The Appearance of k-th order polynomial eigenvalue problems - when

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Fractional Differential Equations. Polynomial Eigenvalue Problems. Examples. Conclusions and Outlook. References. The Appearance of k−th order polynomial.
Fractional Differential Equations

Polynomial Eigenvalue Problems

Examples

Conclusions and Outlook

References

The Appearance of k −th order polynomial eigenvalue problems when damping is modeled by fractional derivatives

Nils Wagner Institut für Angewandte und Experimentelle Mechanik Universität Stuttgart

Third Berlin-Manchester Workshop on Nonlinear Eigenvalue Problems, University of Manchester, March 22-23, 2007

Fractional Differential Equations

Polynomial Eigenvalue Problems

Outline Fractional Differential Equations Introduction Polynomial Eigenvalue Problems Chu’s Homotopy Examples A SDOF system A MDOF system Conclusions and Outlook References

Examples

Conclusions and Outlook

References

Fractional Differential Equations

Polynomial Eigenvalue Problems

Examples

Conclusions and Outlook

References

Definition Fractional Differential Equations ¨ + C Dα u + K u = 0, Mu

M, C, K ∈ Rn×n .

(1)

Riemann-Liouville definition 1 d D u(t) = Γ(1 − α) dt α

Zt

u(t − τ ) dτ, τα

0