R. L. Bagley, P. J. Torvik, Fractional calculus – a different approach to the analysis of viscoelastically damped structures. AIAA Journal, 27, 1412–1417, 1998.

has been cited by the following article:

• TITLE: Dynamic properties of structures with dampers modelled using fractional order derivatives

  AUTHORS: Zdzisław Pawlak, Roman Lewandowski

  KEYWORDS: viscoelastic damper; rheological model; fractional derivative; nonlinear eigenvalue problem; dynamic properties

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.2 No.4B, January 15, 2013

  ABSTRACT: The focus of this paper is on determination of the dynamic parameters of structural systems with viscoelastic (VE) dampers described by Maxwell rheological models. Such parameters could be obtained after solving the appropriately defined nonlinear eigenvalue problem for frames with VE dampers. The solution to the nonlinear eigenvalue problem is obtained by equating to zero the determinant of the considered system of equations. Apart from complex conjugate eigenvalues, the real ones occurred when dampers that are described by the classic Maxwell model, are also determined.