One important fact about the eigenvalues of the stiffness-matrix may be the following: every system which reaches an instability-point (e.g. a buckling point) has at least one zero-eigenvalue.

For a single (isoparametric) element they could be understood as the modes of deformation of the element (as presented in Bathe's book).

Have you seen this: http://people.duke.edu/~hpgavin/cee421/matrix.pdf ?

Eigen values of a stiffness matrix tell you about the stability of a system and also the amount of stretching in each (eigen) direction corresponding to that eigen value.

Eigenvalues are used to find system stability convergence.

Dear Prakash,

Any square matrix of order n can be 'decomposed' into n parts using the system of spectral decomposition. This is what explains the physical significance of characteristic roots of a matrix. Now for your matrix, you can have explanations accordingly.

If your stiffness matrix of size n comes from the discretisation of a partial differential equation, then the eigenvalues of this matrix approximate first n eigenvalues of the continuous operator. These are the eigenfrequencies (free vibration modes) of the continuum system.

In exact dynamic stiffness matrix, real part of eigenvalues of equation of motion are natural frequency of system

See this pdf

Mathematical Properties of Stiffness Matrices

By Henri P. Gavin

Hi Mainak,

Very simple manner we may think if we apply a dynamic force or displacement to system of a frequency same as Eigen frequency of a system then it shows maximum response.