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Part of the book series: Geotechnical, Geological and Earthquake Engineering ((GGEE,volume 45))

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Abstract

The chapter introduces the structural dynamic problem for structures discretized as systems with a finite number of degrees of freedom (Multi-Degree-of-freedom: MDOF). Distinction between shear-type frame and bending-type frame is provided. Modal analysis is introduced and the response of MDOF systems to both harmonic and earthquake excitations for undamped and damped systems. Finally the analysis of a 3D MDOF building is also provided.

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References

  • Bathe KJ, Wilson EL (1976) Numerical methods in finite element analysis, vol 197. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Blevins R (2001) Formulas for natural frequency and mode shape. Krieger Publishing Company, Malabar

    Google Scholar 

  • Chopra AK (2017) Dynamics of structures: theory and applications to earthquake engineering, 5th edn. Pearson Education, Inc., Hoboken, 960 pp

    Google Scholar 

  • Fu ZF, He J (2001) Modal analysis. Butterworth-Heinemann, Oxford/Boston

    Google Scholar 

  • Guyan RJ (1965) Reduction of stiffness and mass matrices. AIAA J 3(2):380

    Article  Google Scholar 

  • Kuttler K (2007) An introduction to linear algebra. Brigham Young University, Provo

    Google Scholar 

  • Liu M, Gorman DG (1995) Formulation of rayleigh damping and its extensions. Comput Struct 57(2):277–285

    Article  Google Scholar 

  • McGuire W, Gallagher RH, Ziemian RD (2000) Matrix structural analysis. Wiley, New York

    Google Scholar 

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Cimellaro, G.P., Marasco, S. (2018). MDOF Systems. In: Introduction to Dynamics of Structures and Earthquake Engineering. Geotechnical, Geological and Earthquake Engineering, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-72541-3_4

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