5. MDOF Systems and Eigenvalue Problems

  1. Debasish Roy1 and
  2. G Visweswara Rao2

Published Online: 3 SEP 2012

DOI: 10.1002/9781118360989.ch5

Elements of Structural Dynamics: A New Perspective

Elements of Structural Dynamics: A New Perspective

How to Cite

Roy, D. and Rao, G. V. (2012) MDOF Systems and Eigenvalue Problems, in Elements of Structural Dynamics: A New Perspective, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781118360989.ch5

Author Information

  1. 1

    Indian Institute of Science, Bangalore, India

  2. 2

    Bangalore, India

Publication History

  1. Published Online: 3 SEP 2012
  2. Published Print: 14 AUG 2012

ISBN Information

Print ISBN: 9781118339626

Online ISBN: 9781118360989



  • MDOF systems and eigenvalue problems;
  • discrete systems through a lumped parameter approach;
  • positive definite and semi-definite systems;
  • coupled Linear ODEs, and the linear differential operator;
  • coupled linear ODEs and eigensolution;
  • first order equations and uncoupling;
  • MDOF systems and modal dynamics;
  • SDOF oscillator and modal solution;
  • damped MDOF systems;
  • system response and measurement of damping


This chapter contains sections titled:

  • Introduction

  • Discrete Systems through a Lumped Parameter Approach

  • Coupled Linear ODEs and the Linear Differential Operator

  • Coupled Linear ODEs and Eigensolution

  • First Order Equations and Uncoupling

  • First Order versus Second Order ODE and Eigensolutions

  • MDOF Systems and Modal Dynamics

  • Damped MDOF Systems

  • Conclusions

  • Exercises

  • Notations

  • References

  • Bibliography