Vibration and Optimization Analysis of Large-Scale Structures using Reduced-Order Models and Reanalysis Methods

Abstract

Addi"ional informa"ion is available a" "he end of "he chap"er h""p://dx.doi.org/10.5772/51402 . IntroductionFinite element analysis FE" is a well-established numerical simulation method for structural dynamics. It serves as the main computational tool for Noise, Vibration and Harshness NVH analysis in the low-frequency range. "ecause of developments in numerical methods and advances in computer software and hardware, FE" can now handle much more complex models far more efficiently than even a few years ago. However, the demand for computational capabilities increases in step with or even beyond the pace of these improvements. For example, automotive companies are constructing more detailed models with millions of degrees of freedom DOFs to study vibro-acoustic problems in higher frequency ranges. "lthough these tasks can be performed with FE", the computational cost can be prohibitive even for high-end workstations with the most advanced software.For large finite element FE models, a modal reduction is commonly used to obtain the system response. "n eigenanalysis is performed using the system stiffness and mass matrices and a smaller in size modal model is formed which is solved more efficiently for the response. The computational cost is also reduced using substructuring superelement analysis . Modal reduction is applied to each substructure to obtain the component modes and the system level response is obtained using Component Mode Synthesis CMS .When design changes are involved, the FE" analysis must be repeated many times in order to obtain the optimum design. Furthermore in probabilistic analysis where parameter uncertainties are present, the FE" analysis must be repeated for a large number of sample points. In such cases, the computational cost is even higher, if not prohibitive. Reanalysis methods © 2012 Mo"rela"os e" al.; licensee InTech. This is an open access ar"icle dis"rib""ed "nder "he "erms of "he Crea"ive Commons A""rib""ion License (h""p://crea"ivecommons.org/licenses/by/3.0), which permi"s "nres"ric"ed "se, dis"rib""ion, and reprod"c"ion in any medi"m, provided "he original work is properly ci"ed.are intended to analyze efficiently structures that are modified due to various changes. They estimate the structural response after such changes without solving the complete set of modified analysis equations. Several reviews have been published on reanalysis methods [ -] which are usually based on local and global approximations. Local approximations are very efficient but they are effective only for small structural changes. Global approximations are preferable for large changes, but they are usually computationally expensive especially for cases with many design parameters. The well-known Rayleigh-Ritz reanalysis procedure [ , ] belongs to the category of local approximation methods. The mode shapes of a nominal design are used to form a Ritz basis for predicting the response in a small parametric zone around the nominal design point. However, it is incapable of capturing relatively large design c...