**Author details**

N. M. M. Maia, Y. E. Lage and M. M. Neves

\*Address all correspondence to: nmaia@dem.ist.utl.pt

IDMEC-IST, Technical University of Lisbon, Department Mechanical Engineering, Lisboa, Portugal

## **References**


[4] Mas, P, Sas, P, & Wyckaert, K. Indirect force identification based on impedance ma‐ trix inversion: a study on statistical and deterministic accuracy. Proceedings of 19th International Seminar on Modal Analysis, Leuven. Belgium, (1994). , 1049-1065.

**i.** it is possible to localize forces acting on a structure, based on the motion transmissi‐

**ii.** finding where the forces are applied corresponds to finding the transmissibility

**iii.** in all the examples the identification of the number of forces and their localization

**iv.** the magnitude of the estimated forces exhibits a very good correlation with the

The current investigation had the support of IDMEC/IST and FCT, under the project PTDC/

IDMEC-IST, Technical University of Lisbon, Department Mechanical Engineering, Lisboa,

[1] Maia, N. M. M, Urgueira, A. P. V, & Almeida, R. A. B. Whys and Wherefores of Transmissibility. In: Dr. Francisco Beltran-Carbajal (ed.) Vibration Analysis and Con‐ trol- New Trends and Developments, InTech; (2011). http://www.intechopen.com/ books/vibration-analysis-and-control-new-trends-and-developments/whys-and-

[2] Hillary, B. Indirect Measurement of Vibration Excitation Forces. PhD Thesis. Imperial College of Science, Technology and Medicine, Dynamics Section, London, UK;

[3] Stevens, K. K. Force Identification Problems- an overview. Proceedings of the (1987). SEM Spring Conference on Experimental Mechanics. Houston, TX, USA; 1987.

structure;

**Acknowledgements**

EME-PME/71488/2006.

**Author details**

Portugal

**References**

(1983).

ones along the frequency range;

measured ones for most of the frequency range.

have been accomplished;

130 Advances in Vibration Engineering and Structural Dynamics

N. M. M. Maia, Y. E. Lage and M. M. Neves

\*Address all correspondence to: nmaia@dem.ist.utl.pt

wherefores-of-transmissibility., 187-216.

bility matrix, comparing the expected responses with the ones measured along the

matrix related to the smallest error between the expected responses and measured


[18] Paulo, P. A Time-Domain Methodology For Rotor Dynamics: Analysis and Force Identification. MSc thesis. Instituto Superior Técnico Lisbon; (2011).

**Chapter 7**

**Vibration and Optimization Analysis of Large-Scale**

Finite element analysis (FEA) is a well-established numerical simulation method for struc‐ tural dynamics. It serves as the main computational tool for Noise, Vibration and Harshness (NVH) analysis in the low-frequency range. Because of developments in numerical methods and advances in computer software and hardware, FEA can now handle much more com‐ plex models far more efficiently than even a few years ago. However, the demand for com‐ putational 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 fre‐ quency ranges. Although these tasks can be performed with FEA, the computational cost

can be prohibitive even for high-end workstations with the most advanced software.

the system level response is obtained using Component Mode Synthesis (CMS).

For large finite element (FE) models, a modal reduction is commonly used to obtain the sys‐ tem response. An 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 re‐ sponse. The computational cost is also reduced using substructuring (superelement analy‐ sis). Modal reduction is applied to each substructure to obtain the component modes and

When design changes are involved, the FEA analysis must be repeated many times in order to obtain the optimum design. Furthermore in probabilistic analysis where parameter uncer‐ tainties are present, the FEA 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 Mourelatos et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

> © 2012 Mourelatos et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Structures using Reduced-Order Models and**

**Reanalysis Methods**

http://dx.doi.org/10.5772/51402

John Skarakis

**1. Introduction**

Zissimos P. Mourelatos, Dimitris Angelis and

Additional information is available at the end of the chapter

