A survey of fractional calculus for structural dynamics applications

Fractional calculus is the term given to mathematics involving integral and differential terms of non-integer order. The concept of fractional calculus followed only shortly supervened the development of calculus itself,but the development of practical applications has proceeded only slowly. There is a small group of structural dynamics problems for which fractional calculus has been adopted and may prove to be the preferred analysis method. This paper presents a summary of applications of fractional calculus and a bibliography of current references.

[1]  E. R. Love,et al.  Fractional Derivatives of Imaginary Order , 1971 .

[2]  The application of fractional calculus to the simulation of stochastic processes , 1989 .

[3]  Mikael Enelund,et al.  Time domain modeling of damping using anelastic displacement fields and fractional calculus , 1999 .

[4]  Michael Stiassnie,et al.  On the application of fractional calculus for the formulation of viscoelastic models , 1979 .

[5]  Luis E. Suarez,et al.  Response of Systems With Damping Materials Modeled Using Fractional Calculus , 1995 .

[6]  R. Koeller Applications of Fractional Calculus to the Theory of Viscoelasticity , 1984 .

[7]  I. Podlubny Fractional differential equations , 1998 .

[8]  M. Enelund Fractional Calculus and Linear Viscoelasticity in Structural Dynamics , 1996 .

[9]  M. Shitikova,et al.  Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids , 1997 .

[10]  Peter J. Torvik,et al.  Fractional calculus in the transient analysis of viscoelastically damped structures , 1983 .

[11]  Ronald L. Bagley,et al.  Power law and fractional calculus model of viscoelasticity , 1989 .

[12]  R. Hilfer Applications Of Fractional Calculus In Physics , 2000 .

[13]  A. Gemant,et al.  XLV. On fractional differentials , 1938 .

[14]  A. Gemant,et al.  A Method of Analyzing Experimental Results Obtained from Elasto‐Viscous Bodies , 1936 .

[15]  Kenneth S. Miller,et al.  Derivatives of Noninteger Order , 1995 .

[16]  Å. Fenander Modelling Stiffness and Damping by Use of Fractional Calculus with Application to Railpads , 1997 .

[17]  R. Bagley,et al.  Improved solution techniques for the eigenstructure of fractional order systems , 1989 .

[18]  N. Engheia On the role of fractional calculus in electromagnetic theory , 1997 .

[19]  Peter J. Torvik,et al.  Fractional calculus-a di erent approach to the analysis of viscoelastically damped structures , 1983 .

[20]  R. Bagley,et al.  Fractional order calculus model of the generalized Theodorsen function , 1993 .

[21]  Luis E. Suarez,et al.  An Eigenvector Expansion Method for the Solution of Motion Containing Fractional Derivatives , 1997 .