true response. 相似文献
14.
S. T. Mau 《地震工程与结构动力学》1988,16(6):931-942
For structures with non-proportional damping, complex eigenvectors or mode shapes must be used in order to decoe the equations of motion. The resulting equations can then be solved in a systematic way. The necessity of solvie complex eigenvalue problem of a large system remains an obstacle for the practical application of the method. This stres utilizes the fact that in practice only a small number of the complex modes are needed. Therefore, these complex modes be approximated by a linear combination of a small number of the undamped modes, which can be obtained by established methods with less cost. An additional eigenvalue problem is then solved in a subspace with a much sm dimension to provide the best combination coefficient for each complex mode. The method of solution for the decoue equations is then carried over, using the approximate complex modes expressed in undamped mode shapes, to resue simple formulas for the time- and frequency-domain solution. Thus, an efficient modal superposition method is develoe for non-proportionally damped systems. The accuracy of this approximate method is studied through an example. Comparing the frequency response result using the approximate method with that using the exact complex modes, found that the error is negligible. 相似文献
15.
Coupling adjacent buildings using discrete viscoelastic dampers for control of response to low and moderate seismic events is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristics, mainly modal damping ratio and modal frequency, of damper-linked linear adjacent buildings for practical use. Random seismic response of linear adjacent buildings linked by dampers is then determined by a combination of the complex modal superposition method and the pseudo-excitation method. This combined method can effectively and accurately determine random seismic response of non-classically damped systems in the frequency domain. Parametric studies are finally performed to identify optimal parameters of viscoelastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of adjacent buildings. It is demonstrated that using discrete viscoelastic dampers of proper parameters to link adjacent buildings can reduce random seismic responses significantly. Copyright © 1999 John Wiley & Sons Ltd. 相似文献
16.
Several types of energy dissipation devices using viscoelastic materials have been proposed to reduce vibration in structures subjected to wind and earthquake excitations. At constant temperature and small strain levels, the mechanical behaviour of Viscoelastic (VE) materials can be described using linear operators. In general, the stiffness and damping matrices of structures using VE devices are frequency dependent; this implies that the classical second-order differential equations for the modal co-ordinates are not a complete model for this type of structures. In this paper, the concept of modal coupling in the frequency domain is addressed, expressions for diagonalizable frequency-dependent stiffness and damping matrices are given, and an iterative technique for the computation of the response of viscoelastic structures is studied. Necessary and sufficient conditions for convergence of the technique are given and numerical examples are developed to illustrate the application of the method. 相似文献
17.
18.
The evaluation of the dynamic response of non-classically damped linear structures requires the solution of an eigenproblem with complex eigenvalues and modal shapes. Since in practice only a small number of complex modes are needed, the complex eigenvalue problem is solved in the modal subspace in which the generalized damping matrix is not uncoupled by classical real modes. It follows that the evaluation of the structural response requires in both cases the determination of complex modes by numerical techniques, which are not as robust as techniques currently used for the solution of the real eigenvalue problem, and the use of complex algebra. In the present paper an unconditionally stable step-by-step procedure is presented for the response of non-classically damped structures in the modal subspace without using complex quantities. The method is based on the evaluation of the fundamental operator in approximated form of the numerical procedure. In addition, the method can be easily modified to incorporate the modal superposition pseudo-static correction terms. 相似文献
19.
为提高大型复杂结构体系的计算效率,在深入分析约束模态综合法原理的基础上,论述了非比例阻尼体系中约束模态综合法对阻尼矩阵的处理方法,并探讨了如何缩减对接界面自由度的问题。同时,通过算例详细说明了该方法在高层建筑结构动力时程分析中的应用。计算结果表明,在利用约束模态综合法求解非比例阻尼体系的动力问题时,文中所采用的阻尼矩阵的处理方法是有效的,与有限元直接法相比具有很好的精度。对于地基土-高层建筑结构体系的地震响应分析问题而言,缩减对接界面自由度的约束模态综合法可达到很好的计算精度,能够更大程度的提高计算效率,为大型复杂结构的动力时程分析研究和工程应用提供了一定的依据和方便。 相似文献
20.
在非比例阻尼情况下结构动力响应的摄动分析方法 总被引：3，自引：0，他引：3
本文将摄动方法应用于非比例阻尼系统，将一个非比例阻尼问题转化为一系列比例阻尼问题叠加的形式，从数学上对结构运动方程进行了较严格的求解，给出了在简谐荷载情况下的响应计算公式，并对所给方法的收敛性进行了研究，给出了相应的收敛条件。文中通过算例证明了本文方法的正确性与有效性。 相似文献