AN INTERPOLATION METHOD FOR DETERMINING THE FREQUENCIES OF PARAMETERIZED LARGE-SCALE STRUCTURES

Abstract

Parametric Model Order Reduction (pMOR) is an emerging category of models developed with the aim of describing reduced first and second-order dynamical systems. The use of a pROM turns out useful in a variety of applications spanning from the analysis of Micro-Electro-Mechanical Systems (MEMS) to the optimization of complex mechanical systems because they allow predicting the dynamical behavior at any values of the quantities of interest within the design space, e.g. material properties, geometric features or loading conditions. The process underlying the construction of a pROM using an SVD-based method [18] accounts for three basic phases: a) construction of several local ROMs (Reduced Order Models); b) projection of the state-space vector onto a common subspace spanned by several transformation matrices derived in the first step; c) use of an interpolation method capable of capturing for one or more parameters the values of the quantity of interest. One of the major difficulties encountered in this process has been identified at the level of the interpolation method and can be encapsulated in the following contradiction: if the number of detailed finite element analyses is high then an interpolation method can better describe the system for a given choice of a parameter but the time of computation is higher. In this paper is proposed a method for removing the above contradiction by introducing a new interpolation method (RSDM). This method allows to restore and make available to the interpolation tool certain natural components belonging to the matrices of the full FE model that are related on one side, to the process of reduction and on the other side, to the characteristics of a solid in the FE theory. This approach shows higher accuracy than methods used for the assessment of the system’s eigenbehavior. To confirm the usefulness of the RSDM a Hexapod will be analyzed.