ON THE ORTHOGONAL WAVELET TRANSFORM FOR MODEL REDUCTION/SYNTHESIS OF STRUCTURES

Abstract

Model reduction techniques are widely used in numerical structural dynamics to synthesize large matrix systems and perform fast computations of natural frequencies and mode shapes. Several new model reduction techniques have been proposed in recent years. Methods such as the Guyan (or static) reduction, dynamic condensation, the improved reduced system (IRS) approach or the system equivalent reduction expansion (SEREP) may be used with good results, especially over low-frequency ranges [1}5]. While the Guyan is based solely on the sti!ness matrix reduction, the SEREP has been shown to map exactly the mass and sti!ness matrices for a desired set of modes at an arbitrary set of d.o.f. using a dynamic condensation technique with the full modal basis of the system. On the other hand, the IRS uses Guyan reduction as an estimate of the reduction system and then makes adjustments to compensate for the inertia e!ects that were ignored in the Guyan process, without the penalty of requiring a full eigensolution. Advantages of using these techniques are their relative e$ciency and cost e!ectiveness when compared with analysis on the full system model. A disadvantage, however, is the approximate system descriptions that result from their use, sometimes leading to serious error. Such methods also require skilled selection of the number and location of the reduced degrees of freedom that can make up the reduced system. If the degrees of freedom that represent the reduced system are chosen improperly, poor solution results will follow [4]. Moreover, classical model reduction techniques are not appropriate for synthesizing the dynamic behaviour of structures in the middleand high-frequency range, or with high modal densities. This fact leads the structural analyst to prepare large numerical (FEM) models with high computational costs or to use statistical energy analysis (SEA) methods to predict the dynamic behaviour of the structure for high-frequency ranges. On the other hand, large nite element models are already prepared for static analysis purposes. Their lack of use for dynamic analysis leads to an increase of the global pre-processing time which greatly consumes manpower resources. The existence of a reliable condensation technique for structural middle and high frequencies would also speed up the evaluation of novel materials and structures concepts for aerospace and naval applications [6]. The aim of this paper is to explore the orthogonal wavelet transform for model synthesis of structures in order to preserve the middleand high-frequency spectra components only. A new technique is illustrated using two simple simulated examples, namely a simply supported beam and a framework structure. The technique is intended as an initial step