Interval eigenvalue analysis for structures with interval parameters

Chen, Su Huan; Lian, Hua Dong; Yang, Xiao

doi:10.1016/s0168-874x(02)00082-3

Cited by 87 publications

(40 citation statements)

References 3 publications

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“…In this section, the first-order parameter perturbation method for the structural eigenvalue problem with interval parameters [11] would be reviewed and compared to the present method. Based on the first-order perturbation theory, the interval of the i th eigenvalue can be approximately obtained as follows:…”

Section: The First-order Parameter Perturbation Methodsmentioning

confidence: 99%

“…As the method above relates to operations of interval multiplication and interval division, the method would have the drawback of overestimation of the interval of the eigenvalues of uncertain structures [10] . To overcome this drawback, making use of the information of the first-order partial derivatives of eigenvalues and the first-order parameter perturbation, Chen et al [11] introduce a parameter perturbation method to approximate the bounds of the structural eigenvalues. Despite the success of the first-order interval analysis method for the eigenvalue problem of structures with small uncertainties in interval parameters, when uncertainties in interval parameters are not very small, the parameter perturbation analysis method above may not work well for the structural eigenvalue problem with interval parameters.…”

Section: Introductionmentioning

confidence: 99%

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Eigenvalue analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

Qiu

Zhang³

2017

Applied Mathematical Modelling

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a b s t r a c tWhen the uncertainties in interval parameters are fairly large, the current analysis methods, which are usually based on the information of the first-order partial derivatives of eigenvalues, may not work well for the structural eigenvalue problem with interval parameters. To overcome this drawback, in this work, the structural eigenvalue problem with interval parameters is modeled as a series of QB (quadratic programming with box constrains) problems by taking advantage of the information of the second-order partial derivatives of eigenvalues. Then the series of QB problems would be solved by using the DCA (difference of convex functions algorithm) which is turn out be very effective for the QB problem. The specific examples, a concrete frame with sixty bars and a plate discretized with 300 finite elements, are given to show the effectiveness and feasibility of the proposed method compared with other methods.

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Section: The First-order Parameter Perturbation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Eigenvalue analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

Qiu

Zhang³

2017

Applied Mathematical Modelling

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“…As an approximation of the uncertain system, the feedback gain matrix can be designed based on the deterministic control system (10). Adding feedback force u = Gx 0 to the deterministic system, we obtain closed-loop systemẋ…”

Section: The Gain Matrix Of the Deterministic Systemmentioning

confidence: 99%

“…Recently, Chen et al [10] have used interval set models to study the eigenvalues of structures with bounded uncertain parameters. In References [11,12], Chen et al investigated the static and dynamic responses of uncertain structures using the interval finite element (IFE) method.…”

Section: Introductionmentioning

confidence: 99%

Interval finite element method for dynamic response of closed‐loop system with uncertain parameters

Zhang

Ding

Chen

2006

Numerical Meth Engineering

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SUMMARYIn practical engineering, it is difficult to obtain all possible solutions of dynamic responses with sharp bounds even if an optimum scheme is adopted where there are many uncertain parameters. In this paper, using the interval finite element (IFE) method and precise time integration (PTI) method, we discuss the dynamic response of vibration control problem of structures with interval parameters. With matrix perturbation theory and interval arithmetic, the algorithm for estimating upper and lower bounds of dynamic response of the closed-loop system is developed directly from the interval parameters. Two numerical examples are given to illustrate the application of the present method. The example 1 is used to show the applicability of the present method. The example 2 is used to show the validity of the present method by comparing the results with those obtained by the classical random perturbation method.

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“…However, because of the complexity of the interval analysis method, it is difficult to apply this method to practical engineering problems, such as the static and dynamic analysis of structures with interval parameters. Recently, Chen et al [2,3] and Qiu et al [12] have investigated the static responses, eigenvalue problems and dynamic responses of structures with uncertain parameters by using the interval perturbation method (IPM). In perturbation method, the uncertainty of all the structural parameters are expressed as small parameters in the structural mass and stiffness matrices.…”

Section: Introductionmentioning

confidence: 99%

Interval Finite Element Analysis using Interval Factor Method

Gao

2006

Comput Mech

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A new method called the interval factor method for the finite element analysis of truss structures with interval parameters is presented in this paper. The structural parameters and applied forces can be considered as interval variables by using the interval factor method, the structural stiffness matrix can then be divided into the product of two parts corresponding to the interval factors and the deterministic value. From the static governing equations of interval finite element method of structures, the structural displacement and stress responses are expressed as the functions of the interval factors. The computational expressions for lower and upper bounds, mean value and interval change ratio of structural static responses are derived by means of the interval operations. The effect of the uncertainty of the structural parameters and applied forces on the structural displacement and stress responses is demonstrated by truss structures.

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Interval eigenvalue analysis for structures with interval parameters

Cited by 87 publications

References 3 publications

Eigenvalue analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

Eigenvalue analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

Interval finite element method for dynamic response of closed‐loop system with uncertain parameters

Interval Finite Element Analysis using Interval Factor Method

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