Dynamic Response Bound Estimation of Structures with Interval Parameters

Dynamic response analysis plays an important role for the structural design. For engineering structures, there exist model inaccuracies and structural parameters uncertainties. Consequently, it is necessary to express these uncertain parameters as interval variables and introduce the interval finite element method (IFEM), in which the elements in stiffness matrix, mass matrix and damping matrix are all the function of interval parameters. The dependence of interval parameters leads to overestimation of dynamic response analysis. In order to reduce the overestimation of IFEM, the element-based subinterval perturbation for static analysis is applied to dynamic response analysis. According to the interval range, the interval parameters are divided into different subintervals. With permutation and combination of each subinterval, the upper and lower bounds of displacement response are obtained. Because of the large number of degrees of freedom and uncertain parameters, the Laplace transform is used to evaluate the dynamic response for avoiding to frequently solve the interval finite element linear equations. The numerical examples illustrate the validity and feasibility of the proposed method.

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Dynamic Response Analysis for Structures with Interval Parameters Based on Affine Arithmetic

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.44-46.157 ◽

2008 ◽

Vol 44-46 ◽

pp. 157-164

Author(s):

Zeng Qing Zhu ◽

J.J. Chen

Keyword(s):

Dynamic Response ◽

Engineering Application ◽

Geometric Dimension ◽

Response Analysis ◽

Physical Parameters ◽

Structural Dynamic ◽

Affine Arithmetic ◽

Interval Parameters ◽

Uncertain Structure ◽

General Affine

This paper aims to study the uncertainty of the MDOF structural dynamic response, taking not only the interval characteristics of structural physical parameters and geometric dimension, but also the interval characteristics of applied load simultaneously . By means of the description of the interval parameters of uncertain structure with affine forms, the interval structural dynamic equation is studied, and an improved affine arithmetic based on interval division is presented, where correlations between the interval elements in eigenvalue and responses equations are considered, independent uncertain parameters are transformed to affine forms, and the solution of eigenvalue and response equations are transformed into the corresponding certain ones. With general affine arithmetic, the eigenvalue of each order and response bounds are determined by searching for the maximum and minimum in the solutions. Finally, some mathematical examples and a further engineering application confirm the feasibility and validity of this approach.

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Interval optimization of dynamic response for structures with interval parameters

Computers & Structures ◽

10.1016/j.compstruc.2003.09.001 ◽

2004 ◽

Vol 82 (1) ◽

pp. 1-11 ◽

Cited By ~ 57

Author(s):

Su Huan Chen ◽

Jie Wu

Keyword(s):

Dynamic Response ◽

Interval Optimization ◽

Interval Parameters

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Reliability-based topology optimization of interval parameters structures with dynamic response constraints

2014 IEEE International Conference on Mechatronics and Automation ◽

10.1109/icma.2014.6885743 ◽

2014 ◽

Author(s):

Ming Li ◽

Wencheng Tang ◽

Man Yuan

Keyword(s):

Topology Optimization ◽

Dynamic Response ◽

Interval Parameters

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Interval dynamic response analysis of structures with interval parameters

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes804 ◽

2008 ◽

Vol 222 (3) ◽

pp. 377-385 ◽

Cited By ~ 5

Author(s):

W Gao ◽

N Zhang ◽

J Ma ◽

X B Wang

Keyword(s):

Dynamic Response ◽

Structural Parameters ◽

Dynamic Responses ◽

Truss Structures ◽

Response Analysis ◽

Superposition Method ◽

Structural Dynamic ◽

Dynamic Response Analysis ◽

Interval Parameters ◽

Mode Superposition Method

Dynamic response analysis of truss structures with interval parameters under interval loads are investigated using a new method called the interval factor method (IFM). Using the IFM, the structural physical parameters, geometric dimensions, and loads can be considered as interval variables. The structural stiffness and mass matrices can then, respectively, be described by the product of two parts corresponding to the deterministic matrix and the interval factors of structural parameters. The computational expressions for the midpoint value, lower and upper bounds of the structural dynamic responses are derived by means of the mode superposition method and interval operations. The influences of the uncertainty of the structural parameters and loads on the structural dynamic responses are demonstrated by using truss structures.

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