The state-space method is frequently used to obtain the eigenvalues of a viscously damped linear mechanical system. Differences in the definition of the state vector and auxiliary matrices found in the literature lead to differences in the formulation of the eigenvalue problems and this in turn can cause difficulties for students on mechanical vibration courses. In this study, various eigenvalue problem formulations in different textbooks have been examined, relationships between them have been established and results have been applied to a numerical example of a system with two degrees of freedom.
MüllerP. C. and SchiehlenW. O., Linear Vibrations (Martinus Nijhoff Publishers, Dordrecht, 1985), pp. 42–46.
2.
ShabanaA. A., Theory of Vibration, Vol. II: Discrete and Continuous Systems (Springer-Verlag, New York, 1991), pp. 132–139.
3.
NewlandD. E., Mechanical Vibration Analysis and Computation (Longman Scientific & Technical, Harlow, 1989), pp. 113–115.
4.
GinsbergJ. H., Mechanical and Structural Vibrations: Theory and Applications (John Wiley, New York, 2001), pp. 565–572.
5.
GeradinM. and RixenD., Mechanical Vibrations: Theory and Application to Structural Dynamics (John Wiley, Chichester, 1994), pp. 117–122.
6.
FrazerR. A.DuncanW. J. and CollarA. R., Elementary Matrices and Some Applications to Dynamics and Differential Equations (Cambridge University Press, Cambridge, 1957), pp. 289–291.
7.
MeirovitchL., Computational Methods in Structural Dynamics (Sijthoff and Noordhoff, Alphen aan den Rijn, 1980), pp. 47–48.
8.
HumarJ. L., Dynamics of Structures (Prentice Hall, Englewood Cliffs, 1990), pp. 437–442.
9.
ShabanaA. A., Theory of Vibration, Vol. I: An Introduction (Springer-Verlag, New York, 1991), pp. 251–252.
