Progress in Computational Structures Technology
Edited by: B.H.V. Topping and C.A. Mota Soares

Chapter 2

Re-Analysis Techniques in Structural Dynamics

G. Muscolino and P. Cacciola
Department of Constructions and Advanced Technologies, University of Messina, Italy

Keywords: reanalysis, dynamic response, random response, uncertain parameters, Monte Carlo simulation.

In the framework of computational mechanics the interest in the reanalysis techniques is increased considerably in last two decades. This is principally owed to the sustained progress of the optimization techniques that require repetitive analysis of slightly modified systems. Moreover various modifications can occur during a design process. Specifically, mechanical and geometrical parameters may change and eventually structural components can be added or deleted leading also to a change in number of the degrees of freedom in the pertinent finite element model. The aim of the reanalysis is the valuation of the structural response of modified systems using the results relative to the original structure, called as reference structure, so reducing the computational effort. In this regard the reanalysis techniques are classified as topological or non-topological if the modifications lead to a change of the degrees of freedom of the system or not.

The objective of the dynamic reanalysis is to determine the eigenproperties and the dynamic response of the modified structure exploiting pertinent results of the original one. In this regard, it is opportune to classify the dynamic response reanalysis techniques proposed in literature according to the analysis performed. That is,

a)

eigenvalues reanalysis

b)

eigenproblem reanalysis

c)

dynamic response reanalysis

The last class of dynamic reanalysis techniques copes with the reanalysis of the dynamic response itself. Generally, the problem is leaded back to the classical eigenproblem reanalysis that, for this reason, is also called vibration reanalysis [1]. So operating the reduction of the computational effort involved in the reanalysis is restricted to the efficiency of the eigenproblem reanalysis techniques employed. In references [1,2] the dynamic response is re-determined also in the time-domain exploiting the results of the eigenproblem reanalysis. In the authors opinion, the dynamic response reanalysis is a methodology aimed to determine the dynamic response of modified structures independently from the eigenproblem reanalysis. In other word, the response dynamic technique does not necessary requires the eigenproblem reanalysis. This has been proved in [3] and [4] in which both the deterministic and stochastic response of a linear system has been reanalyzed avoiding the solution of any eigenproblem.

In this paper a revision of the dynamic response reanalysis recently proposed [3,4] is presented. The method, which clearly belongs to the third class of dynamic response reanalysis, is aimed in re-evaluating the dynamic response in the time domain. The basic idea is that all the dynamic modifications can be viewed as pseudo-forces, according to the so-called dynamic modification method [5]. The response of the modified structure is retrieved starting from the knowledge of the transition matrix and the eigenproperties of the original structure. So that the main differences with the classical vibration reanalysis is that the eigenproblem reanalysis is avoided drastically reducing the computational effort. Therefore, the transient and loading operators involved in the step-by-step numerical procedure are determined in appropriate form from the knowledge of the original ones related to the unmodified structure. Moreover, via this approach the response of nonclassically damped system is determined without the evaluation of complex quantities. Lastly, the present approach is also applied to the random response of linear systems subjected to random loadings, performing the reanalysis of second order moments in the time domain.

The numerical results show the accuracy and the computational efficiency of the described approach to the analysis of multi-degrees-of-freedom (M-D-O-F) systems. Remarkably, it is shown that the approach is computationally very effective and it can be applied also in determining the random response of M-D-O-F systems with random parameters via a pertinent Monte Carlo simulation.

References

1

Kirsh U., "Approximate Vibration Reanalysis of Strucutres", AIAA Journal, 41(3), 504-511, 2003

2

Nack W.V., "Efficient Reanalysis for structural dynamic response", Computers & Structures, 14(1-2), 153-155, 1981

3

Cacciola P., Muscolino G., "A Dynamic Reanalysis Technique for Modifications of Structural Components", The Sixth International Conference on Computational Structures Technology, Prague, Czech Republic, 4-6 September 2002, Civil-Comp Press, Stirling, UK

4

Cacciola P., Impollonia N., Muscolino G., "A reanalysis technique for structures under with noise excitation", Second M.I.T. Conference on Computational Fluid and Solid Mechanics, Cambridge, Massachussetts, USA 17-20 June 2003

5

Muscolino G. "Dynamically Modified Linear Structures: Deterministic and Stochastic Response", J. of Eng. Mech. (ASCE) 1996; 122: 1044-1051.

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